Path Sum II

Given the root of a binary tree and an integer targetSum, return all root-to-leaf paths where the sum of the node values in the path equals targetSum. Each path should be returned as a list of the node values, not node references.

A root-to-leaf path is a path starting from the root and ending at any leaf node. A leaf is a node with no children.

Example 1:

Input: root = [5,4,8,11,null,13,4,7,2,null,null,5,1], targetSum = 22

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

Explanation: There are two paths whose sum equals targetSum:

5 + 4 + 11 + 2 = 22

5 + 8 + 4 + 5 = 22

Example 2:

Input: root = [1,2,3], targetSum = 5

Output: []

Example 3:

Input: root = [1,2], targetSum = 0

Output: []


  • The number of nodes in the tree is in the range [0, 5000].
  • -1000 <= Node.val <= 1000
  • -1000 <= targetSum <= 1000


We wish to fill in the template logic:

  • is_leaf: when node is a leaf in the tree, and there is no remaining left.
  • get_edges: the children of the current node (node.left and node.right).
  • is_valid: an edge (node) is only invalid when it is non-empty (None, null).

In the implementation, we want to check whether node is None first, so that we do not try to get the field of an empty object. On the current node, we calculate the remaining value after adding the current value. Then we check whether the node is a leaf so that path is a root-to-leaf path and whether the remaining value left is 0. If these condition is satisfied, then we have found one solution. If not, we'd have to traverse further until we reach a leaf in the tree (may or may not be a solution).

The below implementation may look different than the template, but essentially one can update and revert path and remaining inside the if-else conditions to gain similarity to the template. We had also left the check of node is None on the outside to accommodate the use of node.val (and to prevent the root being empty).


1def pathSum(self, root: Optional[TreeNode], targetSum: int) -> List[List[int]]:
2    def dfs(node, remaining, path):
3        if (node is None): return
4        path.append(node.val)     # update path
5        remaining -= node.val
6        if node.left is None and node.right is None and remaining == 0: # is_leaf
7            paths.append(path[:])
8        else:     # edges = [node.left, node.right]
9            dfs(node.left, remaining, path)
10            dfs(node.right, remaining, path)
11        path.pop()                # revert path
13    paths = []
14    dfs(root, targetSum, [])
15    return paths

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