[LC] 113. Path Sum II

Given a binary tree and a sum, find all root-to-leaf paths where each path's sum equals the given sum.

Note: A leaf is a node with no children.

Example:

Given the below binary tree and sum = 22,

      5
     / \
    4   8
   /   / \
  11  13  4
 /  \    / \
7    2  5   1

Return:

[
   [5,4,11,2],
   [5,8,4,5]
]

Time: O(N)
Space: O(Height)

# 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) -> List[List[int]]:
        res, lst = [], []
        self.helper(root, sum, res, lst)
        return res
    
    def helper(self, root, sum, res, lst):
        if root is None:
            return
        if root.left is None and root.right is None:
            if sum == root.val:
                lst.append(root.val)
                res.append(list(lst))
                lst.pop()
                return
        lst.append(root.val)
        left = self.helper(root.left, sum - root.val, res, lst)
        right = self.helper(root.right, sum - root.val, res, lst)
        lst.pop()