#59 Hard Time O(n) Space O(n) Animated

Binary Tree Maximum Path Sum

Find the maximum path sum in a binary tree.

LeetCode ↗

Tutor Mode Build the mental model before you memorize the code.

1 Predict
2 Trace
3 Explain
4 Implement

Pattern Tree traversal with recursive contracts

Ask each subtree for exactly the information its parent needs, then combine the two answers.

Approach: DFS (Post-order)

Click play to start

Step 0 / 0

Press play to start the visualization.

1×

Core Insight

Ask each subtree for exactly the information its parent needs, then combine the two answers.

Common Pitfall

Define the base case before combining left and right subtree results.

Description

Find the maximum path sum in a binary tree.

Constraints

Time Complexity: O(n)
Space Complexity: O(n)

Solution — DFS (Post-order)

TimeO(n) SpaceO(n)

Implementation Plan

Translate the invariant into these small, testable moves.

Define what one recursive call returns.
Handle an empty node.
Recurse into children.
Combine the child results at the current node.

def maxPathSum(root):
    res = [root.val]
    
    def dfs(node):
        if not node:
            return 0
            
        leftMax = max(dfs(node.left), 0)
        rightMax = max(dfs(node.right), 0)
        
        # max path WITH split
        res[0] = max(res[0], node.val + leftMax + rightMax)
        
        # return max path WITHOUT split
        return node.val + max(leftMax, rightMax)
        
    dfs(root)
    return res[0]

Construct Binary Tree from Preorder and Inorder Traversal

Serialize and Deserialize Binary Tree

Binary Tree Maximum Path Sum

Steps

Description

Constraints

Tags

Solution — DFS (Post-order)