LeetCode 437. Path Sum III

Problem Statement

(Source) 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   1Return 3. The paths that sum to 8 are:1.  5 -> 32.  5 -> 2 -> 13. -3 -> 11

Tags: Tree.

Solution

Idea: TODO.

# Definition for a binary tree node.# class TreeNode(object):#     def __init__(self, x):#         self.val = x#         self.left = None#         self.right = Noneclass Solution(object):    def pathSum(self, root, sum):        """        :type root: TreeNode        :type sum: int        :rtype: int        """        prefix_sum = {0 : 1}        return self.helper(root, sum, prefix_sum, 0)    def helper(self, root, target, prefix_sum, cur):        if not root: return 0        total = cur + root.val        res = prefix_sum.get(total - target, 0)        prefix_sum[total] = prefix_sum.get(total, 0) + 1        res += self.helper(root.left, target, prefix_sum, total) + \                self.helper(root.right, target, prefix_sum, total)        prefix_sum[total] -= 1        return res

Complexity Analysis:

• Time Complexity: O(n).
• Space Complexity: ?.