题目描述:
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
题意是在树中找出满足和为sum的路径,要求路径的方向必须是由高到低。
解题思路:
采用分治Divide And Conquer的方式,将原问题分成子问题来解决。原问题:找出以root节点为根节点的树的和为sum的路径;子问题有三个:找出包含root节点的和为sum的路径、找出以root.left为根节点的子树的和为sum的路径、找出以root.right为根节点的子树的和为sum的路径。递归解决即可。
Python代码:
# Definition for a binary tree node.
# class TreeNode:
# def __init__(self, x):
# self.val = x
# self.left = None
# self.right = None
class Solution:
def __init__(self):
global res
res = 0
def pathSum(self, root: 'TreeNode', sum: 'int') -> 'int':
if not root:
return 0
self.traval(root, sum)
self.pathSum(root.left, sum)
self.pathSum(root.right, sum)
return res
def traval(self, root, sum):
global res
if not root:
return
if root.val == sum:
res += 1
sum -= root.val
self.traval(root.left, sum)
self.traval(root.right, sum)