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: []
Constraints:
- The number of nodes in the tree is in the range
[0, 5000]
. -1000 <= Node.val <= 1000
-1000 <= targetSum <= 1000
Solution
We wish to fill in the template logic:
is_leaf
: whennode
is a leaf in the tree, and there is no remaining left.get_edges
: the children of the currentnode
(node.left
andnode.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).
Implementation
def pathSum(self, root: Optional[TreeNode], targetSum: int) -> List[List[int]]:
def dfs(node, remaining, path):
if (node is None): return
path.append(node.val) # update path
remaining -= node.val
if node.left is None and node.right is None and remaining == 0: # is_leaf
paths.append(path[:])
else: # edges = [node.left, node.right]
dfs(node.left, remaining, path)
dfs(node.right, remaining, path)
path.pop() # revert path
paths = []
dfs(root, targetSum, [])
return paths
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