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CS-Notes/notes/Leetcode 题解.md
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2018-02-22 14:47:22 +08:00

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<!-- GFM-TOC -->
* [?????](#?????)
* [???????](#???????)
* [??????](#??????)
* [????](#????)
* [????](#????)
* [???????](#???????)
* [??????](#??????)
* [?????](#?????)
* [????](#????)
* [BFS](#bfs)
* [DFS](#dfs)
* [Backtracking](#backtracking)
* [????](#????)
* [???](#???)
* [????滮](#????滮)
* [???????](#???????)
* [????·??](#????·??)
* [??????????](#??????????)
* [????????????](#????????????)
* [???????????](#???????????)
* [0-1 ????](#0-1-????)
* [????????](#????????)
* [???????](#???????)
* [????????](#????????)
* [???](#???)
* [????](#????)
* [??????](#??????)
* [???????](#???????)
* [???](#???)
* [????????????](#????????????)
* [????????](#????????)
* [??????????](#??????????)
* [????](#????)
* [????????](#????????)
* [??????](#??????)
* [?????](#?????)
* [?????](#?????)
* [?????????](#?????????)
* [???????](#???????)
* [????](#????)
* [??](#??)
* [???](#???)
* [??α???](#??α???)
* [??к??????](#??к??????)
* [BST](#bst)
* [Trie](#trie)
* [?](#?)
* [λ????](#λ????)
* [?ο?????](#?ο?????)
<!-- GFM-TOC -->
# ?????
## ???????
?????????????????????????Щ???????????
1. ????? mid ???????? mid = (l + h) / 2 ??????????? l + h ???????????????????? mid = l + (h - l) / 2 ??
2. ?? h ??????????????й???????????? l <= h ???h = mid - 1???????????? l < h ???h = mid??
??????????????????? l <= h ?????? h = mid??????????????????????????? l = 1??h = 1????? mid ????? 1??????????????? h = mid ??????????????????????????? l < h ????? h = mid - 1??????????????????????????????? 1,2,3 ??????? 1 ????? l = 0??h = 2??mid = 1???ж? key < arr[mid] ??? h = mid - 1 = 0??????????????????????????????
3. l ???????? l = mid + 1??
```java
public int search(int key, int[] arr) {
int l = 0, h = arr.length - 1;
while (l <= h) {
int mid = l + (h - l) / 2;
if (key == arr[mid]) return mid;
if (key < arr[mid]) h = mid - 1;
else l = mid + 1;
}
return -1;
}
```
**???**
[Leetcode : 69. Sqrt(x) (Easy)](https://leetcode.com/problems/sqrtx/description/)
????? x ????? sqrt ????? 0 \~ x ??????????? sqrt == x / sqrt ?????????????????? 0 \~ x ?????? sqrt??
```java
public int mySqrt(int x) {
if(x <= 1) return x;
int l = 1, h = x;
while(l <= h){
int mid = l + (h - l) / 2;
int sqrt = x / mid;
if(sqrt == mid) return mid;
else if(sqrt < mid) h = mid - 1;
else l = mid + 1;
}
return h;
}
```
**?????**
[Leetcode : 441. Arranging Coins (Easy)](https://leetcode.com/problems/arranging-coins/description/)
```html
n = 8
The coins can form the following rows:
??
?? ??
?? ?? ??
?? ??
Because the 4th row is incomplete, we return 3.
```
??????????? i ?а? i ?????????????е???????
???? h ?????? l????????????????в?????????
```java
public int arrangeCoins(int n) {
int l = 0, h = n;
while(l <= h){
int m = l + (h - l) / 2;
long x = m * (m + 1L) / 2;
if(x == n) return m;
else if(x < n) l = m + 1;
else h = m - 1;
}
return h;
}
```
??????????????????????????
```java
public int arrangeCoins(int n) {
int level = 1;
while (n > 0) {
n -= level;
level++;
}
return n == 0 ? level - 1 : level - 2;
}
```
**????????? Single Element**
[Leetcode : 540. Single Element in a Sorted Array (Medium)](https://leetcode.com/problems/single-element-in-a-sorted-array/description/)
?????????????????????????????????????Σ???????????
```java
public int singleNonDuplicate(int[] nums) {
int l = 0, h = nums.length - 1;
while(l < h) {
int m = l + (h - l) / 2;
if(m % 2 == 1) m--; // ??? l/h/m ???????λ????ò????????С?????? ????
if(nums[m] == nums[m + 1]) l = m + 2;
else h = m;
}
return nums[l];
}
```
## ??????
?????????β???????????????????????????????????????
**???????**
[Leetcode : 455. Assign Cookies (Easy)](https://leetcode.com/problems/assign-cookies/description/)
???????????????????????????????????????????С????б?????С???????????????????ú????????????????????????????????????
?????С????????????????????????????С?????????????????????????С????????ú???????????????????????????????????
??????????????????У????????????? i ?????????? m ???????????? i ?????????????С???? m ???????????????? i ?????????С?????????????????????????? k ???????????????????????????и? i ?????????? n ?????????????????????? m ??????????????????????????????? k ?????????????????? m ???????????? n ????????????????????????????????????????????????????????????
```java
public int findContentChildren(int[] g, int[] s) {
Arrays.sort(g);
Arrays.sort(s);
int i = 0, j = 0;
while(i < g.length && j < s.length){
if(g[i] <= s[j]) i++;
j++;
}
return i;
}
```
**??????????**
[Leetcode : 452. Minimum Number of Arrows to Burst Balloons (Medium)](https://leetcode.com/problems/minimum-number-of-arrows-to-burst-balloons/description/)
```
Input:
[[10,16], [2,8], [1,6], [7,12]]
Output:
2
```
?????????????????????????????????????????????????????????·???????????????????С????????????
```java
public int findMinArrowShots(int[][] points) {
if(points.length == 0) return 0;
Arrays.sort(points,(a,b) -> (a[1] - b[1]));
int curPos = points[0][1];
int ret = 1;
for (int i = 1; i < points.length; i++) {
if(points[i][0] <= curPos) {
continue;
}
curPos = points[i][1];
ret++;
}
return ret;
}
```
**????????????**
[Leetcode : 122. Best Time to Buy and Sell Stock II (Easy)](https://leetcode.com/problems/best-time-to-buy-and-sell-stock-ii/description/)
?????????????????????????ò??????????档
??????????? [a, b, c, d]??????? a <= b <= c <= d ????????????? d - a = (d - c) + (c - b) + (b - a) ???????????? prices[i] ?? prices[i] - prices[i-1] ???????? prices[i] - prices[i-1] ????????У??????????????????????????????
```java
public int maxProfit(int[] prices) {
int profit = 0;
for(int i = 1; i < prices.length; i++){
if(prices[i] > prices[i-1]) profit += (prices[i] - prices[i-1]);
}
return profit;
}
```
**???????**
[Leetcode : 605. Can Place Flowers (Easy)](https://leetcode.com/problems/can-place-flowers/description/)
```html
Input: flowerbed = [1,0,0,0,1], n = 1
Output: True
```
????????????????????????????λ??????
```java
public boolean canPlaceFlowers(int[] flowerbed, int n) {
int cnt = 0;
for(int i = 0; i < flowerbed.length; i++){
if(flowerbed[i] == 1) continue;
int pre = i == 0 ? 0 : flowerbed[i - 1];
int next = i == flowerbed.length - 1 ? 0 : flowerbed[i + 1];
if(pre == 0 && next == 0) {
cnt++;
flowerbed[i] = 1;
}
}
return cnt >= n;
}
```
**???????????????????**
[Leetcode : 665. Non-decreasing Array (Easy)](https://leetcode.com/problems/non-decreasing-array/description/)
??????????ж?????????????????????????????????顣
?? nums[i] < nums[i - 1] ??????????????????? nums[i - 1] = nums[i]??????????? nums[i] = nums[i - 1] ???????? nums[i] ???????????????п???? nums[i + 1] ???????????? nums[i] ??С??
?????? nums[i] < nums[i - 2] ???????????? nums[i - 1] ??????????????????????????? nums[i] = nums[i - 1] ???С?
```java
public boolean checkPossibility(int[] nums) {
int cnt = 0;
for(int i = 1; i < nums.length; i++){
if(nums[i] < nums[i - 1]){
cnt++;
if(i - 2 >= 0 && nums[i - 2] > nums[i]) nums[i] = nums[i-1];
else nums[i - 1] = nums[i];
}
}
return cnt <= 1;
}
```
**?ж????????**
[Leetcode : 392. Is Subsequence (Medium)](https://leetcode.com/problems/is-subsequence/description/)
```html
s = "abc", t = "ahbgdc"
Return true.
```
```java
public boolean isSubsequence(String s, String t) {
for (int i = 0, pos = 0; i < s.length(); i++, pos++) {
pos = t.indexOf(s.charAt(i), pos);
if(pos == -1) return false;
}
return true;
}
```
**????????????????????????**
[Leetcode : 763. Partition Labels (Medium)](https://leetcode.com/problems/partition-labels/description/)
```java
public List<Integer> partitionLabels(String S) {
List<Integer> ret = new ArrayList<>();
int[] lastIdxs = new int[26];
for(int i = 0; i < S.length(); i++) lastIdxs[S.charAt(i) - 'a'] = i;
int startIdx = 0;
while(startIdx < S.length()) {
int endIdx = startIdx;
for(int i = startIdx; i < S.length() && i <= endIdx; i++) {
int lastIdx = lastIdxs[S.charAt(i) - 'a'];
if(lastIdx == i) continue;
if(lastIdx > endIdx) endIdx = lastIdx;
}
ret.add(endIdx - startIdx + 1);
startIdx = endIdx + 1;
}
return ret;
}
```
**??????????????????**
```html
Input:
[[7,0], [4,4], [7,1], [5,0], [6,1], [5,2]]
Output:
[[5,0], [7,0], [5,2], [6,1], [4,4], [7,1]]
```
???????????????? (h, k) ??????h ???????k ????????????? k ???????????????????????????
????????????k ??????????????????????е?? k ??λ???С?
```java
public int[][] reconstructQueue(int[][] people) {
if(people == null || people.length == 0 || people[0].length == 0) return new int[0][0];
Arrays.sort(people, new Comparator<int[]>() {
public int compare(int[] a, int[] b) {
if(a[0] == b[0]) return a[1] - b[1];
return b[0] - a[0];
}
});
int n = people.length;
List<int[]> tmp = new ArrayList<>();
for(int i = 0; i < n; i++) {
tmp.add(people[i][1], new int[]{people[i][0], people[i][1]});
}
int[][] ret = new int[n][2];
for(int i = 0; i < n; i++) {
ret[i][0] = tmp.get(i)[0];
ret[i][1] = tmp.get(i)[1];
}
return ret;
}
```
## ????
?????????????????飬????????????????????Э????????
**??????????????????в???????????????????? 0**
[Leetcode ??167. Two Sum II - Input array is sorted (Easy)](https://leetcode.com/problems/two-sum-ii-input-array-is-sorted/description/)
????????????????????С???????????????????????????С???????????β???????????????????β?????????
?????????????????? sum == target??????????????????? sum > target?????????????? sum ??С?Щ????? sum < target???????С??????? sum ????Щ??
```java
public int[] twoSum(int[] numbers, int target) {
int i = 0, j = numbers.length - 1;
while (i < j) {
int sum = numbers[i] + numbers[j];
if (sum == target) return new int[]{i + 1, j + 1};
else if (sum < target) i++;
else j--;
}
return null;
}
```
????????????????????? 0 ??????[???????????????? P351](#)
**?????????????????????????鳤??**
[???????????????? P354/P355/P358](#)
**???к??ж???????????в??????**
[???????????????? P347](#)
**?????????е???????**
[Leetcode : 345. Reverse Vowels of a String (Easy)](https://leetcode.com/problems/reverse-vowels-of-a-string/description/)
??????????????????????????????????????β?????????????β?????????
```java
private HashSet<Character> vowels = new HashSet<>(Arrays.asList('a','e','i','o','u','A','E','I','O','U'));
public String reverseVowels(String s) {
if(s.length() == 0) return s;
int i = 0, j = s.length() - 1;
char[] result = new char[s.length()];
while(i <= j){
char ci = s.charAt(i);
char cj = s.charAt(j);
if(!vowels.contains(ci)){
result[i] = ci;
i++;
} else if(!vowels.contains(cj)){
result[j] = cj;
j--;
} else{
result[i] = cj;
result[j] = ci;
i++;
j--;
}
}
return new String(result);
}
```
**?????????**
[Leetcode : 633. Sum of Square Numbers (Easy)](https://leetcode.com/problems/sum-of-square-numbers/description/)
?ж???????????????????????????? 5 = 1<sup>2</sup> + 2<sup>2</sup>??
```java
public boolean judgeSquareSum(int c) {
int left = 0, right = (int) Math.sqrt(c);
while(left <= right){
int powSum = left * left + right * right;
if(powSum == c) return true;
else if(powSum > c) right--;
else left++;
}
return false;
}
```
**??????????????????????????**
[Leetcode : 680. Valid Palindrome II (Easy)](https://leetcode.com/problems/valid-palindrome-ii/description/)
```java
public boolean validPalindrome(String s) {
int i = 0, j = s.length() -1;
while(i < j){
if(s.charAt(i) != s.charAt(j)){
return isPalindrome(s, i, j - 1) || isPalindrome(s, i + 1, j);
}
i++;
j--;
}
return true;
}
private boolean isPalindrome(String s, int l, int r){
while(l < r){
if(s.charAt(l) != s.charAt(r))
return false;
l++;
r--;
}
return true;
}
```
**?鲢????????????**
[Leetcode : 88. Merge Sorted Array (Easy)](https://leetcode.com/problems/merge-sorted-array/description/)
??鲢????浽????????????
```java
public void merge(int[] nums1, int m, int[] nums2, int n) {
int i = m - 1, j = n - 1; // ?????β??????????????? nums1 ??鲢???????????δ???й鲢?????
int idx = m + n - 1;
while(i >= 0 || j >= 0){
if(i < 0) nums1[idx] = nums2[j--];
else if(j < 0) nums1[idx] = nums1[i--];
else if(nums1[i] > nums2[j]) nums1[idx] = nums1[i--];
else nums1[idx] = nums2[j--];
idx--;
}
}
```
**?ж????????????**
[Leetcode : 141. Linked List Cycle (Easy)](https://leetcode.com/problems/linked-list-cycle/description/)
?????????????????????????????????????????????????????????????????????????????
```java
public boolean hasCycle(ListNode head) {
if(head == null) return false;
ListNode l1 = head, l2 = head.next;
while(l1 != null && l2 != null){
if(l1 == l2) return true;
l1 = l1.next;
if(l2.next == null) break;
l2 = l2.next.next;
}
return false;
}
```
**????????**
[Leetcode : 524. Longest Word in Dictionary through Deleting (Medium)](https://leetcode.com/problems/longest-word-in-dictionary-through-deleting/description/)
```
Input:
s = "abpcplea", d = ["ale","apple","monkey","plea"]
Output:
"apple"
```
```java
public String findLongestWord(String s, List<String> d) {
String ret = "";
for (String str : d) {
for (int i = 0, j = 0; i < s.length() && j < str.length(); i++) {
if (s.charAt(i) == str.charAt(j)) j++;
if (j == str.length()) {
if (ret.length() < str.length()
|| (ret.length() == str.length() && ret.compareTo(str) > 0)) {
ret = str;
}
}
}
}
return ret;
}
```
## ????
### ???????
?????????? **Kth Element** ?????????? O(n) ??临????O(1) ??临?????????????
???????????????????????????????????飬?????????????临???? O(n<sup>2</sup>)??
### ??????
????????????? **TopK Elements** ???????????????С? K ???????е??????? TopK Elements??????????????????? Kth Element ??????????????????????? Kth Element????????????????? TopK Elements ?????????? Kth Element ??????????????飬????С????? Kth Element ???????? TopK Elements?????????????????????????????? Kth Element ?? TopK Elements ????????п????????????
**Kth Element**
[Leetocde : 215. Kth Largest Element in an Array (Medium)](https://leetcode.com/problems/kth-largest-element-in-an-array/description/)
????ο???[Solution explained](https://leetcode.com/problems/kth-largest-element-in-an-array/discuss/60294/Solution-explained)
- ??临??? O(nlgn)????临??? O(1) ????????
- ??临??? O(nlgk)????临??? O(k) ??????????
- ??临??? O(n)????临??? O(1) ????QuickSelect
**ToK Elements**
[???????????????? P336](#)
### ?????
**?????????????? k ????**
[Leetcode : 347. Top K Frequent Elements (Medium)](https://leetcode.com/problems/top-k-frequent-elements/description/)
?????
```java
public List<Integer> topKFrequent(int[] nums, int k) {
List<Integer> ret = new ArrayList<>();
Map<Integer, Integer> map = new HashMap<>();
for(int num : nums) {
map.put(num, map.getOrDefault(num, 0) + 1);
}
List<Integer>[] bucket = new List[nums.length + 1];
for(int key : map.keySet()) {
int frequency = map.get(key);
if(bucket[frequency] == null) {
bucket[frequency] = new ArrayList<>();
}
bucket[frequency].add(key);
}
for(int i = bucket.length - 1; i >= 0 && ret.size() < k; i--) {
if(bucket[i] != null) {
ret.addAll(bucket[i]);
}
}
return ret;
}
```
## ????
?????????????????????????????????????У??????????????????????
### BFS
![](https://github.com/CyC2018/InterviewNotes/blob/master/pics/4ff355cf-9a7f-4468-af43-e5b02038facc.jpg)
??????????????????????е????????????б????????? 0 ???????????? 6??2??1 ?? 5 ?????????
?????? 6 ??????????????? 4 ???? 2 ?????????????????????? 1 ?????????????????????? 5 ???????????? 3 ?? 4 ??????????????????????4 ?? 3 ??
????????????????????????????????
??????????????????????????·????????????? d<sub>i</sub> ????? i ????????????·????????????????????????????????? i ?????????? j???? d<sub>i</sub><=d<sub>j</sub>????????????????????????·?? **?????** ????????α????????????????????·??????·????????????????????????????????????????·??????????·????
???????? BFS ????????????????
- ???У??????洢???????????
- ???????????????????????????????????????
**???????????д?????????????·??????**
```html
[[1,1,0,1],
[1,0,1,0],
[1,1,1,1],
[1,0,1,1]]
```
```java
public int minPathLength(int[][] grids, int tr, int tc) {
int[][] next = {{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
int m = grids.length, n = grids[0].length;
Queue<Position> queue = new LinkedList<>();
queue.add(new Position(0, 0, 1));
while (!queue.isEmpty()) {
Position pos = queue.poll();
for (int i = 0; i < 4; i++) {
Position nextPos = new Position(pos.r + next[i][0], pos.c + next[i][1], pos.length + 1);
if (nextPos.r < 0 || nextPos.r >= m || nextPos.c < 0 || nextPos.c >= n) continue;
if (grids[nextPos.r][nextPos.c] != 1) continue;
grids[nextPos.r][nextPos.c] = 0;
if (nextPos.r == tr && nextPos.c == tc) return nextPos.length;
queue.add(nextPos);
}
}
return -1;
}
private class Position {
int r, c, length;
public Position(int r, int c, int length) {
this.r = r;
this.c = c;
this.length = length;
}
}
```
### DFS
![](https://github.com/CyC2018/InterviewNotes/blob/master/pics/f7f7e3e5-7dd4-4173-9999-576b9e2ac0a2.png)
?????????????????????????????????????????????????洢??????????????????????????????????????????????????????????????????б????????? 0 ?????????????????????? 6 ???????????? 6 ???б???????????? 4??????????????????????????????????????????????????????? 0 ?????????????????? 0 ???б???????????? 2??????????????衣
???????????????? DFS ?????????б???????????????????????????????DFS ????????????? **?????** ????
???????? DFS ????????????????
- ???????????浱????????????????????????????????????????????????????
- ?????? BFS ??????????????????????????б???
**??????????????**
[Leetcode : 695. Max Area of Island (Easy)](https://leetcode.com/problems/max-area-of-island/description/)
```html
[[0,0,1,0,0,0,0,1,0,0,0,0,0],
[0,0,0,0,0,0,0,1,1,1,0,0,0],
[0,1,1,0,1,0,0,0,0,0,0,0,0],
[0,1,0,0,1,1,0,0,1,0,1,0,0],
[0,1,0,0,1,1,0,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,0,1,1,1,0,0,0],
[0,0,0,0,0,0,0,1,1,0,0,0,0]]
```
```java
public int maxAreaOfIsland(int[][] grid) {
int m = grid.length, n = grid[0].length;
int max = 0;
for(int i = 0; i < m; i++){
for(int j = 0; j < n; j++){
if(grid[i][j] == 1) max = Math.max(max, dfs(grid, i, j));
}
}
return max;
}
private int dfs(int[][] grid, int i, int j){
int m = grid.length, n = grid[0].length;
if(i < 0 || i >= m || j < 0 || j >= n) return 0;
if(grid[i][j] == 0) return 0;
grid[i][j] = 0;
return dfs(grid, i + 1, j) + dfs(grid, i - 1, j) + dfs(grid, i, j + 1) + dfs(grid, i, j - 1) + 1;
}
```
**??????????**
[Leetcode : 547. Friend Circles (Medium)](https://leetcode.com/problems/friend-circles/description/)
```html
Input:
[[1,1,0],
[1,1,0],
[0,0,1]]
Output: 2
Explanation:The 0th and 1st students are direct friends, so they are in a friend circle.
The 2nd student himself is in a friend circle. So return 2.
```
```java
public int findCircleNum(int[][] M) {
int n = M.length;
int ret = 0;
boolean[] hasFind = new boolean[n];
for(int i = 0; i < n; i++) {
if(!hasFind[i]) {
dfs(M, i, hasFind);
ret++;
}
}
return ret;
}
private void dfs(int[][] M, int i, boolean[] hasFind) {
hasFind[i] = true;
int n = M.length;
for(int k = 0; k < n; k++) {
if(M[i][k] == 1 && !hasFind[k]) {
dfs(M, k, hasFind);
}
}
}
```
**?????е????????????**
[Leetcode : 200. Number of Islands (Medium)](https://leetcode.com/problems/number-of-islands/description/)
```html
11110
11010
11000
00000
Answer: 1
```
```java
private int m, n;
private int[][] direction = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}};
public int numIslands(char[][] grid) {
if (grid == null || grid.length == 0) return 0;
m = grid.length;
n = grid[0].length;
int ret = 0;
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
if (grid[i][j] == '1') {
dfs(grid, i, j);
ret++;
}
}
}
return ret;
}
private void dfs(char[][] grid, int i, int j) {
if (i < 0 || i >= m || j < 0 || j >= n || grid[i][j] == '0') return;
grid[i][j] = '0';
for (int k = 0; k < direction.length; k++) {
dfs(grid, i + direction[k][0], j + direction[k][1]);
}
}
```
**??????????????д????????·??**
[Leetcode : 257. Binary Tree Paths (Easy)](https://leetcode.com/problems/binary-tree-paths/description/)
```html
1
/ \
2 3
\
5
```
```html
["1->2->5", "1->3"]
```
```java
public List<String> binaryTreePaths(TreeNode root) {
List<String> ret = new ArrayList();
if(root == null) return ret;
dfs(root, "", ret);
return ret;
}
private void dfs(TreeNode root, String prefix, List<String> ret){
if(root == null) return;
if(root.left == null && root.right == null){
ret.add(prefix + root.val);
return;
}
prefix += (root.val + "->");
dfs(root.left, prefix, ret);
dfs(root.right, prefix, ret);
}
```
**?????????**
[Leetcode : 130. Surrounded Regions (Medium)](https://leetcode.com/problems/surrounded-regions/description/)
```html
For example,
X X X X
X O O X
X X O X
X O X X
After running your function, the board should be:
X X X X
X X X X
X X X X
X O X X
```
????????????? 'X' ?? 'O' ???? 'X'??
??????????????????????????????
```java
private int[][] direction = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}};
private int m, n;
public void solve(char[][] board) {
if (board == null || board.length == 0) return;
m = board.length;
n = board[0].length;
for (int i = 0; i < m; i++) {
dfs(board, i, 0);
dfs(board, i, n - 1);
}
for (int i = 0; i < n; i++) {
dfs(board, 0, i);
dfs(board, m - 1, i);
}
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
if (board[i][j] == 'T') board[i][j] = 'O';
else if (board[i][j] == 'O') board[i][j] = 'X';
}
}
}
private void dfs(char[][] board, int r, int c) {
if (r < 0 || r >= m || c < 0 || c >= n || board[r][c] != 'O') return;
board[r][c] = 'T';
for (int i = 0; i < direction.length; i++) {
dfs(board, r + direction[i][0], c + direction[i][1]);
}
}
```
**????????????????????**
[Leetcode : 417. Pacific Atlantic Water Flow (Medium)](https://leetcode.com/problems/pacific-atlantic-water-flow/description/)
```html
Given the following 5x5 matrix:
Pacific \~ \~ \~ \~ \~
\~ 1 2 2 3 (5) *
\~ 3 2 3 (4) (4) *
\~ 2 4 (5) 3 1 *
\~ (6) (7) 1 4 5 *
\~ (5) 1 1 2 4 *
* * * * * Atlantic
Return:
[[0, 4], [1, 3], [1, 4], [2, 2], [3, 0], [3, 1], [4, 0]] (positions with parentheses in above matrix).
```
???????????????????????????±?????????????????????Σ????θ??????????????????????????????????????????????е????
```java
private int m, n;
private int[][] matrix;
private int[][] direction = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}};
public List<int[]> pacificAtlantic(int[][] matrix) {
List<int[]> ret = new ArrayList<>();
if (matrix == null || matrix.length == 0) return ret;
this.m = matrix.length;
this.n = matrix[0].length;
this.matrix = matrix;
boolean[][] canReachP = new boolean[m][n];
boolean[][] canReachA = new boolean[m][n];
for (int i = 0; i < m; i++) {
dfs(i, 0, canReachP);
dfs(i, n - 1, canReachA);
}
for (int i = 0; i < n; i++) {
dfs(0, i, canReachP);
dfs(m - 1, i, canReachA);
}
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
if (canReachP[i][j] && canReachA[i][j]) {
ret.add(new int[]{i, j});
}
}
}
return ret;
}
private void dfs(int r, int c, boolean[][] canReach) {
if(canReach[r][c]) return;
canReach[r][c] = true;
for (int i = 0; i < direction.length; i++) {
int nextR = direction[i][0] + r;
int nextC = direction[i][1] + c;
if (nextR < 0 || nextR >= m || nextC < 0 || nextC >= n
|| matrix[r][c] > matrix[nextR][nextC]) continue;
dfs(nextR, nextC, canReach);
}
}
```
**N ???**
[Leetcode : 51. N-Queens (Hard)](https://leetcode.com/problems/n-queens/description/)
![](https://github.com/CyC2018/InterviewNotes/blob/master/pics/1f080e53-4758-406c-bb5f-dbedf89b63ce.jpg)
??????????? n\*n ??????а?? n ?????????????????????У????У??????????????????е? n ????
?????е?????????????е????????????????????????????????????????????????????????????????????????б?????顢45 ????????????? 135 ???????????顣
45 ????????????????? 2\*n - 1??????????????? (r,c) ??λ????????????±?? r + c??
![](https://github.com/CyC2018/InterviewNotes/blob/master/pics/85583359-1b45-45f2-9811-4f7bb9a64db7.jpg)
135 ??????????????????? 2\*n - 1??(r,c) ??λ????????????±?? n - 1 - (r - c)??
![](https://github.com/CyC2018/InterviewNotes/blob/master/pics/9e80f75a-b12b-4344-80c8-1f9ccc2d5246.jpg)
```java
private List<List<String>> ret;
private char[][] nQueens;
private boolean[] colUsed;
private boolean[] diagonals45Used;
private boolean[] diagonals135Used;
private int n;
public List<List<String>> solveNQueens(int n) {
ret = new ArrayList<>();
nQueens = new char[n][n];
Arrays.fill(nQueens, '.');
colUsed = new boolean[n];
diagonals45Used = new boolean[2 * n - 1];
diagonals135Used = new boolean[2 * n - 1];
this.n = n;
backstracking(0);
return ret;
}
private void backstracking(int row) {
if (row == n) {
List<String> list = new ArrayList<>();
for (char[] chars : nQueens) {
list.add(new String(chars));
}
ret.add(list);
return;
}
for (int col = 0; col < n; col++) {
int diagonals45Idx = row + col;
int diagonals135Idx = n - 1 - (row - col);
if (colUsed[col] || diagonals45Used[diagonals45Idx] || diagonals135Used[diagonals135Idx]) {
continue;
}
nQueens[row][col] = 'Q';
colUsed[col] = diagonals45Used[diagonals45Idx] = diagonals135Used[diagonals135Idx] = true;
backstracking(row + 1);
colUsed[col] = diagonals45Used[diagonals45Idx] = diagonals135Used[diagonals135Idx] = false;
nQueens[row][col] = '.';
}
}
```
### Backtracking
?????? DFS ?????????????????????????????????????? **???????** ?????????? { 'a','b','c' } ??????????????????????????????е???????????
???????????????????????????б????????????????????????????????????????????????????????????????????????????????????????????????????????????????鷵??????????????????δ??????????????????????????в?????????????????????????????????????????????????????????е?????
**??????????**
[Leetcode : 17. Letter Combinations of a Phone Number (Medium)](https://leetcode.com/problems/letter-combinations-of-a-phone-number/description/)
![](https://github.com/CyC2018/InterviewNotes/blob/master/pics/a3f34241-bb80-4879-8ec9-dff2d81b514e.jpg)
```html
Input:Digit string "23"
Output: ["ad", "ae", "af", "bd", "be", "bf", "cd", "ce", "cf"].
```
```java
private static final String[] KEYS = {"", "", "abc", "def", "ghi", "jkl", "mno", "pqrs", "tuv", "wxyz"};
public List<String> letterCombinations(String digits) {
List<String> ret = new ArrayList<>();
if (digits != null && digits.length() != 0) {
combination("", digits, 0, ret);
}
return ret;
}
private void combination(String prefix, String digits, int offset, List<String> ret) {
if (offset == digits.length()) {
ret.add(prefix);
return;
}
String letters = KEYS[digits.charAt(offset) - '0'];
for (char c : letters.toCharArray()) {
combination(prefix + c, digits, offset + 1, ret);
}
}
```
**???????????????**
[Leetcode : 79. Word Search (Medium)](https://leetcode.com/problems/word-search/description/)
```html
For example,
Given board =
[
['A','B','C','E'],
['S','F','C','S'],
['A','D','E','E']
]
word = "ABCCED", -> returns true,
word = "SEE", -> returns true,
word = "ABCB", -> returns false.
```
```java
private static int[][] shift = {{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
private static boolean[][] visited;
private int m;
private int n;
public boolean exist(char[][] board, String word) {
if (word == null || word.length() == 0) return true;
if (board == null || board.length == 0 || board[0].length == 0) return false;
m = board.length;
n = board[0].length;
visited = new boolean[m][n];
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
if (dfs(board, word, 0, i, j)) return true;
}
}
return false;
}
private boolean dfs(char[][] board, String word, int start, int r, int c) {
if (start == word.length()) {
return true;
}
if (r < 0 || r >= m || c < 0 || c >= n || board[r][c] != word.charAt(start) || visited[r][c] ) {
return false;
}
visited[r][c] = true;
for (int i = 0; i < shift.length; i++) {
int nextR = r + shift[i][0];
int nextC = c + shift[i][1];
if (dfs(board, word, start + 1, nextR, nextC)) return true;
}
visited[r][c] = false;
return false;
}
```
**IP ???????**
[Leetcode : 93. Restore IP Addresses(Medium)](https://leetcode.com/problems/restore-ip-addresses/description/)
```html
Given "25525511135",
return ["255.255.11.135", "255.255.111.35"].
```
```java
private List<String> ret;
public List<String> restoreIpAddresses(String s) {
ret = new ArrayList<>();
doRestore(0, "", s);
return ret;
}
private void doRestore(int k, String path, String s) {
if (k == 4 || s.length() == 0) {
if (k == 4 && s.length() == 0) {
ret.add(path);
}
return;
}
for (int i = 0; i < s.length() && i <= 2; i++) {
if (i != 0 && s.charAt(0) == '0') break;
String part = s.substring(0, i + 1);
if (Integer.valueOf(part) <= 255) {
doRestore(k + 1, path.length() != 0 ? path + "." + part : part, s.substring(i + 1));
}
}
}
```
**????**
[Leetcode : 46. Permutations (Medium)](https://leetcode.com/problems/permutations/description/)
??????????????????????????С?
```java
public List<List<Integer>> permute(int[] nums) {
List<List<Integer>> ret = new ArrayList<>();
List<Integer> permuteList = new ArrayList<>();
boolean[] visited = new boolean[nums.length];
backtracking(permuteList, visited, nums, ret);
return ret;
}
private void backtracking(List<Integer> permuteList, boolean[] visited, int[] nums, List<List<Integer>> ret){
if(permuteList.size() == nums.length){
ret.add(new ArrayList(permuteList));
return;
}
for(int i = 0; i < visited.length; i++){
if(visited[i]) continue;
visited[i] = true;
permuteList.add(nums[i]);
backtracking(permuteList, visited, nums, ret);
permuteList.remove(permuteList.size() - 1);
visited[i] = false;
}
}
```
**?????????????**
[Leetcode : 47. Permutations II (Medium)](https://leetcode.com/problems/permutations-ii/description/)
```html
[1,1,2] have the following unique permutations:
[[1,1,2], [1,2,1], [2,1,1]]
```
?????????? Permutations ????????????????????????????????ж?????????????????????????????????????????δ?????????????????????
```java
public List<List<Integer>> permuteUnique(int[] nums) {
List<List<Integer>> ret = new ArrayList<>();
List<Integer> permuteList = new ArrayList<>();
Arrays.sort(nums);
boolean[] visited = new boolean[nums.length];
backtracking(permuteList, visited, nums, ret);
return ret;
}
private void backtracking(List<Integer> permuteList, boolean[] visited, int[] nums, List<List<Integer>> ret) {
if (permuteList.size() == nums.length) {
ret.add(new ArrayList(permuteList));
return;
}
for (int i = 0; i < visited.length; i++) {
if (i != 0 && nums[i] == nums[i - 1] && !visited[i - 1]) continue;
if (visited[i]) continue;
visited[i] = true;
permuteList.add(nums[i]);
backtracking(permuteList, visited, nums, ret);
permuteList.remove(permuteList.size() - 1);
visited[i] = false;
}
}
```
**???**
[Leetcode : 77. Combinations (Medium)](https://leetcode.com/problems/combinations/description/)
?????????????? 1 \~ n ????? k ?????????п????????
```java
public List<List<Integer>> combine(int n, int k) {
List<List<Integer>> ret = new ArrayList<>();
List<Integer> combineList = new ArrayList<>();
backtracking(1, n, k, combineList, ret);
return ret;
}
private void backtracking(int start, int n, int k, List<Integer> combineList, List<List<Integer>> ret){
if(k == 0){
ret.add(new ArrayList(combineList)); // ??????????????? List
return;
}
for(int i = start; i <= n - k + 1; i++){ // ???
combineList.add(i); // ?? i ?????????
backtracking(i + 1, n, k - 1, combineList, ret);
combineList.remove(combineList.size() - 1); // ?? i ????δ????
}
}
```
**??????**
[Leetcode : 39. Combination Sum (Medium)](https://leetcode.com/problems/combination-sum/description/)
```html
given candidate set [2, 3, 6, 7] and target 7,
A solution set is:
[[7],[2, 2, 3]]
```
```java
private List<List<Integer>> ret;
public List<List<Integer>> combinationSum(int[] candidates, int target) {
ret = new ArrayList<>();
doCombination(candidates, target, 0, new ArrayList<>());
return ret;
}
private void doCombination(int[] candidates, int target, int start, List<Integer> list) {
if (target == 0) {
ret.add(new ArrayList<>(list));
return;
}
for (int i = start; i < candidates.length; i++) {
if (candidates[i] <= target) {
list.add(candidates[i]);
doCombination(candidates, target - candidates[i], i, list);
list.remove(list.size() - 1);
}
}
}
```
**???????????????**
[Leetcode : 40. Combination Sum II (Medium)](https://leetcode.com/problems/combination-sum-ii/description/)
```html
For example, given candidate set [10, 1, 2, 7, 6, 1, 5] and target 8,
A solution set is:
[
[1, 7],
[1, 2, 5],
[2, 6],
[1, 1, 6]
]
```
```java
private List<List<Integer>> ret;
public List<List<Integer>> combinationSum2(int[] candidates, int target) {
ret = new ArrayList<>();
Arrays.sort(candidates);
doCombination(candidates, target, 0, new ArrayList<>(), new boolean[candidates.length]);
return ret;
}
private void doCombination(int[] candidates, int target, int start, List<Integer> list, boolean[] visited) {
if (target == 0) {
ret.add(new ArrayList<>(list));
return;
}
for (int i = start; i < candidates.length; i++) {
if (i != 0 && candidates[i] == candidates[i - 1] && !visited[i - 1]) continue;
if (candidates[i] <= target) {
list.add(candidates[i]);
visited[i] = true;
doCombination(candidates, target - candidates[i], i + 1, list, visited);
visited[i] = false;
list.remove(list.size() - 1);
}
}
}
```
**???**
[Leetcode : 78. Subsets (Medium)](https://leetcode.com/problems/subsets/description/)
??????????????????????????????????????[1, 2] ?? [2, 1] ????????????
```java
private List<List<Integer>> ret;
private List<Integer> subsetList;
public List<List<Integer>> subsets(int[] nums) {
ret = new ArrayList<>();
subsetList = new ArrayList<>();
for (int i = 0; i <= nums.length; i++) {
backtracking(0, i, nums);
}
return ret;
}
private void backtracking(int startIdx, int size, int[] nums) {
if (subsetList.size() == size) {
ret.add(new ArrayList(subsetList));
return;
}
for (int i = startIdx; i < nums.length; i++) {
subsetList.add(nums[i]);
backtracking(i + 1, size, nums); // startIdx ????????????? subset ?е?????????????
subsetList.remove(subsetList.size() - 1);
}
}
```
**????????????**
[Leetcode : 90. Subsets II (Medium)](https://leetcode.com/problems/subsets-ii/description/)
```html
For example,
If nums = [1,2,2], a solution is:
[
[2],
[1],
[1,2,2],
[2,2],
[1,2],
[]
]
```
```java
private List<List<Integer>> ret;
private List<Integer> subsetList;
private boolean[] visited;
public List<List<Integer>> subsetsWithDup(int[] nums) {
ret = new ArrayList<>();
subsetList = new ArrayList<>();
visited = new boolean[nums.length];
Arrays.sort(nums);
for (int i = 0; i <= nums.length; i++) {
backtracking(0, i, nums);
}
return ret;
}
private void backtracking(int startIdx, int size, int[] nums) {
if (subsetList.size() == size) {
ret.add(new ArrayList(subsetList));
return;
}
for (int i = startIdx; i < nums.length; i++) {
if (i != 0 && nums[i] == nums[i - 1] && !visited[i - 1]) continue;
subsetList.add(nums[i]);
visited[i] = true;
backtracking(i + 1, size, nums);
visited[i] = false;
subsetList.remove(subsetList.size() - 1);
}
}
```
**????????????????????????**
[Leetcode : 131. Palindrome Partitioning (Medium)](https://leetcode.com/problems/palindrome-partitioning/description/)
```java
private List<List<String>> ret;
public List<List<String>> partition(String s) {
ret = new ArrayList<>();
doPartion(new ArrayList<>(), s);
return ret;
}
private void doPartion(List<String> list, String s) {
if (s.length() == 0) {
ret.add(new ArrayList<>(list));
return;
}
for (int i = 0; i < s.length(); i++) {
if (isPalindrome(s, 0, i)) {
list.add(s.substring(0, i + 1));
doPartion(list, s.substring(i + 1));
list.remove(list.size() - 1);
}
}
}
private boolean isPalindrome(String s, int begin, int end) {
while (begin < end) {
if (s.charAt(begin++) != s.charAt(end--)) return false;
}
return true;
}
```
**????**
[Leetcode : 37. Sudoku Solver (Hard)](https://leetcode.com/problems/sudoku-solver/description/)
![](https://github.com/CyC2018/InterviewNotes/blob/master/pics/1ca52246-c443-48ae-b1f8-1cafc09ec75c.png)
```java
private boolean[][] rowsUsed = new boolean[9][10];
private boolean[][] colsUsed = new boolean[9][10];
private boolean[][] cubesUsed = new boolean[9][10];
private char[][] board;
public void solveSudoku(char[][] board) {
this.board = board;
for (int i = 0; i < 9; i++) {
for (int j = 0; j < 9; j++) {
if (board[i][j] == '.') continue;
int num = board[i][j] - '0';
rowsUsed[i][num] = true;
colsUsed[j][num] = true;
cubesUsed[cubeNum(i, j)][num] = true;
}
}
for (int i = 0; i < 9; i++) {
for (int j = 0; j < 9; j++) {
backtracking(i, j);
}
}
}
private boolean backtracking(int row, int col) {
while (row < 9 && board[row][col] != '.') {
row = col == 8 ? row + 1 : row;
col = col == 8 ? 0 : col + 1;
}
if (row == 9) {
return true;
}
for (int num = 1; num <= 9; num++) {
if (rowsUsed[row][num] || colsUsed[col][num] || cubesUsed[cubeNum(row, col)][num]) continue;
rowsUsed[row][num] = colsUsed[col][num] = cubesUsed[cubeNum(row, col)][num] = true;
board[row][col] = (char) (num + '0');
if (backtracking(row, col)) return true;
board[row][col] = '.';
rowsUsed[row][num] = colsUsed[col][num] = cubesUsed[cubeNum(row, col)][num] = false;
}
return false;
}
private int cubeNum(int i, int j) {
int r = i / 3;
int c = j / 3;
return r * 3 + c;
}
```
## ????
**????????????**
[Leetcode : 241. Different Ways to Add Parentheses (Medium)](https://leetcode.com/problems/different-ways-to-add-parentheses/description/)
```html
Input: "2-1-1".
((2-1)-1) = 0
(2-(1-1)) = 2
Output : [0, 2]
```
```java
public List<Integer> diffWaysToCompute(String input) {
int n = input.length();
List<Integer> ret = new ArrayList<>();
for (int i = 0; i < n; i++) {
char c = input.charAt(i);
if (c == '+' || c == '-' || c == '*') {
List<Integer> left = diffWaysToCompute(input.substring(0, i));
List<Integer> right = diffWaysToCompute(input.substring(i + 1));
for (int l : left) {
for (int r : right) {
switch (c) {
case '+': ret.add(l + r); break;
case '-': ret.add(l - r); break;
case '*': ret.add(l * r); break;
}
}
}
}
}
if (ret.size() == 0) ret.add(Integer.valueOf(input));
return ret;
}
```
## ???
????????????С???????????
## ????滮
?????????????????????????????????????????????????????????Ρ?
### ???????
**??????????????**
[Leetcode : 343. Integer Break (Medim)](https://leetcode.com/problems/integer-break/description/)
?????????For example, given n = 2, return 1 (2 = 1 + 1); given n = 10, return 36 (10 = 3 + 3 + 4).
```java
public int integerBreak(int n) {
int[] dp = new int[n + 1];
dp[1] = 1;
for(int i = 2; i <= n; i++) {
for(int j = 1; j <= i - 1; j++) {
dp[i] = Math.max(dp[i], Math.max(j * dp[i - j], j * (i - j)));
}
}
return dp[n];
}
```
**????????????????**
[Leetcode : 279. Perfect Squares(Medium)](https://leetcode.com/problems/perfect-squares/description/)
?????????For example, given n = 12, return 3 because 12 = 4 + 4 + 4; given n = 13, return 2 because 13 = 4 + 9.
```java
public int numSquares(int n) {
List<Integer> squares = new ArrayList<>(); // ?洢С?? n ???????
int diff = 3;
while(square <= n) {
squares.add(square);
square += diff;
diff += 2;
}
int[] dp = new int[n + 1];
for(int i = 1; i <= n; i++) {
int max = Integer.MAX_VALUE;
for(int s : squares) {
if(s > i) break;
max = Math.min(max, dp[i - s] + 1);
}
dp[i] = max;
}
return dp[n];
}
```
**???????????????????**
[Leetcode : 91. Decode Ways (Medium)](https://leetcode.com/problems/decode-ways/description/)
?????????Given encoded message "12", it could be decoded as "AB" (1 2) or "L" (12).
```java
public int numDecodings(String s) {
if(s == null || s.length() == 0) return 0;
int n = s.length();
int[] dp = new int[n + 1];
dp[0] = 1;
dp[1] = s.charAt(0) == '0' ? 0 : 1;
for(int i = 2; i <= n; i++) {
int one = Integer.valueOf(s.substring(i - 1, i));
if(one != 0) dp[i] += dp[i - 1];
if(s.charAt(i - 2) == '0') continue;
int two = Integer.valueOf(s.substring(i - 2, i));
if(two <= 26) dp[i] += dp[i - 2];
}
return dp[n];
}
```
### ????·??
**???????·????**
[Leetcode : 62. Unique Paths (Medium)](https://leetcode.com/problems/unique-paths/description/)
????????????????????????????·????????????????????????????
```java
public int uniquePaths(int m, int n) {
int[] dp = new int[n];
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
if(i == 0) dp[j] = 1;
else if(j != 0) dp[j] = dp[j] + dp[j - 1];
}
}
return dp[n - 1];
}
```
**???????С·????**
[Leetcode : 64. Minimum Path Sum (Medium)](https://leetcode.com/problems/minimum-path-sum/description/)
??????????????????????????????С·?????????????????????????
```java
public int minPathSum(int[][] grid) {
if(grid.length == 0 || grid[0].length == 0) return 0;
int m = grid.length, n = grid[0].length;
int[] dp = new int[n];
for(int i = 0; i < m; i++) {
for(int j = 0; j < n; j++) {
if(j == 0) dp[0] = dp[0] + grid[i][0];
else if(i == 0) dp[j] = dp[j - 1] + grid[0][j];
else dp[j] = Math.min(dp[j - 1], dp[j]) + grid[i][j];
}
}
return dp[n - 1];
}
```
### ??????????
????????????????? 4 ?????????????????? N ???????????????????????????临?????С? O(lgN)??
**?????**
[Leetcode : 70. Climbing Stairs (Easy)](https://leetcode.com/problems/climbing-stairs/description/)
??????????? N ????????ο???????????????????ж????????????????
??????????? dp ?洢?????????????????????????????±?? 1 ???????dp[i] ???????? i ???????????????? i ?????????? i-1 ?? i-2 ????????????????????? i ????????????????? i-1 ??? i-2 ???????????????
<center>dp[i] = dp[i-1] + dp[i-2]</center>
dp[N] ???????
????? dp[i] ??? dp[i - 1] ?? dp[i - 2] ?й??????????????????????洢 dp[i - 1] ?? dp[i - 2] ????????????? O(n) ??临??????? O(1) ??????
```java
public int climbStairs(int n) {
if(n == 1) return 1;
if(n == 2) return 2;
// ????????????????
int pre1 = 2, pre2 = 1;
for(int i = 2; i < n; i++){
int cur = pre1 + pre2;
pre2 = pre1;
pre1 = cur;
}
return pre1;
}
```
**??????**
[????????????????-P181](#)
?????????????????г????????????? 1 ?С?????????????????????????? 1 ?С????????????????????С??????С?? 3 ???????????????С???????????? N???? N ????????????
?? i ????????????????
<center>dp[i] = dp[i-1] + dp[i-3]</center>
**???????**
[Leetcode : 198. House Robber (Easy)](https://leetcode.com/problems/house-robber/description/)
?????????????????????????????????????????????????????
???? dp ?????????洢???????????????? dp[i] ????????? i ??????????????????????????????????????????????????? i ??????????????? i - 2 ?? i - 3 ???????????
![](http://latex.codecogs.com/gif.latex?\\\\dp[i]=max(dp[i-2],dp[i-3])+nums[i])
O(n) ??临???????????
```java
public int rob(int[] nums) {
int n = nums.length;
if(n == 0) return 0;
if(n == 1) return nums[0];
if(n == 2) return Math.max(nums[0], nums[1]);
int[] dp = new int[n];
dp[0] = nums[0];
dp[1] = nums[1];
dp[2] = nums[0] + nums[2];
for(int i = 3; i < n; i++){
dp[i] = Math.max(dp[i -2], dp[i - 3]) + nums[i];
}
return Math.max(dp[n - 1], dp[n - 2]);
}
```
O(1) ??临???????????
```java
public int rob(int[] nums) {
int n = nums.length;
if(n == 0) return 0;
if(n == 1) return nums[0];
if(n == 2) return Math.max(nums[0], nums[1]);
int pre3 = nums[0], pre2 = nums[1], pre1 = nums[2] + nums[0];
for(int i = 3; i < n; i++){
int cur = Math.max(pre2, pre3) + nums[i];
pre3 = pre2;
pre2 = pre1;
pre1 = cur;
}
return Math.max(pre1, pre2);
}
```
**???????ν???????**
[Leetcode : 213. House Robber II (Medium)](https://leetcode.com/problems/house-robber-ii/description/)
```java
public int rob(int[] nums) {
if(nums == null || nums.length == 0) return 0;
int n = nums.length;
if(n == 1) return nums[0];
return Math.max(rob(nums, 0, n - 2), rob(nums, 1, n - 1));
}
private int rob(int[] nums, int s, int e) {
int n = nums.length;
if(e - s == 0) return nums[s];
if(e - s == 1) return Math.max(nums[s], nums[s + 1]);
int[] dp = new int[n];
dp[s] = nums[s];
dp[s + 1] = nums[s + 1];
dp[s + 2] = nums[s] + nums[s + 2];
for (int i = s + 3; i <= e; i++) {
dp[i] = Math.max(dp[i - 2], dp[i - 3]) + nums[i];
}
return Math.max(dp[e], dp[e - 1]);
}
```
**???????**
??????????? N ?? ?? ?? ??????????????????????????????
??????????? dp ?洢???????????dp[i] ???? i ???????????????????????? i ????????? j ????????棬???? j ????????? k ????????档???? i ?? k ??????????????????
?? i==k?????? i ?? k ???????????????????????λ??????????? i-2 ?????? dp[i-2] ????????????????? j ?? i-1 ???????????? (i-1)\*dp[i-2] ????????????
?? i != k?????? i ?? j ?????? i ???????????????λ??????? i-1 ?????? dp[i-1] ???????????????? j ?? i-1 ???????????? (n-1)\*dp[i-1] ????????????
???????????????????????????????
<center> dp[i] = (i-1) \* dp[i-2] + (i-1) \* dp[i-1] </center>
dp[N] ???????
????????????????dp[i] ??? dp[i-1] ?? dp[i-2] ?й????????????????????????洢 dp[i-1] ?? dp[i-2]??
### ????????????
?????????? {S<sub>1</sub>, S<sub>2</sub>,...,S<sub>n</sub>} ????????????????????? {S<sub>i1</sub>, S<sub>i2</sub>,..., S<sub>im</sub>}?????? i1??i2 ... im ??????????????????и??????????????????е???????????????????е????**??????**??
????????????У????±? ix > iy ???S<sub>ix</sub> > S<sub>iy</sub>???????????????е????**??????????**??
??????????? dp ?洢???????????е?????dp[n] ????? S<sub>n</sub> ??β?????е????????????г????????????????????? {S<sub>i1</sub>, S<sub>i2</sub>,...,S<sub>im</sub>}????? im < n ???? S<sub>im</sub> < S<sub>n</sub> ????? {S<sub>i1</sub>, S<sub>i2</sub>,..., S<sub>im</sub>, S<sub>n</sub>} ?????????????У??????????е???????? 1??????????????????????????У?????????????????????о??????????????????????????????? S<sub>n</sub> ????????? S<sub>n</sub> ???β?????????????С???? dp[n] = max{ dp[i]+1 | S<sub>i</sub> < S<sub>n</sub> && i < n} ??
??????? dp[n] ????????????????????????????????У???? {S<sub>n</sub>} ???????????????У?????????????????????????? dp[n] ??С? 1??????
![](http://latex.codecogs.com/gif.latex?\\\\dp[n]=max\{1,dp[i]+1|S_i<S_n\&\&i<n\})
???????????? N ?????У????????в?????????? S<sub>N</sub> ???β????? dp[N] ???????е????????????е???????????? dp ?????????????????????????? max{ dp[i] | 1 <= i <= N} ???????
**????????????**
[Leetcode : 300. Longest Increasing Subsequence (Medium)](https://leetcode.com/problems/longest-increasing-subsequence/description/)
```java
public int lengthOfLIS(int[] nums) {
int n = nums.length;
int[] dp = new int[n];
for(int i = 0; i < n; i++){
int max = 1;
for(int j = 0; j < i; j++){
if(nums[i] > nums[j]) max = Math.max(max, dp[j] + 1);
}
dp[i] = max;
}
int ret = 0;
for(int i = 0; i < n; i++){
ret = Math.max(ret, dp[i]);
}
return ret;
}
```
?????????临???? O(n<sup>2</sup>) ????????????????????临??????? O(nlog<sub>n</sub>)????????? tails ???飬???? tails[i] ?洢????? i + 1 ?????????????е?????????????????????? [4,5,6,3]????
```html
len = 1 : [4], [5], [6], [3] => tails[0] = 3
len = 2 : [4, 5], [5, 6] => tails[1] = 5
len = 3 : [4, 5, 6] => tails[2] = 6
```
?????????? x??????????? tails ???????е??????????????? tails ???棻??? tails[i-1] < x <= tails[i]????????? tails[i] = x ??
??????? tails ???鱣?????????????? S<sub>i</sub> λ?? tails ?????λ??????????????????
```java
public int lengthOfLIS(int[] nums) {
int n = nums.length;
int[] tails = new int[n];
int size = 0;
for(int i = 0; i < n; i++){
int idx = binarySearch(tails, 0, size, nums[i]);
tails[idx] = nums[i];
if(idx == size) size++;
}
return size;
}
private int binarySearch(int[] nums, int sIdx, int eIdx, int key){
while(sIdx < eIdx){
int mIdx = sIdx + (eIdx - sIdx) / 2;
if(nums[mIdx] == key) return mIdx;
else if(nums[mIdx] > key) eIdx = mIdx;
else sIdx = mIdx + 1;
}
return sIdx;
}
```
**???????????**
[Leetcode : 376. Wiggle Subsequence (Medium)](https://leetcode.com/problems/wiggle-subsequence/description/)
?????? O(n) ??临??????
????????? up ?? down??
```java
public int wiggleMaxLength(int[] nums) {
int len = nums.length;
if (len == 0) return 0;
int up = 1, down = 1;
for (int i = 1; i < len; i++) {
if (nums[i] > nums[i - 1]) up = down + 1;
else if (nums[i] < nums[i - 1]) down = up + 1;
}
return Math.max(up, down);
}
```
### ???????????
?????????????? S1 ?? S2?????????????????????С?
?????????????? dp ?????洢???????????е????????? dp[i][j] ??? S1 ??? i ??????? S2 ??? j ????????????????е????????? S1<sub>i</sub> ?? S2<sub>j</sub> ????????????????????
?? ?? S1<sub>i</sub>==S2<sub>j</sub> ???????????? S1 ??? i-1 ??????? S2 ??? j-1 ????????????????е??????????? S1<sub>i</sub> ?????????????????г???? 1 ???? dp[i][j] = dp[i-1][j-1] + 1??
?? ?? S1<sub>i</sub> != S2<sub>j</sub> ??????????????????? S1 ??? i-1 ??????? S2 ??? j ????????????????У??? S1 ??? i ??????? S2 ??? j-1 ????????????????У?????????????? dp[i][j] = max{ dp[i-1][j], dp[i][j-1] }??
???????????????е????????????
![](http://latex.codecogs.com/gif.latex?\\\\
dp[i][j]=\left\{
\begin{array}{rcl}
dp[i-1][j-1]&&{S1_i==S2_j}\\
max(dp[i-1][j],dp[i][j-1])&&{S1_i<>S2_j}
\end{array}\right.
)
???????? N ?????? S<sub>1</sub> ?? ????? M ?????? S<sub>2</sub>??dp[N][M] ???????? S<sub>1</sub> ?????? S<sub>2</sub> ?????????????г????
????????????????????????????????????????
?? ?????????????У???????????????????С?
?? ???????????????У?dp[i] ????? S<sub>i</sub> ???β?????????????г?????????б?????? S<sub>i</sub> ?????????????????У?dp[i][j] ??? S1 ??? i ??????? S2 ??? j ??????????????????г????????????? S1<sub>i</sub> ?? S2<sub>j</sub> ??
?? ???? 2 ???????????????????????????? dp[N][M] ????????????????????????? dp[N] ?????????????? S<sub>N</sub> ???β?????????????в?????????????????????????У??????????? dp ?????????????
```java
public int lengthOfLCS(int[] nums1, int[] nums2) {
int n1 = nums1.length, n2 = nums2.length;
int[][] dp = new int[n1 + 1][n2 + 1];
for (int i = 1; i <= n1; i++) {
for (int j = 1; j <= n2; j++) {
if (nums1[i - 1] == nums2[j - 1]) dp[i][j] = dp[i - 1][j - 1] + 1;
else dp[i][j] = Math.max(dp[i - 1][j], dp[i][j - 1]);
}
}
return dp[n1][n2];
}
```
### 0-1 ????
?????????? N ????????????????????????????????Щ????????????????? w ???? v??
?????????????? dp ?洢??????????? dp[i][j] ???????????? j ????????? i ???????????????????? i ????????? w?????? v??????? i ?????????????????У??????????????????
?? ?? i ??????????????????????????? j ??? i ??????????????????????????? j ??? i-1 ??????????????dp[i][j] = dp[i-1][j]??
?? ?? i ??????????????У?dp[i][j] = dp[i-1][j-w] + v??
?? i ???????????????????????????????????????????
?????0-1 ?????????????????
![](http://latex.codecogs.com/gif.latex?\\\\dp[i][j]=max(dp[i-1][j],dp[i-1][j-w]+v))
```java
public int knapsack(int W, int N, int[] weights, int[] values) {
int[][] dp = new int[N][W];
for (int i = W - 1; i >= 0; i--) {
dp[0][i] = i > weights[0] ? values[0] : 0;
}
for (int i = 1; i < N; i++) {
for (int j = W - 1; j >= weights[i]; j--) {
dp[i][j] = Math.max(dp[i - 1][j], dp[i - 1][j - weights[i]] + values[i]);
}
for (int j = weights[i - 1] - 1; j >= 0; j--) {
dp[i][j] = dp[i - 1][j];
}
}
return dp[N - 1][W - 1];
}
```
**??????**
?????????????? 0-1 ??????????????????????????????? i ?????????????? i-1 ??????????й????????? dp ??????????飬???? dp[j] ??????? dp[i-1][j] ??????? dp[i][j]???????
![](http://latex.codecogs.com/gif.latex?\\\\dp[j]=max(dp[j],dp[j-w]+v))
??? dp[j-w] ??? dp[i-1][j-w]???????????? dp[i][j-w] ????? dp[i-1][j-w] ????????????????? dp[i][j] ????? dp[i][j-w]????????????????????????????
**????????????????**
0-1 ???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 5 ?????????????????? 0 ???????? 1?????????????? 16????????С? 2 ?????????????????? 1 ????? 2?????? 22.
| id | w | v | v/w |
| --- | --- | --- | --- |
| 0 | 1 | 6 | 6 |
| 1 | 2 | 10 | 5 |
| 2 | 3 | 12 | 4 |
**????**
??????????????????????????????? 0-1 ?????????????????????????? 1/2/4... ????????????????????????????????????????????Ρ?
?????????????????????????????????? 0-1 ??????
?????????????????????????????????????????????????????
???????????????????????????
**?????????????????????**
[Leetcode : 416. Partition Equal Subset Sum (Medium)](https://leetcode.com/problems/partition-equal-subset-sum/description/)
????????????????С? sum/2 ?? 0-1 ??????????????в??????????????м????????????????????????
???????????????????
```java
public boolean canPartition(int[] nums) {
int sum = 0;
for (int num : nums) {
sum += num;
}
if (sum % 2 != 0) {
return false;
}
int W = sum / 2;
boolean[] dp = new boolean[W + 1];
int n = nums.length;
for(int i = 0; i <= W; i++) {
if(nums[0] == i) dp[i] = true;
}
for(int i = 1; i < n; i++) {
for(int j = W; j >= nums[i]; j--) {
dp[j] = dp[j] || dp[j - nums[i]];
}
}
return dp[W];
}
```
**????????????б???**
[Leetcode : 139. Word Break (Medium)](https://leetcode.com/problems/word-break/description/)
```html
s = "leetcode",
dict = ["leet", "code"].
Return true because "leetcode" can be segmented as "leet code".
```
```java
public boolean wordBreak(String s, List<String> wordDict) {
int n = s.length();
boolean[] dp = new boolean[n + 1];
dp[0] = true;
for (int i = 1; i <= n; i++) {
for (String word : wordDict) {
if (word.length() <= i
&& word.equals(s.substring(i - word.length(), i))) {
dp[i] = dp[i] || dp[i - word.length()];
}
}
}
return dp[n];
}
```
**?????????????????????????????????**
[Leetcode : 494. Target Sum (Medium)](https://leetcode.com/problems/target-sum/description/)
```html
Input: nums is [1, 1, 1, 1, 1], S is 3.
Output: 5
Explanation:
-1+1+1+1+1 = 3
+1-1+1+1+1 = 3
+1+1-1+1+1 = 3
+1+1+1-1+1 = 3
+1+1+1+1-1 = 3
There are 5 ways to assign symbols to make the sum of nums be target 3.
```
????????????? subset sum ?????????? 0-1 ????????????????????????????????????P ?? N?????? P ????????N ??????????????????
```html
sum(P) - sum(N) = target
sum(P) + sum(N) + sum(P) - sum(N) = target + sum(P) + sum(N)
2 * sum(P) = target + sum(nums)
```
????????????????????????????????????? (target + sum(nums))/2????????????
```java
public int findTargetSumWays(int[] nums, int S) {
int sum = 0;
for (int num : nums) {
sum += num;
}
if (sum < S || (sum + S) % 2 == 1) {
return 0;
}
return subsetSum(nums, (sum + S) >>> 1);
}
private int subsetSum(int[] nums, int targetSum) {
Arrays.sort(nums);
int[] dp = new int[targetSum + 1];
dp[0] = 1;
for (int i = 0; i < nums.length; i++) {
int num = nums[i];
for (int j = targetSum; j >= num; j--) {
dp[j] = dp[j] + dp[j - num];
}
}
return dp[targetSum];
}
```
**01????????????????**
[Leetcode : 474. Ones and Zeroes (Medium)](https://leetcode.com/problems/ones-and-zeroes/description/)
```html
Input: Array = {"10", "0001", "111001", "1", "0"}, m = 5, n = 3
Output: 4
Explanation: This are totally 4 strings can be formed by the using of 5 0s and 3 1s, which are ??10,??0001??,??1??,??0??
```
??????????????? 0-1 ????????????????????С??0 ???????? 1 ????????
```java
public int findMaxForm(String[] strs, int m, int n) {
if (strs == null || strs.length == 0) return 0;
int l = strs.length;
int[][] dp = new int[m + 1][n + 1];
for (int i = 0; i < l; i++) {
String s = strs[i];
int ones = 0, zeros = 0;
for (char c : s.toCharArray()) {
if (c == '0') zeros++;
else if (c == '1') ones++;
}
for (int j = m; j >= zeros; j--) {
for (int k = n; k >= ones; k--) {
if (zeros <= j && ones <= k) {
dp[j][k] = Math.max(dp[j][k], dp[j - zeros][k - ones] + 1);
}
}
}
}
return dp[m][n];
}
```
**?????**
[Leetcode : 322. Coin Change (Medium)](https://leetcode.com/problems/coin-change/description/)
????????????Щ???????????????Щ??????????????????????????????????????????????????á?
?????????????????????????????? 0-1???????????????Ψ??????????????????? 0 ?????????????β???????
```java
public int coinChange(int[] coins, int amount) {
int[] dp = new int[amount + 1];
Arrays.fill(dp, amount + 1);
dp[0] = 0;
for (int i = 1; i <= amount; i++) {
for (int j = 0; j < coins.length; j++) {
if (coins[j] <= i) {
dp[i] = Math.min(dp[i], dp[i - coins[j]] + 1);
}
}
}
return dp[amount] > amount ? -1 : dp[amount];
}
```
**??????**
[Leetcode : 377. Combination Sum IV (Medium)](https://leetcode.com/problems/combination-sum-iv/description/)
```html
nums = [1, 2, 3]
target = 4
The possible combination ways are:
(1, 1, 1, 1)
(1, 1, 2)
(1, 2, 1)
(1, 3)
(2, 1, 1)
(2, 2)
(3, 1)
Note that different sequences are counted as different combinations.
Therefore the output is 7.
```
```java
public int combinationSum4(int[] nums, int target) {
int[] dp = new int[target + 1];
dp[0] = 1;
for (int i = 1; i <= target; i++) {
for (int j = 0; j < nums.length; j++) {
if(nums[j] <= i) {
dp[i] += dp[i - nums[j]];
}
}
}
return dp[target];
}
```
**?????????ε???????**
[Leetcode : 123. Best Time to Buy and Sell Stock III (Hard)](https://leetcode.com/problems/best-time-to-buy-and-sell-stock-iii/description/)
```java
public int maxProfit(int[] prices) {
int firstBuy = Integer.MIN_VALUE, firstSell = 0;
int secondBuy = Integer.MIN_VALUE, secondSell = 0;
for (int curPrice : prices) {
if (firstBuy < -curPrice) firstBuy = -curPrice;
if (firstSell < firstBuy + curPrice) firstSell = firstBuy + curPrice;
if (secondBuy < firstSell - curPrice) secondBuy = firstSell - curPrice;
if (secondSell < secondBuy + curPrice) secondSell = secondBuy + curPrice;
}
return secondSell;
}
```
**?????? k ?ε???????**
[Leetcode : 188. Best Time to Buy and Sell Stock IV (Hard)](https://leetcode.com/problems/best-time-to-buy-and-sell-stock-iv/description/)
```html
dp[i, j] = max(dp[i, j-1], prices[j] - prices[jj] + dp[i-1, jj]) { jj in range of [0, j-1] } = max(dp[i, j-1], prices[j] + max(dp[i-1, jj] - prices[jj]))
```
```java
public int maxProfit(int k, int[] prices) {
int n = prices.length;
if (k >= n/2) {
int maxPro = 0;
for (int i = 1; i < n; i++) {
if (prices[i] > prices[i-1])
maxPro += prices[i] - prices[i-1];
}
return maxPro;
}
int[][] dp = new int[k + 1][n];
for (int i = 1; i <= k; i++) {
int localMax = dp[i - 1][0] - prices[0];
for (int j = 1; j < n; j++) {
dp[i][j] = Math.max(dp[i][j - 1], prices[j] + localMax);
localMax = Math.max(localMax, dp[i - 1][j] - prices[j]);
}
}
return dp[k][n - 1];
}
```
### ????????
**?????????**
[Leetcode : 303. Range Sum Query - Immutable (Easy)](https://leetcode.com/problems/range-sum-query-immutable/description/)
?????? i \~ j ???????????? sum[j] - sum[i-1]?????? sum[i] ? 0 \~ j ????
```java
class NumArray {
int[] nums;
public NumArray(int[] nums) {
for(int i = 1; i < nums.length; i++)
nums[i] += nums[i - 1];
this.nums = nums;
}
public int sumRange(int i, int j) {
return i == 0 ? nums[j] : nums[j] - nums[i - 1];
}
}
```
**???????????**
[Leetcode : 53. Maximum Subarray (Easy)](https://leetcode.com/problems/maximum-subarray/description/)
?? sum[i] ??? num[i] ???β???????????????????? sum[i-1] ??? sum[i] ???????? sum[i-1] С?? 0??????? num[i] ???β???????鲻???????????????????????????????????????? num[i] ??С??
```java
public int maxSubArray(int[] nums) {
int n = nums.length;
int[] sum = new int[n];
sum[0] = nums[0];
int max = sum[0];
for(int i = 1; i < n; i++){
sum[i] = (sum[i-1] > 0 ? sum[i-1] : 0) + nums[i];
max = Math.max(max, sum[i]);
}
return max;
}
```
**?????е???????????????**
[Leetcode : 413. Arithmetic Slices (Medium)](https://leetcode.com/problems/arithmetic-slices/description/)
```html
A = [1, 2, 3, 4]
return: 3, for 3 arithmetic slices in A: [1, 2, 3], [2, 3, 4] and [1, 2, 3, 4] itself.
```
???? (1,2,3,4)????????????????????????????????? (1,2,3,4,5)??????????????????????? (1,2,3,4) ?????????????????? (1,2,3,4,5)????? dp[i] = dp[i - 1] + 1??
```java
public int numberOfArithmeticSlices(int[] A) {
int n = A.length;
int[] dp = new int[n];
for(int i = 2; i < n; i++) {
if(A[i] - A[i - 1] == A[i - 1] - A[i - 2]) {
dp[i] = dp[i - 1] + 1;
}
}
int ret = 0;
for(int cnt : dp) {
ret += cnt;
}
return ret;
}
```
### ???????
**?????????????????????????**
[Leetcode : 583. Delete Operation for Two Strings (Medium)](https://leetcode.com/problems/delete-operation-for-two-strings/description/)
?????????????????????????????????????
```java
public int minDistance(String word1, String word2) {
int m = word1.length(), n = word2.length();
int[][] dp = new int[m + 1][n + 1];
for (int i = 0; i <= m; i++) {
for (int j = 0; j <= n; j++) {
if (i == 0 || j == 0) continue;
dp[i][j] = word1.charAt(i - 1) == word2.charAt(j - 1) ? dp[i - 1][j - 1] + 1
: Math.max(dp[i][j - 1], dp[i - 1][j]);
}
}
return m + n - 2 * dp[m][n];
}
```
**????????????????????????** // TODO
[Leetcode : 72. Edit Distance (Hard)](https://leetcode.com/problems/edit-distance/description/)
**??????????????????????????**// TODO
[????????????????-?????](#)
### ????????
**???????????????**
[Leetcode : 309. Best Time to Buy and Sell Stock with Cooldown(Medium)](https://leetcode.com/problems/best-time-to-buy-and-sell-stock-with-cooldown/description/)
???????????????????????????????
![](https://github.com/CyC2018/InterviewNotes/blob/master/pics/ac9b31ec-cef1-4880-a875-fc4571ca10e1.png)
```html
s0[i] = max(s0[i - 1], s2[i - 1]); // Stay at s0, or rest from s2
s1[i] = max(s1[i - 1], s0[i - 1] - prices[i]); // Stay at s1, or buy from s0
s2[i] = s1[i - 1] + prices[i]; // Only one way from s1
```
```java
public int maxProfit(int[] prices) {
if (prices == null || prices.length == 0) return 0;
int n = prices.length;
int[] s0 = new int[n];
int[] s1 = new int[n];
int[] s2 = new int[n];
s0[0] = 0;
s1[0] = -prices[0];
s2[0] = Integer.MIN_VALUE;
for (int i = 1; i < n; i++) {
s0[i] = Math.max(s0[i - 1], s2[i - 1]);
s1[i] = Math.max(s1[i - 1], s0[i - 1] - prices[i]);
s2[i] = Math.max(s2[i - 1], s1[i - 1] + prices[i]);
}
return Math.max(s0[n - 1], s2[n - 1]);
}
```
**???? 0 \~ n ???????????????? 1 ?????**
[Leetcode : 338. Counting Bits (Medium)](https://leetcode.com/problems/counting-bits/description/)
???????? 6(110)????????????????? 2(10) ????????? 1 ????? dp[i] = dp[i&(i-1)] + 1;
```java
public int[] countBits(int num) {
int[] ret = new int[num + 1];
for(int i = 1; i <= num; i++){
ret[i] = ret[i&(i-1)] + 1;
}
return ret;
}
```
**?????????????????????**
[Leetcode : 646. Maximum Length of Pair Chain (Medium)](https://leetcode.com/problems/maximum-length-of-pair-chain/description/)
???? (a, b) ?? (c, d) ????? b < c?????????????????????
```java
public int findLongestChain(int[][] pairs) {
if(pairs == null || pairs.length == 0) {
return 0;
}
Arrays.sort(pairs, (a, b) -> (a[0] - b[0]));
int n = pairs.length;
int[] dp = new int[n];
Arrays.fill(dp, 1);
for(int i = 0; i < n; i++) {
for(int j = 0; j < i; j++) {
if(pairs[i][0] > pairs[j][1]){
dp[i] = Math.max(dp[i], dp[j] + 1);
}
}
}
int ret = 0;
for(int num : dp) {
ret = Math.max(ret, num);
}
return ret;
}
```
**???????????????????**
[Leetcode : 121. Best Time to Buy and Sell Stock (Easy)](https://leetcode.com/problems/best-time-to-buy-and-sell-stock/description/)
???????ν????
???????????С?????????С???????????????????????????????????????????????????
```java
public int maxProfit(int[] prices) {
int n = prices.length;
if(n == 0) return 0;
int soFarMin = prices[0];
int max = 0;
for(int i = 1; i < n; i++){
if(soFarMin > prices[i]) soFarMin = prices[i];
else max = Math.max(max, prices[i] - soFarMin);
}
return max;
}
```
**??????????**
[Leetcode : 650. 2 Keys Keyboard (Medium)](https://leetcode.com/problems/2-keys-keyboard/description/)
```java
public int minSteps(int n) {
int[] dp = new int[n + 1];
for (int i = 2; i <= n; i++) {
dp[i] = i;
for (int j = i - 1; j >= 0; j--) {
if (i % j == 0) {
dp[i] = dp[j] + dp[i / j];
break;
}
}
}
return dp[n];
}
```
```java
public int minSteps(int n) {
if (n == 1) return 0;
for (int i = 2; i <= Math.sqrt(n); i++) {
if (n % i == 0) return i + minSteps(n / i);
}
return n;
}
```
## ???
### ????
**???????**
????????????????????????????? 84 = 2<sup>2</sup> \* 3<sup>1</sup> \* 5<sup>0</sup> \* 7<sup>1</sup> \* 11<sup>0</sup> \* 13<sup>0</sup> \* 17<sup>0</sup> \* ??
**????**
?? x = 2<sup>m0</sup> \* 3<sup>m1</sup> \* 5<sup>m2</sup> \* 7<sup>m3</sup> \* 11<sup>m4</sup> \* ??
?? y = 2<sup>n0</sup> \* 3<sup>n1</sup> \* 5<sup>n2</sup> \* 7<sup>n3</sup> \* 11<sup>n4</sup> \* ??
??? x ???? y??y mod x == 0????????????? i??mi <= ni??
x ?? y ?? **??????** ???gcd(x,y) = 2<sup>min(m0,n0)</sup> \* 3<sup>min(m1,n1)</sup> \* 5<sup>min(m2,n2)</sup> \* ...
x ?? y ?? **??С??????** ???lcm(x,y) = 2<sup>max(m0,n0)</sup> \* 3<sup>max(m1,n1)</sup> \* 5<sup>max(m2,n2)</sup> \* ...
**????????????**
[Leetcode : 204. Count Primes (Easy)](https://leetcode.com/problems/count-primes/description/)
????????????????????????????????????????????????????????
```java
public int countPrimes(int n) {
boolean[] notPrimes = new boolean[n + 1];
int cnt = 0;
for(int i = 2; i < n; i++){
if(notPrimes[i]) continue;
cnt++;
// ?? i * i ??????????? k < i????? k * i ??????????????????
for(long j = (long) i * i; j < n; j += i){
notPrimes[(int) j] = true;
}
}
return cnt;
}
```
### ??????
```java
int gcd(int a, int b) {
if (b == 0) return a;
return gcd(b, a % b);
}
```
???????????????????????????
```java
int lcm(int a, int b){
return a * b / gcd(a, b);
}
```
???????????????????????? a % b ??????????????????????????? [ ????????2.7]() ??????????ü???????λ???????滻????
???? a ?? b ???????? f(a, b)???У?
1\. ??? a ?? b ????????f(a, b) = 2\*f(a/2, b/2);
2\. ??? a ????? b ????????f(a, b) = f(a/2, b);
3\. ??? b ????? a ????????f(a, b) = f(a, b/2);
4\. ??? a ?? b ?????????f(a, b) = f(a, a-b);
?? 2 ??? 2 ????????????λ??????
### ???????
Java ?? static String toString(int num, int radix) ???????????????? redix ???????????????
**7 ????**
[Leetcode : 504. Base 7 (Easy)](https://leetcode.com/problems/base-7/description/)
```java
public String convertToBase7(int num) {
if (num < 0) {
return '-' + convertToBase7(-num);
}
if (num < 7) {
return num + "";
}
return convertToBase7(num / 7) + num % 7;
}
```
**16 ????**
[Leetcode : 405. Convert a Number to Hexadecimal (Easy)](https://leetcode.com/problems/convert-a-number-to-hexadecimal/description/)
```java
public String toHex(int num) {
char[] map = {'0','1','2','3','4','5','6','7','8','9','a','b','c','d','e','f'};
if(num == 0) return "0";
String ret = "";
while(num != 0){
ret = map[(num & 0b1111)] + ret;
num >>>= 4;
}
return ret;
}
```
### ???
**?????β???ж???? 0**
[Leetcode : 172. Factorial Trailing Zeroes (Easy)](https://leetcode.com/problems/factorial-trailing-zeroes/description/)
β???? 0 ?? 2 * 5 ??????2 ????????????? 5 ?????????????????ж???? 5 ???ɡ?
????????? N?????????? 5 ????????N/5 + N/5<sup>2</sup> + N/5<sup>3</sup> + ...?????? N/5 ????????? N ?????? 5 ???????????? 5??N/5<sup>2</sup> ????????? N ?????? 5<sup>2</sup> ????????????? 5 ...??
```java
public int trailingZeroes(int n) {
return n == 0 ? 0 : n / 5 + trailingZeroes(n / 5);
}
```
????????? N! ??????????????λ 1 ??λ?????????ж???? 2 ?????????????? [ ????????2.2](#) ????????ж???? 5 ?????2 ?????? N/2 + N/2<sup>2</sup> + N/2<sup>3</sup> + ...
### ????????????
**????????**
[Leetcode : 67. Add Binary (Easy)](https://leetcode.com/problems/add-binary/description/)
```java
public String addBinary(String a, String b) {
int i = a.length() - 1, j = b.length() - 1, carry = 0;
String str = "";
while(i >= 0 || j >= 0){
if(i >= 0 && a.charAt(i--) == '1') carry++;
if(j >= 0 && b.charAt(j--) == '1') carry++;
str = (carry % 2) + str;
carry /= 2;
}
if(carry == 1) str = "1" + str;
return str;
}
```
**????????**
[Leetcode : 415. Add Strings (Easy)](https://leetcode.com/problems/add-strings/description/)
?????????????????????????
```java
public String addStrings(String num1, String num2) {
StringBuilder sb = new StringBuilder();
int carry = 0;
for(int i = num1.length() - 1, j = num2.length() - 1; i >= 0 || j >= 0 || carry == 1; i--, j--){
int x = i < 0 ? 0 : num1.charAt(i) - '0';
int y = j < 0 ? 0 : num2.charAt(j) - '0';
sb.append((x + y + carry) % 10);
carry = (x + y + carry) / 10;
}
return sb.reverse().toString();
}
```
### ????????
**??????????????е????????????**
[Leetcode : 462. Minimum Moves to Equal Array Elements II (Medium)](https://leetcode.com/problems/minimum-moves-to-equal-array-elements-ii/description/)
???????????ο????????????????????????????С?????????
???????????????????????????С?????????????????????λ?????????????
?? m ???λ????a ?? b ?? m ??????????????? b > a???? a ?? b ???????????????????? b - a?????????? (b - m) + (m - a)???????????????????????λ?????????????
?????鳤??? N?????????? N/2 ?? a ?? b ????????????????? m ??λ?á?
**?? 1**
????????临????O(NlgN)
```java
public int minMoves2(int[] nums) {
Arrays.sort(nums);
int ret = 0;
int l = 0, h = nums.length - 1;
while(l <= h) {
ret += nums[h] - nums[l];
l++;
h--;
}
return ret;
}
```
**?? 2**
???????????????λ??????临??? O(N)
```java
public int minMoves2(int[] nums) {
int ret = 0;
int n = nums.length;
int median = quickSelect(nums, 0, n - 1, n / 2 + 1);
for(int num : nums) ret += Math.abs(num - median);
return ret;
}
private int quickSelect(int[] nums, int start, int end, int k) {
int l = start, r = end, privot = nums[(l + r) / 2];
while(l <= r) {
while(nums[l] < privot) l++;
while(nums[r] > privot) r--;
if(l >= r) break;
swap(nums, l, r);
l++; r--;
}
int left = l - start + 1;
if(left > k) return quickSelect(nums, start, l - 1, k);
if(left == k && l == r) return nums[l];
int right = r - start + 1;
return quickSelect(nums, r + 1, end, k - right);
}
private void swap(int[] nums, int i, int j) {
int tmp = nums[i]; nums[i] = nums[j]; nums[j] = tmp;
}
```
### ??????????
**?????г?????????? n / 2 ?????**
[Leetcode : 169. Majority Element (Easy)](https://leetcode.com/problems/majority-element/description/)
??????????????м???????????????????? n / 2
```java
public int majorityElement(int[] nums) {
Arrays.sort(nums);
return nums[nums.length / 2];
}
```
???????? Boyer-Moore Majority Vote Algorithm ?????????????????临???? O(n)???????????????????? cnt ????????????????????????????????????????????????? cnt--????????????? i ???????? cnt == 0 ?????? i ???????? majority???????? majority????????????????? i / 2 ???????????? i / 2 ??? cnt ?????????? 0 ????????? n - i ??????У?majority ????????? (n - i) / 2?????????????????? majority??
```java
public int majorityElement(int[] nums) {
int cnt = 0, majority = 0;
for(int i = 0; i < nums.length; i++){
if(cnt == 0) {
majority = nums[i];
cnt++;
}
else if(majority == nums[i]) cnt++;
else cnt--;
}
return majority;
}
```
**?????г?????????? n / k ?????**
[???????????????? P343](#)
? k - 1 ?????
### ????
**?????**
[Leetcode : 367. Valid Perfect Square (Easy)](https://leetcode.com/problems/valid-perfect-square/description/)
??????У?1,4,9,16,..
?????3,5,7,...
??????????У?????????????????? 1 ???????????С?
```java
public boolean isPerfectSquare(int num) {
int subNum = 1;
while (num > 0) {
num -= subNum;
subNum += 2;
}
return num == 0;
}
```
**3 ?? n ?η?**
[Leetcode : 326. Power of Three (Easy)](https://leetcode.com/problems/power-of-three/description/)
```java
public boolean isPowerOfThree(int n) {
return n > 0 && (1162261467 % n == 0);
}
```
**????????е?????????????**
[Leetcode : 628. Maximum Product of Three Numbers (Easy)](https://leetcode.com/problems/maximum-product-of-three-numbers/description/)
```java
public int maximumProduct(int[] nums) {
int max1 = Integer.MIN_VALUE, max2 = Integer.MIN_VALUE, max3 = Integer.MIN_VALUE, min1 = Integer.MAX_VALUE, min2 = Integer.MAX_VALUE;
for (int n : nums) {
if (n > max1) {
max3 = max2;
max2 = max1;
max1 = n;
} else if (n > max2) {
max3 = max2;
max2 = n;
} else if (n > max3) {
max3 = n;
}
if (n < min1) {
min2 = min1;
min1 = n;
} else if (n < min2) {
min2 = n;
}
}
return Math.max(max1*max2*max3, max1*min1*min2);
}
```
**???????**
[Leetcode : 238. Product of Array Except Self (Medium)](https://leetcode.com/problems/product-of-array-except-self/description/)
???????????????????飬????????????飬?????????????????????г????λ???????????????????????
????????临???? O(n)???????????ó?????
```java
public int[] productExceptSelf(int[] nums) {
int n = nums.length;
int[] ret = new int[n];
ret[0] = 1;
for(int i = 1; i < n; i++) {
ret[i] = ret[i - 1] * nums[i - 1];
}
int right = 1;
for(int i = n - 1; i >= 0; i--) {
ret[i] *= right;
right *= nums[i];
}
return ret;
}
```
# ????????
## ??????
**?????????**
????????
```java
class MyQueue {
private Stack<Integer> st = new Stack();
public void push(int x) {
Stack<Integer> temp = new Stack();
while(!st.isEmpty()){
temp.push(st.pop());
}
st.push(x);
while(!temp.isEmpty()){
st.push(temp.pop());
}
}
public int pop() {
return st.pop();
}
public int peek() {
return st.peek();
}
public boolean empty() {
return st.isEmpty();
}
}
```
?????????
```java
class MyQueue {
private Stack<Integer> in = new Stack();
private Stack<Integer> out = new Stack();
public void push(int x) {
in.push(x);
}
public int pop() {
in2out();
return out.pop();
}
public int peek() {
in2out();
return out.peek();
}
private void in2out(){
if(out.isEmpty()){
while(!in.isEmpty()){
out.push(in.pop());
}
}
}
public boolean empty() {
return in.isEmpty() && out.isEmpty();
}
}
```
**?????????**
[Leetcode : 225. Implement Stack using Queues (Easy)](https://leetcode.com/problems/implement-stack-using-queues/description/)
```java
class MyStack {
private Queue<Integer> queue;
public MyStack() {
queue = new LinkedList<>();
}
public void push(int x) {
queue.add(x);
for(int i = 1; i < queue.size(); i++){ // ???
queue.add(queue.remove());
}
}
public int pop() {
return queue.remove();
}
public int top() {
return queue.peek();
}
public boolean empty() {
return queue.isEmpty();
}
}
```
**??С??**
[Leetcode : 155. Min Stack (Easy)](https://leetcode.com/problems/min-stack/description/)
???????????????洢?????????洢??С???
```java
class MinStack {
private Stack<Integer> dataStack;
private Stack<Integer> minStack;
private int min;
public MinStack() {
dataStack = new Stack<>();
minStack = new Stack<>();
min = Integer.MAX_VALUE;
}
public void push(int x) {
dataStack.add(x);
if(x < min) {
min = x;
}
minStack.add(min);
}
public void pop() {
dataStack.pop();
minStack.pop();
if(!minStack.isEmpty()) {
min = minStack.peek();
} else{
min = Integer.MAX_VALUE;
}
}
public int top() {
return dataStack.peek();
}
public int getMin() {
return min;
}
}
```
?????????С?????????????????????????????????????????????С???????????????? ????????3.7??
**?????????????**
[Leetcode : 20. Valid Parentheses (Easy)](https://leetcode.com/problems/valid-parentheses/description/)
```html
"()[]{}"
Output : true
```
```java
public boolean isValid(String s) {
Stack<Character> stack = new Stack<>();
for(int i = 0; i < s.length(); i++){
char c = s.charAt(i);
if(c == '(' || c == '{' || c == '[') stack.push(c);
else{
if(stack.isEmpty()) return false;
char cStack = stack.pop();
if(c == ')' && cStack != '(' ||
c == ']' && cStack != '[' ||
c == '}' && cStack != '{' ) {
return false;
}
}
}
return stack.isEmpty();
}
```
**?????б????????????????????????**
```html
Input: [73, 74, 75, 71, 69, 72, 76, 73]
Output: [1, 1, 4, 2, 1, 1, 0, 0]
```
[Leetcode : 739. Daily Temperatures (Medium)](https://leetcode.com/problems/daily-temperatures/description/)
???????洢??δ???????????????????????????????????????????????????????????????????У????????????????????????????????????
```java
public int[] dailyTemperatures(int[] temperatures) {
int n = temperatures.length;
int[] ret = new int[n];
Stack<Integer> stack = new Stack<>();
for(int i = 0; i < n; i++) {
while(!stack.isEmpty() && temperatures[i] > temperatures[stack.peek()]) {
int idx = stack.pop();
ret[idx] = i - idx;
}
stack.add(i);
}
return ret;
}
```
**??????????????????????**
[Leetcode : 496. Next Greater Element I (Easy)](https://leetcode.com/problems/next-greater-element-i/description/)
```html
Input: nums1 = [4,1,2], nums2 = [1,3,4,2].
Output: [-1,3,-1]
```
???????????? Stack ???????е????????????????????????????????????????????????????????????????????????
```java
public int[] nextGreaterElement(int[] nums1, int[] nums2) {
Map<Integer, Integer> map = new HashMap<>();
Stack<Integer> stack = new Stack<>();
for(int num : nums2){
while(!stack.isEmpty() && num > stack.peek()){
map.put(stack.pop(), num);
}
stack.add(num);
}
int[] ret = new int[nums1.length];
for(int i = 0; i < nums1.length; i++){
if(map.containsKey(nums1[i])) ret[i] = map.get(nums1[i]);
else ret[i] = -1;
}
return ret;
}
```
**?????????????????????????**
[Leetcode : 503. Next Greater Element II (Medium)](https://leetcode.com/problems/next-greater-element-ii/description/)
```java
public int[] nextGreaterElements(int[] nums) {
int n = nums.length, next[] = new int[n];
Arrays.fill(next, -1);
Stack<Integer> stack = new Stack<>();
for (int i = 0; i < n * 2; i++) {
int num = nums[i % n];
while (!stack.isEmpty() && nums[stack.peek()] < num)
next[stack.pop()] = num;
if (i < n) stack.push(i);
}
return next;
}
```
## ?????
???? Hash Table ????????????????????????????????????????????洢?????????????临?????????????????? Hash Table ?????任???????????
Java ?е? **HashSet** ????洢???????????? O(1) ????临??????????????????С?
???????????????Χ???????????????????????????洢???????????????????????Сд???????????????????????? 26 ????????????洢???????????????临??????? O(1)??
Java ?е? **HashMap** ???????????????????????????????????
?????????????????????????????????? HashMap ?????????????????????????????????????????? url ?????У?[Leetcdoe : 535. Encode and Decode TinyURL (Medium)](https://leetcode.com/problems/encode-and-decode-tinyurl/description/)???????? HashMap ?????洢?????? url ???? url ???????ò????????????? url???????????? url ????? url ?????λ????????????
HashMap ????????????????м??????????????????????????? HashSet ??????????????????Χ???????????????????????????
**?????е???????????????**
[Leetcode : 1. Two Sum (Easy)](https://leetcode.com/problems/two-sum/description/)
???????????????????????????????????????????????????????临???? O(nlg<sub>n</sub>)????临???? O(1)??
?? HashMap ?洢??????????????????????? nums[i] ????ж? HashMap ???????? target - nums[i] ???????????? target - nums[i] ??????????? i ?????????????????÷???????临???? O(n)????临???? O(n)???????????????
```java
public int[] twoSum(int[] nums, int target) {
HashMap<Integer, Integer> map = new HashMap<>();
for(int i = 0; i < nums.length; i++){
if(map.containsKey(target - nums[i])) return new int[]{map.get(target - nums[i]), i};
else map.put(nums[i], i);
}
return null;
}
```
**????г????**
??г???????????????С?????????? 1
[Leetcode : 594. Longest Harmonious Subsequence (Easy)](https://leetcode.com/problems/longest-harmonious-subsequence/description/)
```java
public int findLHS(int[] nums) {
Map<Long, Integer> map = new HashMap<>();
for (long num : nums) {
map.put(num, map.getOrDefault(num, 0) + 1);
}
int result = 0;
for (long key : map.keySet()) {
if (map.containsKey(key + 1)) {
result = Math.max(result, map.get(key + 1) + map.get(key));
}
}
return result;
}
```
## ?????
**????????????????????????????**
[Leetcode : 242. Valid Anagram (Easy)](https://leetcode.com/problems/valid-anagram/description/)
??????????Сд?????????? 26 ??Сд??????????? Hash Table ??????????????????????????Χ??С???????????????????????
??ó???? 26 ????????????????????????????????????????????????????????????????
```java
public boolean isAnagram(String s, String t) {
int[] cnts = new int[26];
for(int i = 0; i < s.length(); i++) cnts[s.charAt(i) - 'a'] ++;
for(int i = 0; i < t.length(); i++) cnts[t.charAt(i) - 'a'] --;
for(int i = 0; i < 26; i++) if(cnts[i] != 0) return false;
return true;
}
```
**????????**
[Leetcode : 205. Isomorphic Strings (Easy)](https://leetcode.com/problems/isomorphic-strings/description/)
???? "egg" ?? "add" ????????????????
???????????γ????λ?????????????????????????γ????λ?????????????????????
```java
public boolean isIsomorphic(String s, String t) {
int[] m1 = new int[256];
int[] m2 = new int[256];
for(int i = 0; i < s.length(); i++){
if(m1[s.charAt(i)] != m2[t.charAt(i)]) {
return false;
}
m1[s.charAt(i)] = i + 1;
m2[t.charAt(i)] = i + 1;
}
return true;
}
```
**???????????????????????????????????**
[Leetcode : 409. Longest Palindrome](https://leetcode.com/problems/longest-palindrome/description/)
??ó???? 128 ?????????????????????????????????????????????????????????????????????????????????м????????????????????????????е???????????????????м?
```java
public int longestPalindrome(String s) {
int[] cnts = new int[128]; // ascii ????? 128 ??
for(char c : s.toCharArray()) cnts[c]++;
int ret = 0;
for(int cnt : cnts) ret += (cnt / 2) * 2;
if(ret < s.length()) ret ++; // ????????? s ??????е???δ??????????????????????????????????м?
return ret;
}
```
**?ж??????????????????**
[Leetcode : 9. Palindrome Number (Easy)](https://leetcode.com/problems/palindrome-number/description/)
??????????????????????????????????????ж??
???????????????????????????????????????ж????????????????
```java
public boolean isPalindrome(int x) {
if(x == 0) return true;
if(x < 0) return false;
if(x % 10 == 0) return false;
int right = 0;
while(x > right){
right = right * 10 + x % 10;
x /= 10;
}
return x == right || x == right / 10;
}
```
**???????????**
[Leetcode : 647. Palindromic Substrings (Medium)](https://leetcode.com/problems/palindromic-substrings/description/)
???????????????????λ????????????????????????
```java
private int cnt = 0;
public int countSubstrings(String s) {
for(int i = 0; i < s.length(); i++) {
extendSubstrings(s, i, i); // ????????
extendSubstrings(s, i, i + 1); // ???????
}
return cnt;
}
private void extendSubstrings(String s, int start, int end) {
while(start >= 0 && end < s.length() && s.charAt(start) == s.charAt(end)) {
start--;
end++;
cnt++;
}
}
```
**??????????????????? 1 ?? ???? 0 ????????????????????**
```html
Input: "00110011"
Output: 6
Explanation: There are 6 substrings that have equal number of consecutive 1's and 0's: "0011", "01", "1100", "10", "0011", and "01".
```
[Leetcode : 696. Count Binary Substrings (Easy)](https://leetcode.com/problems/count-binary-substrings/description/)
```java
public int countBinarySubstrings(String s) {
int preLen = 0, curLen = 1, ret = 0;
for(int i = 1; i < s.length(); i++){
if(s.charAt(i) == s.charAt(i-1)) curLen++;
else{
preLen = curLen;
curLen = 1;
}
if(preLen >= curLen) ret++;
}
return ret;
}
```
**??????????λ????**
[ ????????3.1](#)
????????????? s1 ?? s2 ??????ж? s2 ???????? s1 ???????λ????????????????
```html
s1 = AABCD, s2 = CDAA
Return : true
```
s1 ?????????λ?????? s1s1 ?????????????????ж? s2 ????? s1s1 ????????????ɡ?
**??????????λ**
[ ????????2.17](#)
????????????????? k λ??
???? abcd123 ??????? 3 λ ??? 123abcd
?? abcd123 ?е? abcd ?? 123 ?????????? dcba321?????????????????????????123abcd??
**??????е??????**
[????????????????](#)
???罫 "I am a student" ????? "student a am I"
?????????????????????????????
## ?????????
**???????** // TODO
[??????????? P114](#)
**???????** //TODO
[???????????????? P335](#)
**???????е? 0 ????β**
[Leetcode : 283. Move Zeroes (Easy)](https://leetcode.com/problems/move-zeroes/description/)
```java
public void moveZeroes(int[] nums) {
int n = nums.length;
int idx = 0;
for(int i = 0; i < n; i++){
if(nums[i] != 0) nums[idx++] = nums[i];
}
while(idx < n){
nums[idx++] = 0;
}
}
```
**???????????? [1, n] ???????????????滻?????????????????????????????**
[Leetcode : 645. Set Mismatch (Easy)](https://leetcode.com/problems/set-mismatch/description/)
??????????????????????????????????临???? O(nlog<sub>n</sub>)??????????? O(n) ????临????O(1) ??临????????
?????????????????????????????????????????????λ?????
???????飬????? i λ????????? i + 1 ???????????? i λ ?? nums[i] - 1 λ?????????? num[i] - 1 ?????? nums[i] ????????λ??????????????????????????????У??????ν?????????? i λ???????????????????????????????????????????????????????????????????????????????????? nums[i] != nums[nums[i] - 1 ??????
?????????
- [Leetcode :448. Find All Numbers Disappeared in an Array (Easy)](https://leetcode.com/problems/find-all-numbers-disappeared-in-an-array/description/)????????ж???????
- [Leetcode : 442. Find All Duplicates in an Array (Medium)](https://leetcode.com/problems/find-all-duplicates-in-an-array/description/)??????????????????
```java
public int[] findErrorNums(int[] nums) {
for(int i = 0; i < nums.length; i++){
while(nums[i] != i + 1 && nums[i] != nums[nums[i] - 1]) swap(nums, i, nums[i] - 1);
}
for(int i = 0; i < nums.length; i++){
if(i + 1 != nums[i]) return new int[]{nums[i], i + 1};
}
return null;
}
private void swap(int[] nums, int i, int j){
int tmp = nums[i];
nums[i] = nums[j];
nums[j] = tmp;
}
```
**????????????????????????? [0, n-1] ???**
[Leetcode : 287. Find the Duplicate Number (Medium)](https://leetcode.com/problems/find-the-duplicate-number/description/)
??????????
```java
public int findDuplicate(int[] nums) {
int l = 1, h = nums.length - 1;
while (l <= h) {
int mid = l + (h - l) / 2;
int cnt = 0;
for (int i = 0; i < nums.length; i++) {
if (nums[i] <= mid) cnt++;
}
if (cnt > mid) h = mid - 1;
else l = mid + 1;
}
return l;
}
```
??????????????л??????????????????
```java
public int findDuplicate(int[] nums) {
int slow = nums[0], fast = nums[nums[0]];
while (slow != fast) {
slow = nums[slow];
fast = nums[nums[fast]];
}
fast = 0;
while (slow != fast) {
slow = nums[slow];
fast = nums[fast];
}
return slow;
}
```
### ???????
?????????????к??з??????????
??????????????????????????????
```html
[
[ 1, 5, 9],
[10, 11, 13],
[12, 13, 15]
]
```
**??????????**
[Leetocde : 240. Search a 2D Matrix II (Medium)](https://leetcode.com/problems/search-a-2d-matrix-ii/description/)
```java
public boolean searchMatrix(int[][] matrix, int target) {
if (matrix == null || matrix.length == 0 || matrix[0].length == 0) return false;
int m = matrix.length, n = matrix[0].length;
int row = 0, col = n - 1;
while (row < m && col >= 0) {
if (target == matrix[row][col]) return true;
else if (target < matrix[row][col]) col--;
else row++;
}
return false;
}
```
**???????? Kth Element**
[Leetcode : 378. Kth Smallest Element in a Sorted Matrix ((Medium))](https://leetcode.com/problems/kth-smallest-element-in-a-sorted-matrix/description/)
```html
matrix = [
[ 1, 5, 9],
[10, 11, 13],
[12, 13, 15]
],
k = 8,
return 13.
```
????ο???[Share my thoughts and Clean Java Code](https://leetcode.com/problems/kth-smallest-element-in-a-sorted-matrix/discuss/85173)
??????????
```java
public int kthSmallest(int[][] matrix, int k) {
int m = matrix.length, n = matrix[0].length;
int lo = matrix[0][0], hi = matrix[m - 1][n - 1];
while(lo <= hi) {
int mid = lo + (hi - lo) / 2;
int cnt = 0;
for(int i = 0; i < m; i++) {
for(int j = 0; j < n && matrix[i][j] <= mid; j++) {
cnt++;
}
}
if(cnt < k) lo = mid + 1;
else hi = mid - 1;
}
return lo;
}
```
?????
```java
public int kthSmallest(int[][] matrix, int k) {
int m = matrix.length, n = matrix[0].length;
PriorityQueue<Tuple> pq = new PriorityQueue<Tuple>();
for(int j = 0; j < n; j++) pq.offer(new Tuple(0, j, matrix[0][j]));
for(int i = 0; i < k - 1; i++) { // С???????? k - 1 ?????????????????????? k ????
Tuple t = pq.poll();
if(t.x == m - 1) continue;
pq.offer(new Tuple(t.x + 1, t.y, matrix[t.x + 1][t.y]));
}
return pq.poll().val;
}
class Tuple implements Comparable<Tuple> {
int x, y, val;
public Tuple(int x, int y, int val) {
this.x = x; this.y = y; this.val = val;
}
@Override
public int compareTo(Tuple that) {
return this.val - that.val;
}
}
```
## ????
**?ж?????????????**
[Leetcode : 160. Intersection of Two Linked Lists](https://leetcode.com/problems/intersection-of-two-linked-lists/description/)
```html
A: a1 ?? a2
?K
c1 ?? c2 ?? c3
?J
B: b1 ?? b2 ?? b3
```
?????临???? O(n) ??临???? O(1)
?? A ?????? a + c??B ?????? b + c?????? c ?β????????????????? a + c + b = b + c + a??
?????? A ????????????????β??????????????? B ???????????????? B?????????????? B ????????????????β??????????????? A ???????????????? A???????????????? A ?? B ?????????????????????????
```java
public ListNode getIntersectionNode(ListNode headA, ListNode headB) {
if(headA == null || headB == null) return null;
ListNode l1 = headA, l2 = headB;
while(l1 != l2){
l1 = (l1 == null) ? headB : l1.next;
l2 = (l2 == null) ? headA : l2.next;
}
return l1;
}
```
???????ж???????????????????????????? ????????3.6 ???????????????????????????β???????????????????????????????????????????????????????????????????????????????????????????
**?????**
[Leetcode : 206. Reverse Linked List](https://leetcode.com/problems/reverse-linked-list/description/)
??巨??????????????
```java
public ListNode reverseList(ListNode head) {
ListNode newHead = null; // ??? null ?????????????β
while(head != null){
ListNode nextNode = head.next;
head.next = newHead;
newHead = head;
head = nextNode;
}
return newHead;
}
```
**?鲢?????????????**
[Leetcode : 21. Merge Two Sorted Lists](https://leetcode.com/problems/merge-two-sorted-lists/description/)
???????????????????鷽??????壺??????????????????????????????????????????????????????????????????
```java
public ListNode mergeTwoLists(ListNode l1, ListNode l2) {
if(l1 == null) return l2;
if(l2 == null) return l1;
ListNode newHead = null;
if(l1.val < l2.val){
newHead = l1;
newHead.next = mergeTwoLists(l1.next, l2);
} else{
newHead = l2;
newHead.next = mergeTwoLists(l1, l2.next);
}
return newHead;
}
```
**?????????????????????**
[Leetcode : 83. Remove Duplicates from Sorted List (Easy)](https://leetcode.com/problems/remove-duplicates-from-sorted-list/description/)
```java
public ListNode deleteDuplicates(ListNode head) {
if(head == null || head.next == null) return head;
head.next = deleteDuplicates(head.next);
return head.next != null && head.val == head.next.val ? head.next : head;
}
```
**????????**
[Leetcode : 234. Palindrome Linked List (Easy)](https://leetcode.com/problems/palindrome-linked-list/description/)
?г?????????η????????????????????
```java
public boolean isPalindrome(ListNode head) {
if(head == null || head.next == null) return true;
ListNode slow = head, fast = head.next;
while(fast != null && fast.next != null){
slow = slow.next;
fast = fast.next.next;
}
if(fast != null){ // ???????? slow ???????????
slow = slow.next;
}
cut(head, slow); // ?г?????????
ListNode l1 = head, l2 = slow;
l2 = reverse(l2);
return isEqual(l1, l2);
}
private void cut(ListNode head, ListNode cutNode){
while( head.next != cutNode ) head = head.next;
head.next = null;
}
private ListNode reverse(ListNode head){
ListNode newHead = null;
while(head != null){
ListNode nextNode = head.next;
head.next = newHead;
newHead = head;
head = nextNode;
}
return newHead;
}
private boolean isEqual(ListNode l1, ListNode l2){
while(l1 != null && l2 != null){
if(l1.val != l2.val) return false;
l1 = l1.next;
l2 = l2.next;
}
return true;
}
```
**??????????????**
[????????3.4]()
![](https://github.com/CyC2018/InterviewNotes/blob/master/pics/2c968ec5-0967-49ce-ac06-f8f5c9ab33bc.jpg)
```java
B.val = C.val;
B.next = C.next;
```
**??????????????**
[Leetcode : 328. Odd Even Linked List (Medium)](https://leetcode.com/problems/odd-even-linked-list/description/)
```java
public ListNode oddEvenList(ListNode head) {
if (head == null) {
return head;
}
ListNode odd = head, even = head.next, evenHead = even;
while (even != null && even.next != null) {
odd.next = odd.next.next;
odd = odd.next;
even.next = even.next.next;
even = even.next;
}
odd.next = evenHead;
return head;
}
```
## ??
### ???
??????????????????????????????????????????????????????????????????????????????
**??????**
[Leetcode : 104. Maximum Depth of Binary Tree (Easy)](https://leetcode.com/problems/maximum-depth-of-binary-tree/description/)
```java
public int maxDepth(TreeNode root) {
if(root == null) return 0;
return Math.max(maxDepth(root.left), maxDepth(root.right)) + 1;
}
```
**?????**
[Leetcode : 226. Invert Binary Tree (Easy)](https://leetcode.com/problems/invert-binary-tree/description/)
```java
public TreeNode invertTree(TreeNode root) {
if(root == null) return null;
TreeNode left = root.left; // ???????????? left ???????????????
root.left = invertTree(root.right);
root.right = invertTree(left);
return root;
}
```
**?鲢??????**
[Leetcode : 617. Merge Two Binary Trees (Easy)](https://leetcode.com/problems/merge-two-binary-trees/description/)
```java
public TreeNode mergeTrees(TreeNode t1, TreeNode t2) {
if(t1 == null && t2 == null) return null;
if(t1 == null) return t2;
if(t2 == null) return t1;
TreeNode root = new TreeNode(t1.val + t2.val);
root.left = mergeTrees(t1.left, t2.left);
root.right = mergeTrees(t1.right, t2.right);
return root;
}
```
**?ж?·???????????????**
[Leetcdoe : 112. Path Sum (Easy)](https://leetcode.com/problems/path-sum/description/)
?????????·?????????? root ?? leaf ?????н????
```java
public boolean hasPathSum(TreeNode root, int sum) {
if(root == null) return false;
if(root.left == null && root.right == null && root.val == sum) return true;
return hasPathSum(root.left, sum - root.val) || hasPathSum(root.right, sum - root.val);
}
```
**???·??????????????·??????**
[Leetcode : 437. Path Sum III (Easy)](https://leetcode.com/problems/path-sum-iii/description/)
?????????·????????? root ??????? leaf ??β?????????????
pathSumStartWithRoot() ??????????????????·????????
```java
public int pathSum(TreeNode root, int sum) {
if(root == null) return 0;
int ret = pathSumStartWithRoot(root, sum) + pathSum(root.left, sum) + pathSum(root.right, sum);
return ret;
}
private int pathSumStartWithRoot(TreeNode root, int sum){
if(root == null) return 0;
int ret = 0;
if(root.val == sum) ret++;
ret += pathSumStartWithRoot(root.left, sum - root.val) + pathSumStartWithRoot(root.right, sum - root.val);
return ret;
}
```
**??????**
[Leetcode : 101. Symmetric Tree (Easy)](https://leetcode.com/problems/symmetric-tree/description/)
```java
public boolean isSymmetric(TreeNode root) {
if(root == null) return true;
return isSymmetric(root.left, root.right);
}
private boolean isSymmetric(TreeNode t1, TreeNode t2){
if(t1 == null && t2 == null) return true;
if(t1 == null || t2 == null) return false;
if(t1.val != t2.val) return false;
return isSymmetric(t1.left, t2.right) && isSymmetric(t1.right, t2.left);
}
```
**?????**
[Leetcode : 110. Balanced Binary Tree (Easy)](https://leetcode.com/problems/balanced-binary-tree/description/)
????????????????????????С????? 1
```java
private boolean result = true;
public boolean isBalanced(TreeNode root) {
maxDepth(root);
return result;
}
public int maxDepth(TreeNode root) {
if (root == null) return 0;
int l = maxDepth(root.left);
int r = maxDepth(root.right);
if (Math.abs(l - r) > 1) result = false;
return 1 + Math.max(l, r);
}
```
**??С·??**
[Leetcode : 111. Minimum Depth of Binary Tree (Easy)](https://leetcode.com/problems/minimum-depth-of-binary-tree/description/)
?????????????????????????С????
```java
public int minDepth(TreeNode root) {
if(root == null) return 0;
int left = minDepth(root.left);
int right = minDepth(root.right);
if(left == 0 || right == 0) return left + right + 1;
return Math.min(left, right) + 1;
}
```
**????????????**
[Leetcode : 404. Sum of Left Leaves (Easy)](https://leetcode.com/problems/sum-of-left-leaves/description/)
```java
public int sumOfLeftLeaves(TreeNode root) {
if(root == null) return 0;
if(isLeaf(root.left)) return root.left.val + sumOfLeftLeaves(root.right);
return sumOfLeftLeaves(root.left) + sumOfLeftLeaves(root.right);
}
private boolean isLeaf(TreeNode node){
if(node == null) return false;
return node.left == null && node.right == null;
}
```
**????????**
[Leetcode : 669. Trim a Binary Search Tree (Easy)](https://leetcode.com/problems/trim-a-binary-search-tree/description/)
????????????????? L \~ R ??????
```java
public TreeNode trimBST(TreeNode root, int L, int R) {
if(root == null) return null;
if(root.val > R) return trimBST(root.left, L, R);
if(root.val < L) return trimBST(root.right, L, R);
root.left = trimBST(root.left, L, R);
root.right = trimBST(root.right, L, R);
return root;
}
```
**????**
[Leetcode : 572. Subtree of Another Tree (Easy)](https://leetcode.com/problems/subtree-of-another-tree/description/)
```java
public boolean isSubtree(TreeNode s, TreeNode t) {
if(s == null && t == null) return true;
if(s == null || t == null) return false;
if(s.val == t.val && isSame(s, t)) return true;
return isSubtree(s.left, t) || isSubtree(s.right, t);
}
private boolean isSame(TreeNode s, TreeNode t){
if(s == null && t == null) return true;
if(s == null || t == null) return false;
if(s.val != t.val) return false;
return isSame(s.left, t.left) && isSame(s.right, t.right);
}
```
**???????????й???????????**
[Leetcode : 108. Convert Sorted Array to Binary Search Tree (Easy)](https://leetcode.com/problems/convert-sorted-array-to-binary-search-tree/description/)
???????????BST????????????????????????н??С??????????????н??
```java
public TreeNode sortedArrayToBST(int[] nums) {
return toBST(nums, 0, nums.length - 1);
}
private TreeNode toBST(int[] nums, int sIdx, int eIdx){
if(sIdx > eIdx) return null;
int mIdx = (sIdx + eIdx) / 2;
TreeNode root = new TreeNode(nums[mIdx]);
root.left = toBST(nums, sIdx, mIdx - 1);
root.right = toBST(nums, mIdx + 1, eIdx);
return root;
}
```
**????????·??**
```html
1
/ \
2 3
/ \
4 5
Return 3, which is the length of the path [4,2,1,3] or [5,2,1,3].
```
```java
private int max = 0;
public int diameterOfBinaryTree(TreeNode root) {
depth(root);
return max;
}
private int depth(TreeNode root) {
if (root == null) {
return 0;
}
int leftDepth = depth(root.left);
int rightDepth = depth(root.right);
max = Math.max(max, leftDepth + rightDepth);
return Math.max(leftDepth, rightDepth) + 1;
}
```
**??????????е??С????**
[Leetcode : 671. Second Minimum Node In a Binary Tree (Easy)](https://leetcode.com/problems/second-minimum-node-in-a-binary-tree/description/)
```html
Input:
2
/ \
2 5
/ \
5 7
Output: 5
```
???????????? 0 ???? 2 ???????????????????????????С????
```java
public int findSecondMinimumValue(TreeNode root) {
if(root == null) return -1;
if(root.left == null && root.right == null) return -1;
int leftVal = root.left.val;
int rightVal = root.right.val;
if(leftVal == root.val) leftVal = findSecondMinimumValue(root.left);
if(rightVal == root.val) rightVal = findSecondMinimumValue(root.right);
if(leftVal != -1 && rightVal != -1) return Math.min(leftVal, rightVal);
if(leftVal != -1) return leftVal;
return rightVal;
}
```
**??????????????????????**
[Leetcode : 235. Lowest Common Ancestor of a Binary Search Tree (Easy)](https://leetcode.com/problems/lowest-common-ancestor-of-a-binary-search-tree/description/)
```java
public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
if(root.val > p.val && root.val > q.val) return lowestCommonAncestor(root.left, p, q);
if(root.val < p.val && root.val < q.val) return lowestCommonAncestor(root.right, p, q);
return root;
}
```
**???????????**
[Leetcode : 236. Lowest Common Ancestor of a Binary Tree (Medium) ](https://leetcode.com/problems/lowest-common-ancestor-of-a-binary-tree/description/)
```java
public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
if (root == null || root == p || root == q) return root;
TreeNode left = lowestCommonAncestor(root.left, p, q);
TreeNode right = lowestCommonAncestor(root.right, p, q);
return left == null ? right : right == null ? left : root;
}
```
**????????????·??????**
[Leetcode : 687. Longest Univalue Path (Easy)](https://pomotodo.com/app/)
```html
1
/ \
4 5
/ \ \
4 4 5
Output : 2
```
```java
private int path = 0;
public int longestUnivaluePath(TreeNode root) {
dfs(root);
return path;
}
private int dfs(TreeNode root){
if(root == null) return 0;
int left = dfs(root.left);
int right = dfs(root.right);
int leftPath = root.left != null && root.left.val == root.val ? left + 1 : 0;
int rightPath = root.right != null && root.right.val == root.val ? right + 1 : 0;
path = Math.max(path, leftPath + rightPath);
return Math.max(leftPath, rightPath);
}
```
**???????**
[Leetcode : 337. House Robber III (Medium)](https://leetcode.com/problems/house-robber-iii/description/)
```java
public int rob(TreeNode root) {
if (root == null) return 0;
int val1 = root.val;
if (root.left != null) {
val1 += rob(root.left.left) + rob(root.left.right);
}
if (root.right != null) {
val1 += rob(root.right.left) + rob(root.right.right);
}
int val2 = rob(root.left) + rob(root.right);
return Math.max(val1, val2);
}
```
### ??α???
??? BFS???????????????????????洢????????????????? ????????????????????????????е????????????????????????????????????????????????α???????????????
**????????????????????**
[637. Average of Levels in Binary Tree (Easy)](https://leetcode.com/problems/average-of-levels-in-binary-tree/description/)
```java
public List<Double> averageOfLevels(TreeNode root) {
List<Double> ret = new ArrayList<>();
if(root == null) return ret;
Queue<TreeNode> queue = new LinkedList<>();
queue.add(root);
while(!queue.isEmpty()){
int cnt = queue.size();
double sum = 0;
for(int i = 0; i < cnt; i++){
TreeNode node = queue.poll();
sum += node.val;
if(node.left != null) queue.add(node.left);
if(node.right != null) queue.add(node.right);
}
ret.add(sum / cnt);
}
return ret;
}
```
**???????????**
[Leetcode : 513. Find Bottom Left Tree Value (Easy)](https://leetcode.com/problems/find-bottom-left-tree-value/description/)
```java
public int findBottomLeftValue(TreeNode root) {
Queue<TreeNode> queue = new LinkedList<>();
queue.add(root);
while(!queue.isEmpty()){
root = queue.poll();
if(root.right != null) queue.add(root.right);
if(root.left != null) queue.add(root.left);
}
return root.val;
}
```
### ??к??????
```html
1
/ \
2 3
/ \ \
4 5 6
```
??α??????[1 2 3 4 5 6]
?????????[1 2 4 5 3 6]
??????????[4 2 5 1 3 6]
??????????[4 5 2 6 3 1]
??α?????? BFS ???????????? BFS ????????????????????????????????????? DFS ????
?????????????????????????????????????????????
?? ???
```java
void dfs(TreeNode root){
visit(root);
dfs(root.left);
dfs(root.right);
}
```
?? ????
```java
void dfs(TreeNode root){
dfs(root.left);
visit(root);
dfs(root.right);
}
```
?? ????
```java
void dfs(TreeNode root){
dfs(root.left);
dfs(root.right);
visit(root);
}
```
**????????????????????**
[Leetcode : 144. Binary Tree Preorder Traversal (Medium)](https://leetcode.com/problems/binary-tree-preorder-traversal/description/)
```java
public List<Integer> preorderTraversal(TreeNode root) {
List<Integer> ret = new ArrayList<>();
if (root == null) return ret;
Stack<TreeNode> stack = new Stack<>();
stack.push(root);
while (!stack.isEmpty()) {
TreeNode node = stack.pop();
ret.add(node.val);
if (node.right != null) stack.push(node.right);
if (node.left != null) stack.push(node.left); // ??????????????????????????????????????????????
}
return ret;
}
```
**?????????????????????**
[Leetcode : ### 145. Binary Tree Postorder Traversal (Medium)](https://leetcode.com/problems/binary-tree-postorder-traversal/description/)
??????? root -> left -> right?????????? left -> right -> root?????????????????? root -> right -> left???????????????????????????
```java
public List<Integer> postorderTraversal(TreeNode root) {
List<Integer> ret = new ArrayList<>();
if (root == null) return ret;
Stack<TreeNode> stack = new Stack<>();
stack.push(root);
while (!stack.isEmpty()) {
TreeNode node = stack.pop();
ret.add(node.val);
if (node.left != null) stack.push(node.left);
if (node.right != null) stack.push(node.right);
}
Collections.reverse(ret);
return ret;
}
```
**?????????????????????**
[Leetcode : 94. Binary Tree Inorder Traversal (Medium)](https://leetcode.com/problems/binary-tree-inorder-traversal/description/)
```java
public List<Integer> inorderTraversal(TreeNode root) {
List<Integer> ret = new ArrayList<>();
Stack<TreeNode> stack = new Stack<>();
TreeNode cur = root;
while(cur != null || !stack.isEmpty()) {
while(cur != null) { // ???????????????
stack.add(cur);
cur = cur.left;
}
TreeNode node = stack.pop();
ret.add(node.val);
cur = node.right;
}
return ret;
}
```
**???????????????????????????????** //TODO
### BST
??????? BST ???????????????
**?? BST ??????????????????????????????**
[653. Two Sum IV - Input is a BST](https://leetcode.com/problems/two-sum-iv-input-is-a-bst/description/)
?????????????????????????????????????????в????
????????????????÷?????????????????????????????????????????????????????????????С?
```java
public boolean findTarget(TreeNode root, int k) {
List<Integer> nums = new ArrayList<>();
inOrder(root, nums);
int i = 0, j = nums.size() - 1;
while(i < j){
int sum = nums.get(i) + nums.get(j);
if(sum == k) return true;
if(sum < k) i++;
else j--;
}
return false;
}
private void inOrder(TreeNode root, List<Integer> nums){
if(root == null) return;
inOrder(root.left, nums);
nums.add(root.val);
inOrder(root.right, nums);
}
```
**?? BST ?в?????С?????????????????**
[Leetcode : 530. Minimum Absolute Difference in BST (Easy)](https://leetcode.com/problems/minimum-absolute-difference-in-bst/description/)
???? BST ??????????????????????????????????????????????????????????С???
```java
private int minDiff = Integer.MAX_VALUE;
private int preVal = -1;
public int getMinimumDifference(TreeNode root) {
inorder(root);
return minDiff;
}
private void inorder(TreeNode node){
if(node == null) return;
inorder(node.left);
if(preVal != -1) minDiff = Math.min(minDiff, Math.abs(node.val - preVal));
preVal = node.val;
inorder(node.right);
}
```
**?? BST ????????????????????????**
[Leetcode : Convert BST to Greater Tree (Easy)](https://leetcode.com/problems/convert-bst-to-greater-tree/description/)
?????????????
```java
private int sum = 0;
public TreeNode convertBST(TreeNode root) {
traver(root);
return root;
}
private void traver(TreeNode root) {
if (root == null) {
return;
}
if (root.right != null) {
traver(root.right);
}
sum += root.val;
root.val = sum;
if (root.left != null) {
traver(root.left);
}
}
```
**??? BST ?г????????????**
```java
private int cnt = 1;
private int maxCnt = 1;
private TreeNode preNode = null;
private List<Integer> list;
public int[] findMode(TreeNode root) {
list = new ArrayList<>();
inorder(root);
int[] ret = new int[list.size()];
int idx = 0;
for(int num : list){
ret[idx++] = num;
}
return ret;
}
private void inorder(TreeNode node){
if(node == null) return;
inorder(node.left);
if(preNode != null){
if(preNode.val == node.val) cnt++;
else cnt = 1;
}
if(cnt > maxCnt){
maxCnt = cnt;
list.clear();
list.add(node.val);
} else if(cnt == maxCnt){
list.add(node.val);
}
preNode = node;
inorder(node.right);
}
```
**??? BST ??? k ?????**
[Leetcode : 230. Kth Smallest Element in a BST (Medium)](https://leetcode.com/problems/kth-smallest-element-in-a-bst/description/)
??????
```java
public int kthSmallest(TreeNode root, int k) {
int leftCnt = count(root.left);
if(leftCnt == k - 1) return root.val;
if(leftCnt > k - 1) return kthSmallest(root.left, k);
return kthSmallest(root.right, k - leftCnt - 1);
}
private int count(TreeNode node) {
if(node == null) return 0;
return 1 + count(node.left) + count(node.right);
}
```
???????????
```java
private int cnt = 0;
private int val;
public int kthSmallest(TreeNode root, int k) {
inorder(root, k);
return val;
}
private void inorder(TreeNode node, int k) {
if(node == null) return;
inorder(node.left, k);
cnt++;
if(cnt == k) {
val = node.val;
return;
}
inorder(node.right, k);
}
```
### Trie
![](https://github.com/CyC2018/InterviewNotes/blob/master/pics/5c638d59-d4ae-4ba4-ad44-80bdc30f38dd.jpg)
Trie???????????????????????ж?????????????????????????????????
**?????? Trie**
[Leetcode : 208. Implement Trie (Prefix Tree) (Medium)](https://leetcode.com/problems/implement-trie-prefix-tree/description/)
```java
class Trie {
private class Node{
Node[] childs = new Node[26];
boolean isLeaf;
}
private Node root = new Node();
/** Initialize your data structure here. */
public Trie() {
}
/** Inserts a word into the trie. */
public void insert(String word) {
int idx = word.charAt(0) - 'a';
insert(word, root);
}
private void insert(String word, Node node){
int idx = word.charAt(0) - 'a';
if(node.childs[idx] == null){
node.childs[idx] = new Node();
}
if(word.length() == 1) node.childs[idx].isLeaf = true;
else insert(word.substring(1), node.childs[idx]);
}
/** Returns if the word is in the trie. */
public boolean search(String word) {
return search(word, root);
}
private boolean search(String word, Node node){
if(node == null) return false;
int idx = word.charAt(0) - 'a';
if(node.childs[idx] == null) return false;
if(word.length() == 1) return node.childs[idx].isLeaf;
return search(word.substring(1), node.childs[idx]);
}
/** Returns if there is any word in the trie that starts with the given prefix. */
public boolean startsWith(String prefix) {
return startWith(prefix, root);
}
private boolean startWith(String prefix, Node node){
if(node == null) return false;
if(prefix.length() == 0) return true;
int idx = prefix.charAt(0) - 'a';
return startWith(prefix.substring(1), node.childs[idx]);
}
}
```
**?????? Trie????????????**
[Leetcode : 677. Map Sum Pairs (Medium)](https://leetcode.com/problems/map-sum-pairs/description/)
```java
class MapSum {
private class Trie {
int val;
Map<Character, Trie> childs;
boolean isWord;
Trie() {
childs = new HashMap<>();
}
}
private Trie root;
public MapSum() {
root = new Trie();
}
public void insert(String key, int val) {
Trie cur = root;
for(char c : key.toCharArray()) {
if(!cur.childs.containsKey(c)) {
Trie next = new Trie();
cur.childs.put(c, next);
}
cur = cur.childs.get(c);
}
cur.val = val;
cur.isWord = true;
}
public int sum(String prefix) {
Trie cur = root;
for(char c : prefix.toCharArray()) {
if(!cur.childs.containsKey(c)) return 0;
cur = cur.childs.get(c);
}
return dfs(cur);
}
private int dfs(Trie cur) {
int sum = 0;
if(cur.isWord) {
sum += cur.val;
}
for(Trie next : cur.childs.values()) {
sum += dfs(next);
}
return sum;
}
}
```
## ?
## λ????
**1. ???????**
0s ??? ??? 0 ??1s ?????? 1??
```
x ^ 0s = x x & 0s = 0 x | 0s = x
x ^ 1s = \~x x & 1s = x x | 1s = 1s
x ^ x = 0 x & x = x x | x = x
```
?? ???? x ^ 1s = \~x ??????????λ?????????????? x ^ x = 0 ????????????????????????????????????????????????
?? ???? x & 0s = 0 ?? x & 1s = x ?????????????????????????? num ?? mask ??00111100 ????λ???????????? num ???? mask ?? 1 ??????????λ??
?? ???? x | 0s = x ?? x | 1s = 1s ???????????????ò?????????? num ?? mask??00111100 ????λ????????? num ???? mask ?? 1 ??????????λ??????? 1 ??
\>\> n ????????????????? 2<sup>n</sup>??
\>\>\> n ????????????????? 0??
&lt;&lt; n ????????????????? 2<sup>n</sup>??
n&(n-1) ??λ????????? n ??λ??????????????λ???????????????? 10110**100**????? 1 ??? 10110**011**???????????????? 10110**000**??
n-n&(\~n+1) ??????????? n ??λ??????????????λ??
n&(-n) ???????? n ??λ??????????????λ??-n ??? n ?????? 1????????????? 10110**100**??-n ??? 01001**100**???????? 00000**100**
**2. mask ????**
???? 111111111???? 0 ????????\~0??
??????е? i λ? 1 ?? mask???? 1 ??????? i λ?????1&lt;&lt;i ?????? 1&lt;&lt;5 ?????е? 5 λ? 1 ?? mask ??00010000??
???? 1 ?? i λ? 1 ?? mask??1&lt;&lt;(i+1)-1 ????????罫 1&lt;&lt;(4+1)-1 = 00010000-1 = 00001111??
???? 1 ?? i λ? 0 ?? mask????轫 1 ?? i λ? 1 ?? mask ??????? \~(1&lt;&lt;(i+1)-1)??
**3. λ????????**
?? ????? i λ
num & 00010000 != 0
```java
(num & (1 << i)) != 0;
```
?? ???? i λ????? 1
num | 00010000
```java
num | (1 << i);
```
?? ???? i λ???? 0
num & 11101111
```java
num & (\~(1 << i))
```
?? ?????λ???? i λ???? 0
num & 00001111
```java
num & ((1 << i) - 1);
```
?? ???? 0 λ???? i λ???? 0
num & 11110000
```java
num & (\~((1 << (i+1)) - 1));
```
?? ???? i λ????? 0 ???? 1
????? i λ??????? v ???? i λ????С?λ??????
```java
(num & (1 << i)) | (v << i);
```
**4. Java ?е?λ????**
```html
static int Integer.bitCount() // ??? 1 ??????
static int Integer.highestOneBit() // ??????λ
static String toBinaryString(int i) // ???λ???????????????
```
**???????????????????ж???λ???**
[Leetcode : 461. Hamming Distance (Easy)](https://leetcode.com/problems/hamming-distance/)
????????????????????????????λ???? 1 ??????ж???? 1 ???ɡ?
```java
public int hammingDistance(int x, int y) {
int z = x ^ y;
int cnt = 0;
while(z != 0){
if((z & 1) == 1) cnt++;
z = z >> 1;
}
return cnt;
}
```
??????? Integer.bitcount() ????? 1 ?????????
```java
public int hammingDistance(int x, int y) {
return Integer.bitCount(x ^ y);
}
```
**?????????????λ**
[Leetcode : 190. Reverse Bits (Easy)](https://leetcode.com/problems/reverse-bits/description/)
```java
public int reverseBits(int n) {
int ret = 0;
for(int i = 0; i < 32; i++){
ret <<= 1;
ret |= (n & 1);
n >>>= 1;
}
return ret;
}
```
**??????????????????????**
[???????????????? ??P317](#)
```java
a = a ^ b;
b = a ^ b;
a = a ^ b;
```
?? c = a ^ b????? b ^ c = b ^ b ^ a = a??a ^ c = a ^ a ^ b = b??
**?ж??????????? 4 ?? n ?η?**
[Leetcode : 342. Power of Four (Easy)](https://leetcode.com/problems/power-of-four/)
??????????????????????????λ? 1 ????????? 0 ?????? 16 ?? 10000?????????? 1 ??????? 2 λ??????????????????????????????????????ж????????????
```java
public boolean isPowerOfFour(int num) {
int i = 1;
while(i > 0){
if(i == num) return true;
i = i << 2;
}
return false;
}
```
??????? Java ?? Integer.toString() ?????????????? 4 ????????????????????ж??????????? 1 ?????
```java
public boolean isPowerOfFour(int num) {
return Integer.toString(num, 4).matches("10*");
}
```
**?ж??????????? 2 ?? n ?η?**
[Leetcode : 231. Power of Two (Easy)](https://leetcode.com/problems/power-of-two/description/)
????????? Power of Four ??????????? 2 ?? n ?η???????????????????????? 1 ?????
```java
public boolean isPowerOfTwo(int n) {
return n > 0 && Integer.bitCount(n) == 1;
}
```
???? 1000 & 0111 == 0 ???????????????????
```java
public boolean isPowerOfTwo(int n) {
return n > 0 && (n & (n - 1)) == 0;
}
```
**??????Ψ??????????????**
[Leetcode : 136. Single Number (Easy)](https://leetcode.com/problems/single-number/description/)
?????????????????? 0???????????????????????????????????????????????
??????У?[Leetcode : 389. Find the Difference (Easy)](https://leetcode.com/problems/find-the-difference/description/)??????????????????????????????????????????? O(1) ???临?????????????????? HashSet??
```java
public int singleNumber(int[] nums) {
int ret = 0;
for(int n : nums) ret = ret ^ n;
return ret;
}
```
**?????в?????????????**
[Leetcode : 260. Single Number III (Medium)](https://leetcode.com/problems/single-number-iii/description/)
???????????????λ??????????????λ????????
??????????????????????????????????????????????????
diff &= -diff ????? diff ?????? 0 ??λ??????????????????????????λ??????????????????λ?????????λ??????????????????????
```java
public int[] singleNumber(int[] nums) {
int diff = 0;
for(int num : nums) diff ^= num;
// ????????λ
diff &= -diff;
int[] ret = new int[2];
for(int num : nums) {
if((num & diff) == 0) ret[0] ^= num;
else ret[1] ^= num;
}
return ret;
}
```
**?ж????????λ?????????????????? 0 ?? 1**
[Leetcode : 693. Binary Number with Alternating Bits (Easy)](https://leetcode.com/problems/binary-number-with-alternating-bits/description/)
???? 10101 ????λ?????????????????????? 1 λ??? 1010 ?????????????λ???????????????????? 11111??
```java
public boolean hasAlternatingBits(int n) {
int a = (n ^ (n >> 1));
return (a & (a + 1)) == 0;
}
```
**????????????**
[Leetcode : 476. Number Complement (Easy)](https://leetcode.com/problems/number-complement/description/)
??????????????е??? 0 ????
???? 00000101??????????????? 00000111 ?????????????????????????????? 00000111??
```java
public int findComplement(int num) {
if(num == 0) return 1;
int mask = 1 << 30;
while((num & mask) == 0) mask >>= 1;
mask = (mask << 1) - 1;
return num ^ mask;
}
```
???????? Java ?? Integer.highestOneBit() ????????ú????? 1 ??????
```java
public int findComplement(int num) {
if(num == 0) return 1;
int mask = Integer.highestOneBit(num);
mask = (mask << 1) - 1;
return num ^ mask;
}
```
???? 10000000 ?????????????? 11111111?????????????·?????
```html
mask |= mask >> 1 11000000
mask |= mask >> 2 11110000
mask |= mask >> 4 11111111
```
```java
public int findComplement(int num) {
int mask = num;
mask |= mask >> 1;
mask |= mask >> 2;
mask |= mask >> 4;
mask |= mask >> 8;
mask |= mask >> 16;
return (mask ^ num);
}
```
**???????????**
[Leetcode : 371. Sum of Two Integers (Easy)](https://leetcode.com/problems/sum-of-two-integers/description/)
a ^ b ?????п????λ???????????????(a & b) << 1 ?????λ???????????????? (a & b) << 1 ?????????? 0???????????飬??λ?????? 0 ??????????????λ???? 0??????????
```java
public int getSum(int a, int b) {
return b == 0 ? a : getSum((a ^ b), (a & b) << 1);
}
```
**??????????**
[???????????????? P319](#)
**??????????????**
[Leetcode : 318. Maximum Product of Word Lengths (Medium)](https://leetcode.com/problems/maximum-product-of-word-lengths/description/)
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```java
public int maxProduct(String[] words) {
int n = words.length;
if (n == 0) return 0;
int[] val = new int[n];
for (int i = 0; i < n; i++) {
for (char c : words[i].toCharArray()) {
val[i] |= 1 << (c - 'a');
}
}
int ret = 0;
for (int i = 0; i < n; i++) {
for (int j = i + 1; j < n; j++) {
if ((val[i] & val[j]) == 0) {
ret = Math.max(ret, words[i].length() * words[j].length());
}
}
}
return ret;
}
```
# ?ο?????
- [Leetcode](https://leetcode.com/problemset/algorithms/?status=Todo)
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