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

前序遍历，对于每个遍历到的节点进行处理，维护一个变量pre来记录之前路径之和，然后cur为pre加上当前节点值，如果cur等于sum，那么返回结果时要加1，然后对当前节点的左右子节点调用递归函数求解

/**
 * 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 pathSumFrom(root, sum) + pathSum(root.left, sum) +
            pathSum(root.right, sum);
    }
    
    private int pathSumFrom(TreeNode node, int sum) {
        if (node == null) {
            return 0;
        }
        return (node.val == sum ? 1 : 0) +
            pathSumFrom(node.left, sum - node.val) + 
            pathSumFrom(node.right, sum - node.val);
    }
}

用递归和Prefix sum. HashMap to store ( key : the prefix sum, value : how many ways get to this prefix sum) , and whenever reach a node, we check if prefix sum - target exists in hashmap or not, if it does, we added up the ways of prefix sum - target into res.
For instance : in one path we have 1,2,-1,-1,2, then the prefix sum will be: 1, 3, 2, 1, 3, let's say we want to find target sum is 2, then we will have{2}, {1,2,-1}, {2,-1,-1,2} and {2}ways.

/**
 * 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) {
        HashMap preSum = new HashMap<>();
        preSum.put(0, 1);
        return helper(root, 0, sum, preSum);
    }
    
    private int helper(TreeNode node, int currSum, int target,
                      HashMap preSum) {
        if (node == null) {
            return 0;
        }
        currSum += node.val;
        int res = preSum.getOrDefault(currSum - target, 0);
        preSum.put(currSum, preSum.getOrDefault(currSum, 0) + 1);
        res += helper(node.left, currSum, target, preSum) +
            helper(node.right, currSum, target, preSum);
        preSum.put(currSum, preSum.get(currSum) - 1);
        return res;
    }
}