How do you solve Path Sum III on LeetCode?

Path Sum III (LeetCode #437) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Paths can start and end at any node, not just root or leaves.

What is the brute force solution for Path Sum III?

The brute force approach for Path Sum III is Brute Force, with O(n²) time complexity and O(1) space complexity. In this approach, we explore every possible path in the binary tree and calculate the sum of the node values along each path. If the sum matches the targetSum, we count that path. This method is straightforward but inefficient for larger trees. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Path Sum III?

Path Sum III uses the following concepts: Tree, Depth-First Search, Binary Tree. The recommended patterns to study are: Hash Map, Depth-First Search.

What are the interview tips for Path Sum III?

Think about how you can reduce redundant calculations. Use data structures like HashMap to keep track of counts efficiently. Practice writing recursive DFS functions, as they are common in tree problems.

What are common mistakes when solving Path Sum III?

Not considering paths that start from nodes other than the root. Forgetting to backtrack the cumulative sum count in the HashMap.

#437

Path Sum III

Medium

TreeDepth-First SearchBinary TreeHash MapDepth-First Search

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

This approach uses a HashMap to store the cumulative sums encountered so far. By keeping track of how many times each cumulative sum has been seen, we can efficiently determine how many paths sum to targetSum as we traverse the tree.

⚙️

Algorithm

5 steps

1Step 1: Initialize a HashMap to store the cumulative sum counts and set the initial cumulative sum to zero.
2Step 2: Perform a depth-first search (DFS) through the tree, updating the cumulative sum at each node.
3Step 3: For each node, check if (cumulative sum - targetSum) exists in the HashMap. If it does, it means there are paths that sum to targetSum.
4Step 4: Update the HashMap with the current cumulative sum count before moving to the next node.
5Step 5: After visiting the node's children, decrement the count of the current cumulative sum in the HashMap to backtrack.

solution.py24 lines

1# Full working Python code
2class TreeNode:
3    def __init__(self, val=0, left=None, right=None):
4        self.val = val
5        self.left = left
6        self.right = right
7
8class Solution:
9    def pathSum(self, root: TreeNode, targetSum: int) -> int:
10        self.count = 0
11        self.cumulative_sum_counts = {0: 1}
12        self.dfs(root, 0, targetSum)
13        return self.count
14
15    def dfs(self, node: TreeNode, current_sum: int, targetSum: int):
16        if not node:
17            return
18        current_sum += node.val
19        self.count += self.cumulative_sum_counts.get(current_sum - targetSum, 0)
20        self.cumulative_sum_counts[current_sum] = self.cumulative_sum_counts.get(current_sum, 0) + 1
21        self.dfs(node.left, current_sum, targetSum)
22        self.dfs(node.right, current_sum, targetSum)
23        self.cumulative_sum_counts[current_sum] -= 1
24

ℹ

Complexity note: The time complexity is O(n) because we visit each node once, and the space complexity is O(n) due to the storage of cumulative sums in the HashMap.

1Paths can start and end at any node, not just root or leaves.
2Using cumulative sums allows us to efficiently track paths without recalculating sums repeatedly.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.