algo437.py

'''
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

'''
# Definition for a binary tree node.
# class TreeNode(object):
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution(object):
    
    def pathSum(self, root, sum):
        """
        :type root: TreeNode
        :type sum: int
        :rtype: int
        """
        if root == None:
            return 0
        return self.findSumPaths(root,sum)+self.pathSum(root.left,sum)+self.pathSum(root.right,sum)
        
    def findSumPaths(self,node,sum):
        if node==None:
            return 0
        return 1 + self.findSumPaths(node.left,sum-node.val) + self.findSumPaths(node.right,sum-node.val) if node.val==sum else 0 + self.findSumPaths(node.left,sum-node.val) + self.findSumPaths(node.right,sum-node.val)