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
Solutions
1. DFS-递归
两层递归。
# Time Complexity: O(n^2)
# Space Complexity: O(1)
# Definition for a binary tree node.
# class TreeNode:
# def __init__(self, x):
# self.val = x
# self.left = None
# self.right = None
class Solution:
def pathSum(self, root: TreeNode, sum: int) -> int:
if not root:
return 0
res = self.dfs_traverse(root, sum)
res += self.pathSum(root.left, sum)
res += self.pathSum(root.right, sum)
return res
def dfs_traverse(self, root, sum):
if not root:
return 0
res = (sum == root.val)
cur_sum = sum - root.val
res += self.dfs_traverse(root.left, cur_sum)
res += self.dfs_traverse(root.right, cur_sum)
return res
# Runtime: 992 ms, faster than 34.16% of Python3 online submissions for Path Sum III.
# Memory Usage: 15 MB, less than 6.82% of Python3 online submissions for Path Sum III.
2. 用字典记忆化
不是很好理解。
# Time Complexity: O(n)
# Space Complexity: O(n)
# Definition for a binary tree node.
# class TreeNode:
# def __init__(self, x):
# self.val = x
# self.left = None
# self.right = None
class Solution:
def pathSum(self, root: TreeNode, sum: int) -> int:
self.res = 0
memo_sum = collections.defaultdict()
memo_sum[0] = 1
self.dfs(root, sum, 0, memo_sum)
return self.res
def dfs(self, root, sum, cur_sum, memo_sum):
if not root:
return
cur_sum += root.val
diff = cur_sum - sum
# update result and memo
self.res += memo_sum.get(diff, 0)
memo_sum[cur_sum] = memo_sum.get(cur_sum, 0) + 1
self.dfs(root.left, sum, cur_sum, memo_sum)
self.dfs(root.right, sum, cur_sum, memo_sum)
memo_sum[cur_sum] -= 1
# Runtime: 52 ms, faster than 97.83% of Python3 online submissions for Path Sum III.
# Memory Usage: 15.1 MB, less than 6.82% of Python3 online submissions for Path Sum III.