[LeetCode] 437. Path Sum III

You 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

路径和III。题意和前两个版本类似，但是这个题找的路径和，起点可以不是根节点，问满足路径和为sum的路径有多少。

这个题出的非常好。思路是前缀和。利用前缀和的思路，递归统计你遍历到的子树上的前缀和presum是多少，并将这个前缀和存入hashmap。其他的部分就是很常规的前序遍历。

时间O(n)

空间O(n)

Java实现

 1 /**
 2  * Definition for a binary tree node.
 3  * public class TreeNode {
 4  *     int val;
 5  *     TreeNode left;
 6  *     TreeNode right;
 7  *     TreeNode() {}
 8  *     TreeNode(int val) { this.val = val; }
 9  *     TreeNode(int val, TreeNode left, TreeNode right) {
10  *         this.val = val;
11  *         this.left = left;
12  *         this.right = right;
13  *     }
14  * }
15  */
16 class Solution {
17     public int pathSum(TreeNode root, int sum) {
18         HashMap<Integer, Integer> map = new HashMap();
19         map.put(0, 1);
20         helper(root, 0, sum, map);
21         return count;
22     }
23     
24     int count = 0;
25     public void helper(TreeNode root, int curSum, int target, HashMap<Integer, Integer> map) {
26         // corner case
27         if (root == null) {
28             return;
29         }
30         
31         // normal case
32         curSum += root.val;
33         if (map.containsKey(curSum - target)) {
34             count += map.get(curSum - target);
35         }
36         if (!map.containsKey(curSum)) {
37             map.put(curSum, 1);
38         } else {
39             map.put(curSum, map.get(curSum) + 1);
40         }
41         helper(root.left, curSum, target, map);
42         helper(root.right, curSum, target, map);
43         map.put(curSum, map.get(curSum) - 1);
44     }
45 }

前缀和prefix sum题目总结

LeetCode 题目总结