437\. 路径总和 III
# 437. 路径总和 III (opens new window)
# Description
Difficulty: 中等
Related Topics: 树 (opens new window), 深度优先搜索 (opens new window), 二叉树 (opens new window)
给定一个二叉树的根节点 root
,和一个整数 targetSum
,求该二叉树里节点值之和等于 targetSum
的 路径 的数目。
路径 不需要从根节点开始,也不需要在叶子节点结束,但是路径方向必须是向下的(只能从父节点到子节点)。
示例 1:
输入:root = [10,5,-3,3,2,null,11,3,-2,null,1], targetSum = 8
输出:3
解释:和等于 8 的路径有 3 条,如图所示。
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3
示例 2:
输入:root = [5,4,8,11,null,13,4,7,2,null,null,5,1], targetSum = 22
输出:3
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提示:
- 二叉树的节点个数的范围是
[0,1000]
- -109 <= Node.val <= 109
-1000 <= targetSum <= 1000
# Solution
Language: JavaScript
/**
* Definition for a binary tree node.
* function TreeNode(val, left, right) {
* this.val = (val===undefined ? 0 : val)
* this.left = (left===undefined ? null : left)
* this.right = (right===undefined ? null : right)
* }
*/
/**
* @param {TreeNode} root
* @param {number} targetSum
* @return {number}
*/
// 方法一:深度优先搜索
var pathSum = function(root, targetSum) {
if (root == null) {
return 0;
}
let ret = rootSum(root, targetSum);
ret += pathSum(root.left, targetSum);
ret += pathSum(root.right, targetSum);
return ret;
};
const rootSum = (root, targetSum) => {
let ret = 0;
if (root == null) {
return 0;
}
const val = root.val;
if (val === targetSum) {
ret++;
}
ret += rootSum(root.left, targetSum - val);
ret += rootSum(root.right, targetSum - val);
return ret;
}
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DFS
var pathSum = function (root, targetSum) {
let cnt = 0;
function dfs(node, sum, flag) {
if (!node) return;
sum += node.val;
if (sum === targetSum) cnt++;
dfs(node.left, sum, true);
dfs(node.right, sum, true);
if (flag) return;
dfs(node.left, 0, false);
dfs(node.right, 0, false);
}
dfs(root, 0, false);
return cnt;
};
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var pathSum = (root, targetSum) => {
// 深度优先遍历
// 参数:(当前节点,当前节点前缀和)
const dfs = (root, sum) => {
if (!root) return 0;
map.set(sum, (map.get(sum) || 0) + 1);
const newSum = sum + root.val;
// 寻找有无(newSum - targetSum)
res += map.get(newSum - targetSum) || 0;
// 向下遍历
dfs(root.left, newSum);
dfs(root.right, newSum);
// 避免相同节点值被重复计算,确保算出的sum是从上到下的一条路径
map.set(sum, map.get(sum) - 1);
};
// map中,key存的是前缀和,value存的是前缀和的数目
const map = new Map();
let res = 0;
dfs(root, 0);
return res;
};
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