437 - Path Sum III

2020/04/26

leetcode

Problem

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

Solution

Important:

Three parts in recursion:

  1. the path sum of the left child
  2. the path sum of the right child
  3. the path sum only from the root
class Solution:
    def pathSum(self, root, sum):
        if not root:
            return 0

        return self.pathSum(root.left, sum) + self.pathSum(
            root.right, sum) + self.pathSumFrom(root, sum)

    def pathSumFrom(self, root, sum):

        if not root:
            return 0

        if root.val == sum:
            return 1 + self.pathSumFrom(root.left, 0) + self.pathSumFrom(
                root.right, 0)
        else:
            return self.pathSumFrom(root.left,
                                    sum - root.val) + self.pathSumFrom(
                                        root.right, sum - root.val)