ou are given a binary tree in which each node contains an integer value.Find the number of paths that sum to a given value.

The path does not need to start or end at the root or a leaf, but it must go downwards (traveling only from parent nodes to child nodes).

The tree has no more than 1,000 nodes and the values are in the range -1,000,000 to 1,000,000.

Example:

root = [10,5,-3,3,2,null,11,3,-2,null,1], sum = 8

      10
     /  \
    5   -3
   / \    \
  3   2   11
 / \   \
3  -2   1

Return 3. The paths that sum to 8 are:

1.  5 -> 3
2.  5 -> 2 -> 1
3. -3 -> 11

方法1：(利用深度優先演算法)

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    public int pathSum(TreeNode root, int sum) {
        if(root == null) return 0;
        return dfs(root, sum) + pathSum(root.left, sum) + pathSum(root.right, sum);
    }
    
    private int dfs(TreeNode root, int sum) {
        if(root == null) return 0;
        int res = 0;
        if(root.val == sum) res++;
        res += dfs(root.left, sum - root.val);
        res += dfs(root.right, sum - root.val);
        return res;
    }
}
 

時間複雜度：O(n^2)

空間複雜度：O(n)