0437. Path Sum III

https://leetcode.com/problems/path-sum-iii

Description

Given the root of a binary tree and an integer targetSum, return the number of paths where the sum of the values along the path equals targetSum.

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

Example 1:

**Input:** root = [10,5,-3,3,2,null,11,3,-2,null,1], targetSum = 8
**Output:** 3
**Explanation:** The paths that sum to 8 are shown.

Example 2:

**Input:** root = [5,4,8,11,null,13,4,7,2,null,null,5,1], targetSum = 22
**Output:** 3

Constraints:

• The number of nodes in the tree is in the range [0, 1000].

• -109 <= Node.val <= 109

• -1000 <= targetSum <= 1000

ac1: backtracking + prefix sum

class Solution {
    int num;
    Map<Integer, Integer> map;

    public int pathSum(TreeNode root, int targetSum) {
        num = 0;
        map = new HashMap<>();
        // Important initiation: when prefixSum == targetSum.
        map.put(0, 1);

        process(root, 0, targetSum);

        return num;
    }

    private void process(TreeNode node, int prefixSum, int targetSum) {
        if (node == null) return;

        prefixSum += node.val;
        num += map.getOrDefault(prefixSum - targetSum, 0);

        map.put(prefixSum, map.getOrDefault(prefixSum, 0) + 1);

        process(node.left, prefixSum, targetSum);
        process(node.right, prefixSum, targetSum);

        map.put(prefixSum, map.getOrDefault(prefixSum, 0) - 1);
    }
}

// Backtracking for tree traversal + prefixSum to calculate sub-path sum.