Maximum Path Sum in Binary Tree in DSA Go - Build from Scratch

Maximum Path Sum in Binary Tree

📖 Scenario: You are working on a program that analyzes a binary tree representing a network of connected nodes. Each node has a value that can be positive or negative. Your task is to find the maximum sum of values along any path in the tree. A path can start and end at any node, but it must follow parent-child connections.

🎯 Goal: Build a Go program that creates a binary tree, sets a variable to track the maximum path sum, implements a recursive function to find the maximum path sum, and prints the final maximum path sum.

📋 What You'll Learn

Create a binary tree with the exact structure and values given

Create a variable called maxSum to track the maximum path sum

Write a recursive function called maxPathSumHelper that calculates the maximum path sum

Print the value of maxSum after processing the tree

💡 Why This Matters

🌍 Real World

Finding maximum path sums in trees is useful in network analysis, game development, and decision-making systems where the best route or combination needs to be found.

💼 Career

Understanding tree traversal and recursive algorithms is essential for software engineering roles, especially those involving data structures, algorithms, and system design.

1

Create the Binary Tree Structure

Create a struct type called TreeNode with fields Val int, Left *TreeNode, and Right *TreeNode. Then create the binary tree with root node value 1, left child 2, and right child 3. Assign the left child of node 2 to 4 and right child to 5. Assign the right child of node 3 to 6.

DSA Go

// Define TreeNode struct and create the binary tree as described
// Your code here

Hint

Define the TreeNode struct first. Then create nodes and link them as left and right children exactly as described.

2

Add a Variable to Track Maximum Path Sum

Inside the main function, create a variable called maxSum of type int and initialize it to the smallest possible integer value int(^uint(0) >> 1) * -1 - 1.

DSA Go

package main

import "fmt"

type TreeNode struct {
    Val   int
    Left  *TreeNode
    Right *TreeNode
}

func main() {
    root := &TreeNode{Val: 1}
    root.Left = &TreeNode{Val: 2}
    root.Right = &TreeNode{Val: 3}
    root.Left.Left = &TreeNode{Val: 4}
    root.Left.Right = &TreeNode{Val: 5}
    root.Right.Right = &TreeNode{Val: 6}

    // Create maxSum variable initialized to smallest int
    // Your code here
}

Hint

Use bitwise operations to get the smallest int value in Go and assign it to maxSum.

3

Implement Recursive Function to Find Maximum Path Sum

Write a recursive function called maxPathSumHelper that takes a pointer to TreeNode and a pointer to int called maxSum. The function returns an int. It should calculate the maximum path sum starting from the current node and update *maxSum if a larger path sum is found. Use the logic: calculate left and right max sums recursively, ignore negative sums by comparing with zero, update *maxSum with the sum of node value plus left and right max sums, and return the node value plus the maximum of left or right max sums.

DSA Go

package main

import "fmt"

type TreeNode struct {
    Val   int
    Left  *TreeNode
    Right *TreeNode
}

func maxPathSumHelper(node *TreeNode, maxSum *int) int {
    // Your code here
}

func main() {
    root := &TreeNode{Val: 1}
    root.Left = &TreeNode{Val: 2}
    root.Right = &TreeNode{Val: 3}
    root.Left.Left = &TreeNode{Val: 4}
    root.Left.Right = &TreeNode{Val: 5}
    root.Right.Right = &TreeNode{Val: 6}

    maxSum := int(^uint(0) >> 1) * -1 - 1

    // Call maxPathSumHelper here
    // Your code here
}

Hint

Use recursion to find max sums from left and right children. Ignore negative sums by comparing with zero. Update *maxSum if current path sum is larger. Return max path sum including current node and one child.

4

Print the Maximum Path Sum

In the main function, after calling maxPathSumHelper, print the value of maxSum using fmt.Println(maxSum).

DSA Go

package main

import "fmt"

type TreeNode struct {
    Val   int
    Left  *TreeNode
    Right *TreeNode
}

func maxPathSumHelper(node *TreeNode, maxSum *int) int {
    if node == nil {
        return 0
    }

    leftMax := max(0, maxPathSumHelper(node.Left, maxSum))
    rightMax := max(0, maxPathSumHelper(node.Right, maxSum))

    currentSum := node.Val + leftMax + rightMax
    if currentSum > *maxSum {
        *maxSum = currentSum
    }

    return node.Val + max(leftMax, rightMax)
}

func max(a, b int) int {
    if a > b {
        return a
    }
    return b
}

func main() {
    root := &TreeNode{Val: 1}
    root.Left = &TreeNode{Val: 2}
    root.Right = &TreeNode{Val: 3}
    root.Left.Left = &TreeNode{Val: 4}
    root.Left.Right = &TreeNode{Val: 5}
    root.Right.Right = &TreeNode{Val: 6}

    maxSum := int(^uint(0) >> 1) * -1 - 1

    maxPathSumHelper(root, &maxSum)

    // Print maxSum
    // Your code here
}

Hint

Use fmt.Println(maxSum) to print the maximum path sum after the recursive call.

Practice

1. What does the term Maximum Path Sum in a binary tree mean?

easy

A. The largest sum of values along any path between two nodes in the tree

B. The sum of all node values in the tree

C. The sum of values from root to the leftmost leaf

D. The smallest sum of values along any path in the tree

Solution

1. Step 1: Understand the path definition

   The path can start and end at any two nodes, not necessarily root or leaf.

2. Step 2: Identify maximum sum meaning

   We look for the path with the highest total sum of node values.

3. Final Answer:

   The largest sum of values along any path between two nodes in the tree -> Option A

4. Quick Check:

   Maximum path sum means highest sum between any two nodes [OK]

Hint: Maximum path sum is any path with highest total node values [OK]

Common Mistakes:

• Thinking path must start at root
• Confusing maximum path sum with total tree sum
• Assuming path must end at leaf

2. Which of the following Go function signatures is correct for a function that calculates maximum path sum in a binary tree node defined as type TreeNode struct { Val int; Left, Right *TreeNode }?

easy

A. func maxPathSum(root *TreeNode) int

B. func maxPathSum(root TreeNode) int

C. func maxPathSum(root *TreeNode) *int

D. func maxPathSum(root *TreeNode) string

Solution

1. Step 1: Check parameter type

   Function should accept pointer to TreeNode to avoid copying the whole tree.

2. Step 2: Check return type

   Maximum path sum is an integer value, so return type should be int.

3. Final Answer:

   func maxPathSum(root *TreeNode) int -> Option A

4. Quick Check:

   Pointer input and int output for max path sum [OK]

Hint: Use pointer receiver and int return for tree max path sum [OK]

Common Mistakes:

• Passing TreeNode by value causing copies
• Returning pointer instead of int
• Returning string instead of int

3. Given the following Go code snippet, what is the printed output?

type TreeNode struct {
    Val   int
    Left  *TreeNode
    Right *TreeNode
}

func maxPathSum(root *TreeNode) int {
    maxSum := -1 << 31
    var maxGain func(node *TreeNode) int
    maxGain = func(node *TreeNode) int {
        if node == nil {
            return 0
        }
        leftGain := max(0, maxGain(node.Left))
        rightGain := max(0, maxGain(node.Right))
        priceNewPath := node.Val + leftGain + rightGain
        if priceNewPath > maxSum {
            maxSum = priceNewPath
        }
        return node.Val + max(leftGain, rightGain)
    }
    maxGain(root)
    return maxSum
}

func max(a, b int) int {
    if a > b {
        return a
    }
    return b
}

func main() {
    root := &TreeNode{Val: -10}
    root.Left = &TreeNode{Val: 9}
    root.Right = &TreeNode{Val: 20}
    root.Right.Left = &TreeNode{Val: 15}
    root.Right.Right = &TreeNode{Val: 7}
    fmt.Println(maxPathSum(root))
}

medium

A. 27

B. 42

C. 35

D. 20

Solution

1. Step 1: Trace maxGain for each node

   Calculate max gain from left and right subtree ignoring negatives: - Node 9: maxGain = 9 - Node 15: maxGain = 15 - Node 7: maxGain = 7 - Node 20: maxGain = 20 + max(15,7) = 35 - Root -10: maxGain = -10 + max(9,35) = 25 Check maxSum updates: - At node 9: maxSum = 9 - At node 15: maxSum = 15 - At node 7: maxSum = 15 (unchanged) - At node 20: priceNewPath = 20 + 15 + 7 = 42, maxSum = 42 - At root: priceNewPath = -10 + 9 + 35 = 34 (maxSum stays 42)

2. Step 2: Return maxSum

   maxSum is 42 after full traversal.

3. Final Answer:

   42 -> Option B

4. Quick Check:

   Max path sum = 42 [OK]

Hint: Add node value plus max gains from left and right, track max sum [OK]

Common Mistakes:

• Not ignoring negative gains
• Returning max gain instead of max path sum
• Miscomputing path sums including negative nodes

4. The following Go function attempts to compute the maximum path sum in a binary tree but has a bug. What is the bug?

func maxPathSum(root *TreeNode) int {
    maxSum := -1 << 31
    var maxGain func(node *TreeNode) int
    maxGain = func(node *TreeNode) int {
        if node == nil {
            return 0
        }
        leftGain := maxGain(node.Left)
        rightGain := maxGain(node.Right)
        priceNewPath := node.Val + leftGain + rightGain
        if priceNewPath > maxSum {
            maxSum = priceNewPath
        }
        return node.Val + max(leftGain, rightGain)
    }
    maxGain(root)
    return maxSum
}

medium

A. It does not handle nil root

B. It returns maxSum before traversal

C. It does not ignore negative gains from left or right subtrees

D. It uses incorrect initial value for maxSum

Solution

1. Step 1: Analyze gain calculation

   The function uses leftGain and rightGain directly without ignoring negative values, which can reduce the path sum.

2. Step 2: Identify fix

   To fix, use max(0, leftGain) and max(0, rightGain) to ignore negative gains.

3. Final Answer:

   It does not ignore negative gains from left or right subtrees -> Option C

4. Quick Check:

   Negative gains must be ignored for correct max path sum [OK]

Hint: Always ignore negative subtree sums by max(0, gain) [OK]

Common Mistakes:

• Not ignoring negative subtree sums
• Wrong initial maxSum value
• Returning before traversal completes

5. You want to find the maximum path sum in a binary tree where some nodes have negative values. Which approach correctly handles this scenario? A) Use a recursive function that returns the maximum gain from each node, ignoring negative gains by taking max(0, gain), and update a global max sum including both left and right gains plus node value. B) Use a recursive function that sums all node values and returns the total. C) Use a breadth-first search to find the maximum node value and return it. D) Use a recursive function that only considers paths from root to leaf nodes.

hard

A. Consider only root-to-leaf paths recursively

B. Sum all node values recursively and return total

C. Find maximum node value using BFS and return it

D. Use recursion with max(0, gain) and update max sum including both children

Solution

1. Step 1: Understand negative values impact

   Negative node values can reduce path sums, so ignoring negative gains is necessary.

2. Step 2: Choose correct approach

   Use recursion with max(0, gain) and update max sum including both children uses recursion with max(0, gain) to ignore negative paths and updates max sum considering both left and right children plus current node, which correctly finds maximum path sum anywhere in the tree.

3. Final Answer:

   Use recursion with max(0, gain) and update max sum including both children -> Option D

4. Quick Check:

   Ignore negative gains and consider all paths for max sum [OK]

Hint: Ignore negative gains and consider all paths recursively [OK]

Common Mistakes:

• Summing all nodes ignoring path constraints
• Only considering root-to-leaf paths
• Returning max node value instead of path sum