797. All Paths From Source to Target

Given a directed acyclic graph (DAG) of n nodes labeled from 0 to n - 1, find all possible paths from node 0 to node n - 1 and return them in any order.

The graph is given as follows: graph[i] is a list of all nodes you can visit from node i (i.e., there is a directed edge from node i to node graph[i][j]).

回溯。DFS搜索所有的路径。
当搜索到最后一个位置时,保存动态数组并返回。(此处需要深拷贝数组。)
回到上一层,取走动态数组的最后一个节点。

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class Solution {
public List<List<Integer>> allPathsSourceTarget(int[][] graph) {
List<List<Integer>> ret = new LinkedList<>();
dfs(ret, new ArrayList<>(), graph, 0);
return ret;
}

private void dfs(List<List<Integer>> ret, List<Integer> arr, int[][] graph, int i){
if( i == graph.length - 1){
arr.add(i);
ret.add(new ArrayList(arr));
return;
}
arr.add(i);
for( int j : graph[i] ){
dfs(ret, arr, graph, j);
arr.remove(arr.size()-1);
}
}
}

547. Number of Provinces

There are n cities. Some of them are connected, while some are not. If city a is connected directly with city b, and city b is connected directly with city c, then city a is connected indirectly with city c.

A province is a group of directly or indirectly connected cities and no other cities outside of the group.

You are given an n x n matrix isConnected where isConnected[i][j] = 1 if the ith city and the jth city are directly connected, and isConnected[i][j] = 0 otherwise.

Return the total number of provinces.

DFS搜索,当map[i][i] = 1时加入搜索。
搜索时将map[i][i]设为0。遍历并递归其数列。
当map[i][i]等于0时,返回。

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class Solution {
int[][] map;
public int findCircleNum(int[][] isConnected) {
map = isConnected;
int count = 0;

for(int i = 0; i < isConnected.length; i++){
if(map[i][i] == 1){
count++;
dfs(i);
}
}
return count;
}

private void dfs(int i){
if(map[i][i] == 0){
return;
}
map[i][i] = 0;
for(int j = 0; j < map[0].length; j++){
if(map[i][j] == 1){
dfs(j);
}
}
}
}
200. Number of Islands

200. Number of Islands

Question

Given an m x n 2D binary grid grid which represents a map of ‘1’s (land) and ‘0’s (water), return the number of islands.

An island is surrounded by water and is formed by connecting adjacent lands horizontally or vertically. You may assume all four edges of the grid are all surrounded by water.

Solution

遍历所有点,如果等于1则对其进行DFS搜索。
在搜索的同时将1设为0。
如果等于0则递归返回。

Code

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class Solution {
char[][] area;
public int numIslands(char[][] grid) {
area = grid;
int count = 0;

for(int i = 0; i < area.length; i++){
for(int j = 0; j < area[0].length; j++){
if(area[i][j] == '1'){
dfs(i, j);
count++;
}
}
}
return count;
}

private void dfs(int i, int j){
if(area[i][j] == '0'){
return;
}
area[i][j] = '0';

if( i+1 < area.length ){
dfs(i+1, j);
}
if( i-1 >= 0 ){
dfs(i-1, j);
}
if( j+1 < area[0].length ){
dfs(i, j+1);
}
if( j-1 >= 0 ){
dfs(i, j-1);
}
}
}

Solution 2

同样是dfs搜索遍历每个位置,然而这个方法使用visited[][]数组来记录点是否被访问过。

Code

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class Solution {
int[][] visited;
char[][] map;
int[][] operations;
public int numIslands(char[][] grid) {
visited = new int[grid.length][grid[0].length];
map = grid;
int count = 0;
operations = new int[][]{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};

for(int i = 0; i < grid.length; i++){
for(int j = 0; j < grid[0].length; j++){
if(visited[i][j] == 1 || map[i][j] == '0') continue;
dfs(i, j);
count++;
}
}
return count;
}

private void dfs(int x, int y){
if(x < 0 || x >= map.length || y < 0 || y >= map[0].length ) return;
if(visited[x][y] == 1 || map[x][y] == '0') return;
visited[x][y] = 1;
for(int[] operation : operations){
int m = x + operation[0];
int n = y + operation[1];
dfs(m, n);
}

}
}

173. Binary Search Tree Iterator

Implement the BSTIterator class that represents an iterator over the in-order traversal of a binary search tree (BST):

BSTIterator(TreeNode root) Initializes an object of the BSTIterator class. The root of the BST is given as part of the constructor. The pointer should be initialized to a non-existent number smaller than any element in the BST.
boolean hasNext() Returns true if there exists a number in the traversal to the right of the pointer, otherwise returns false.
int next() Moves the pointer to the right, then returns the number at the pointer.
Notice that by initializing the pointer to a non-existent smallest number, the first call to next() will return the smallest element in the BST.

You may assume that next() calls will always be valid. That is, there will be at least a next number in the in-order traversal when next() is called.

此方法不用将所有节点一次性入栈,而是在获得next时更新栈内的节点,因此更省时间。
将根节点的所有左子节点入栈,此时栈顶为最小值。
next方法:返回当前的栈顶节点。如果栈顶节点存在右子节点,则将其所有的左子节点入栈。
hasNext方法:返回栈是否为空的非值。

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/**
* Definition for a binary tree node.
* public class TreeNode {
* int val;
* TreeNode left;
* TreeNode right;
* TreeNode() {}
* TreeNode(int val) { this.val = val; }
* TreeNode(int val, TreeNode left, TreeNode right) {
* this.val = val;
* this.left = left;
* this.right = right;
* }
* }
*/
class BSTIterator {
Stack<TreeNode> stack;
public BSTIterator(TreeNode root) {
stack = new Stack();
updateStack(root);
}

public int next() {
TreeNode node = stack.pop();
updateStack(node.right);
return node.val;
}

public boolean hasNext() {
return !stack.isEmpty();
}

private void updateStack(TreeNode root){
while(root != null){
stack.push(root);
root = root.left;
}
}
}

/**
* Your BSTIterator object will be instantiated and called as such:
* BSTIterator obj = new BSTIterator(root);
* int param_1 = obj.next();
* boolean param_2 = obj.hasNext();
*/

DFS搜索,中序搜索,从右子节点至左子节点,先将所有元素入栈。
next方法:挤出栈顶并返回。
hasNext方法: 返回栈是否为空的非值。

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/**
* Definition for a binary tree node.
* public class TreeNode {
* int val;
* TreeNode left;
* TreeNode right;
* TreeNode() {}
* TreeNode(int val) { this.val = val; }
* TreeNode(int val, TreeNode left, TreeNode right) {
* this.val = val;
* this.left = left;
* this.right = right;
* }
* }
*/
class BSTIterator {
Stack<TreeNode> stack;
public BSTIterator(TreeNode root) {
stack = new Stack();
initiateStack(root);
}

public int next() {
return stack.pop().val;
}

public boolean hasNext() {
return !stack.isEmpty();
}

private void initiateStack(TreeNode root){
if(root == null){
return;
}
initiateStack(root.right);
stack.push(root);
initiateStack(root.left);
}
}

/**
* Your BSTIterator object will be instantiated and called as such:
* BSTIterator obj = new BSTIterator(root);
* int param_1 = obj.next();
* boolean param_2 = obj.hasNext();
*/

99. Recover Binary Search Tree

You are given the root of a binary search tree (BST), where the values of exactly two nodes of the tree were swapped by mistake. Recover the tree without changing its structure.

DFS中序搜索,额外记录访问的前一个节点。
如果当前节点与前一个节点的顺序不对,则暂且认为先后两个节点的位置均不正确。
(前一个大于后一个的值,由于是第一个不满足递增条件的位置,因此前一个的位置一定是错误的。但此时当前值不一定是错误的。)
继续递归,如果发现新的节点位置不正确,则后一个节点位置正确,更新当前节点为不正确的节点。
(由于是第二个不满足递增条件的位置,因此当前值是错误的。)
交换两个位置不正确的节点的值。

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/**
* Definition for a binary tree node.
* public class TreeNode {
* int val;
* TreeNode left;
* TreeNode right;
* TreeNode() {}
* TreeNode(int val) { this.val = val; }
* TreeNode(int val, TreeNode left, TreeNode right) {
* this.val = val;
* this.left = left;
* this.right = right;
* }
* }
*/
class Solution {
TreeNode prev;
boolean flag;
TreeNode[] wrong;
public void recoverTree(TreeNode root) {
wrong = new TreeNode[2];
prev = new TreeNode(Integer.MIN_VALUE);
flag = true;

dfs(root);

int swap = wrong[0].val;
wrong[0].val = wrong[1].val;
wrong[1].val = swap;


}

private void dfs(TreeNode root){
if(root == null){
return;
}
dfs(root.left);
if(prev.val > root.val){
if(flag){
wrong[0] = prev;
flag = false;
}
wrong[1] = root;
}
prev = root;
dfs(root.right);
}
}

230. Kth Smallest Element in a BST

Given the root of a binary search tree, and an integer k, return the kth smallest value (1-indexed) of all the values of the nodes in the tree.

DFS搜索,遍历的时候更新全局变量count。
采用中序搜索,当count等于k时,将全局变量ans设置为root.val。
搜索完毕返回ans。

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/**
* Definition for a binary tree node.
* public class TreeNode {
* int val;
* TreeNode left;
* TreeNode right;
* TreeNode() {}
* TreeNode(int val) { this.val = val; }
* TreeNode(int val, TreeNode left, TreeNode right) {
* this.val = val;
* this.left = left;
* this.right = right;
* }
* }
*/
class Solution {
int ans;
int count;
public int kthSmallest(TreeNode root, int k) {
ans = -1;
count = 0;
dfs(root,k);
return ans;
}

private void dfs(TreeNode root, int k){
if(root == null){
return;
}
dfs(root.left,k);
count++;
if (k == count){
ans = root.val;
}
dfs(root.right,k);
}
}

897. Increasing Order Search Tree

Given the root of a binary search tree, rearrange the tree in in-order so that the leftmost node in the tree is now the root of the tree, and every node has no left child and only one right child.

DFS搜索,在递归时将in-order遍历节点,并将其加入队列。
从队列中挤出节点,将上一个节点的右子节点设置为下一个节点。
同时需要将下一个节点的左子节点设置为null。
`

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/**
* Definition for a binary tree node.
* public class TreeNode {
* int val;
* TreeNode left;
* TreeNode right;
* TreeNode() {}
* TreeNode(int val) { this.val = val; }
* TreeNode(int val, TreeNode left, TreeNode right) {
* this.val = val;
* this.left = left;
* this.right = right;
* }
* }
*/
class Solution {
Queue<TreeNode> q;
public TreeNode increasingBST(TreeNode root) {
q = new LinkedList();
dfs(root);
TreeNode head = q.poll();
TreeNode curr = head;
while(!q.isEmpty()){
curr.left = null;
curr.right = q.poll();
curr = curr.right;
}
curr.left = null;
return head;
}

private void dfs(TreeNode root){
if(root == null){
return;
}
dfs(root.left);
q.offer(root);
dfs(root.right);
}
}

653. Two Sum IV - Input is a BST

问题
Given the root of a Binary Search Tree and a target number k, return true if there exist two elements in the BST such that their sum is equal to the given target.

DFS搜索,每次递归时检查HashSet中是否有当前节点的值。如没有则将目标值减去当前节点的值加入HashSet。如有则返回true。
递归左侧节点和右侧节点,并返回二者的或运算。

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/**
* Definition for a binary tree node.
* public class TreeNode {
* int val;
* TreeNode left;
* TreeNode right;
* TreeNode() {}
* TreeNode(int val) { this.val = val; }
* TreeNode(int val, TreeNode left, TreeNode right) {
* this.val = val;
* this.left = left;
* this.right = right;
* }
* }
*/
class Solution {
HashSet<Integer> set;
public boolean findTarget(TreeNode root, int k) {
set = new HashSet();
return dfs(root,k);
}

private boolean dfs(TreeNode root, int k){
if(root == null){
return false;
}
if(set.contains(root.val)){
return true;
}
set.add(k - root.val);

return dfs(root.left,k) || dfs(root.right,k);
}
}

235. Lowest Common Ancestor of a BST

问题
Given a binary search tree (BST), find the lowest common ancestor (LCA) of two given nodes in the BST.

According to the definition of LCA on Wikipedia: “The lowest common ancestor is defined between two nodes p and q as the lowest node in T that has both p and q as descendants (where we allow a node to be a descendant of itself).”

DFS搜索,如果当前节点为null,则返回null。
如果当前节点小于p和q的值,则递归其左子节点。
反之递归其右子节点。
如果当前节点在p与q之间,则返回当前节点。
该节点是p与q的Lowest Common Ancestor。

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/**
* Definition for a binary tree node.
* public class TreeNode {
* int val;
* TreeNode left;
* TreeNode right;
* TreeNode(int x) { val = x; }
* }
*/

class Solution {
public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
if(root == null){
return null;
}
if(p.val < root.val && q.val < root.val){
return lowestCommonAncestor(root.left, p, q);
}
if(p.val > root.val && q.val > root.val){
return lowestCommonAncestor(root.right, p, q);
}
return root;
}
}

538. Convert BST to Greater Tree

问题
Given the root of a Binary Search Tree (BST), convert it to a Greater Tree such that every key of the original BST is changed to the original key plus the sum of all keys greater than the original key in BST.

As a reminder, a binary search tree is a tree that satisfies these constraints:

  • The left subtree of a node contains only >->- nodes with keys less than the node’s key.
  • The right subtree of a node contains only nodes with keys greater than the node’s key.
  • Both the left and right subtrees must also be binary search trees.
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/**
* Definition for a binary tree node.
* public class TreeNode {
* int val;
* TreeNode left;
* TreeNode right;
* TreeNode() {}
* TreeNode(int val) { this.val = val; }
* TreeNode(int val, TreeNode left, TreeNode right) {
* this.val = val;
* this.left = left;
* this.right = right;
* }
* }
*/

DFS搜索,设置一个成员变量记录上一个节点的值。
先递归右侧节点。
设置当前节点的值为自身的值加上temp中的值。
更新temp中的值,再递归左侧节点。


class Solution {
int temp;
public TreeNode convertBST(TreeNode root) {
temp = 0;
dfs(root);
return root;
}

private void dfs(TreeNode root){
if(root == null){
return;
}
dfs(root.right);
root.val += temp;
temp = root.val;
dfs(root.left);
}
}

669. Trim a Binary Search Tree

问题
Given the root of a binary search tree and the lowest and highest boundaries as low and high, trim the tree so that all its elements lies in [low, high]. Trimming the tree should not change the relative structure of the elements that will remain in the tree (i.e., any node’s descendant should remain a descendant). It can be proven that there is a unique answer.

Return the root of the trimmed binary search tree. Note that the root may change depending on the given bounds.

DFS搜索,每次递归带上搜索的范围值。
如果当前节点小于搜索范围,递归当前节点的右子节点。
反之递归当前节点的左子节点。
如果当前节点在搜索范围中,则其左子节点等于递归后的左子节点,右子节点等于递归后的右子节点。
然后返回当前节点。

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/**
* Definition for a binary tree node.
* public class TreeNode {
* int val;
* TreeNode left;
* TreeNode right;
* TreeNode() {}
* TreeNode(int val) { this.val = val; }
* TreeNode(int val, TreeNode left, TreeNode right) {
* this.val = val;
* this.left = left;
* this.right = right;
* }
* }
*/
class Solution {
public TreeNode trimBST(TreeNode root, int low, int high) {
if(root == null){
return null;
}
if(root.val < low){
return trimBST(root.right, low, high);
}
if(root.val > high){
return trimBST(root.left, low, high);
}

root.left = trimBST(root.left, low, high);
root.right = trimBST(root.right, low, high);
return root;
}
}

70. Climbing Stairs

问题
You are climbing a staircase. It takes n steps to reach the top.

Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?

递归,传入根节点,进行BFS搜索。
如果当前节点小于搜索的最低点,则抛弃该节点,继续搜索其右子节点。(由于是BST,右子节点大于节点本身)
如果当前节点大于搜索的最高点,则抛弃该节点,继续搜索其左子节点。
如果当前节点在搜索范围内,则保留该节点,继续递归该节点的两个子节点。
最后返回根节点。

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/**
* Definition for a binary tree node.
* public class TreeNode {
* int val;
* TreeNode left;
* TreeNode right;
* TreeNode() {}
* TreeNode(int val) { this.val = val; }
* TreeNode(int val, TreeNode left, TreeNode right) {
* this.val = val;
* this.left = left;
* this.right = right;
* }
* }
*/
class Solution {
public TreeNode trimBST(TreeNode root, int low, int high) {
if(root == null){
return null;
}
if(root.val < low){
return trimBST(root.right, low, high);
}
if(root.val > high){
return trimBST(root.left, low, high);
}

root.left = trimBST(root.left, low, high);
root.right = trimBST(root.right, low, high);
return root;
}
}
695. Max Area of Island

695. Max Area of Island

Question

You are given an m x n binary matrix grid. An island is a group of 1’s (representing land) connected 4-directionally (horizontal or vertical.) You may assume all four edges of the grid are surrounded by water.

The area of an island is the number of cells with a value 1 in the island.

Return the maximum area of an island in grid. If there is no island, return 0.

Solution

DFS搜索, 维护一个变量count,为连续执行DFS搜索的次数。
遍历地图上所有为1的位置。

运行BFS时每次将全局变量count增加1。
执行完毕后BFS时将全局变量count清零。

遍历每个等于1的地图块。
递归周围四个地图块,当超越数组范围,或者当前位置不为1时返回。
进行搜索时将搜索过的地图块标记为0,不再重复搜索。

Code

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class Solution {
int[][] visited, directions;
int count;
public int maxAreaOfIsland(int[][] grid) {
int res = 0;
directions = new int[][]{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
for(int x = 0; x < grid.length; x++){
for(int y = 0; y < grid[0].length; y++){
if(grid[x][y] == 1){
count = 0;
dfs(grid, x, y);
res = Math.max(res, count);
}
}
}
return res;
}

private void dfs(int[][] grid, int x, int y){
if(x < 0 || y < 0 || x >= grid.length || y >= grid[0].length || grid[x][y] == 0) return;
grid[x][y] = 0;
count++;
for(int[] direction : directions){
int i = x + direction[0];
int j = y + direction[1];
dfs(grid, i, j);
}
}
}

733. Flood Fill

答案
An image is represented by an m x n integer grid image where image[i][j] represents the pixel value of the image.

You are also given three integers sr, sc, and newColor. You should perform a flood fill on the image starting from the pixel image[sr][sc].

To perform a flood fill, consider the starting pixel, plus any pixels connected 4-directionally to the starting pixel of the same color as the starting pixel, plus any pixels connected 4-directionally to those pixels (also with the same color), and so on. Replace the color of all of the aforementioned pixels with newColor.

Return the modified image after performing the flood fill.

深度优先搜索。
如果当前像素颜色等于最初的颜色,则变更为新颜色。
然后继续递归四个周围的像素。

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class Solution { 
public int[][] floodFill(int[][] image, int sr, int sc, int newColor) {
int oldColor = image[sr][sc];
if (oldColor != newColor){
dfs(image,sr,sc,oldColor,newColor);
}

return image;
}

private void dfs(int[][] image, int r, int c, int oldColor, int newColor){
if (image[r][c] == oldColor){
image[r][c] = newColor;

if (r>=1){
dfs(image,r-1,c,oldColor,newColor);
}
if (c>=1){
dfs(image,r,c-1,oldColor,newColor);
}
if (r<image.length-1){
dfs(image,r+1,c,oldColor,newColor);
}
if (c<image[0].length-1){
dfs(image,r,c+1,oldColor,newColor);
}
}
}
}