Maximum Path Sum in Binary Tree in DSA Go - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to define the TreeNode struct with integer value and pointers to left and right children.

DSA Go

type TreeNode struct {
    Val   int
    Left  *[1]
    Right *TreeNode
}

Drag options to blanks, or click blank then click option'

ATreeNode

BNode

CTree

DNodeTree

Attempts:

3 left

💡 Hint

Common Mistakes

Using a different struct name for Left or Right pointer.

Forgetting the pointer symbol * before the type.

The TreeNode struct has Left and Right fields that are pointers to TreeNode type.

2fill in blank

medium

Complete the code to return the maximum of two integers a and b.

DSA Go

func max(a, b int) int {
    if a [1] b {
        return a
    }
    return b
}

Drag options to blanks, or click blank then click option'

A>

B<

C==

D<=

Attempts:

3 left

💡 Hint

Common Mistakes

Using '<' instead of '>' causing minimum to be returned.

Using '==' which only checks equality.

To find the maximum, return a if a is greater than b, else return b.

3fill in blank

hard

Fix the error in the recursive function to compute max path sum from a node.

DSA Go

func maxPathSumHelper(root *TreeNode, maxSum *int) int {
    if root == nil {
        return 0
    }
    left := max(0, maxPathSumHelper(root.Left, maxSum))
    right := max(0, maxPathSumHelper(root.Right, maxSum))
    *maxSum = max(*maxSum, root.Val + left + [1])
    return root.Val + max(left, right)
}

Drag options to blanks, or click blank then click option'

Aleft

B0

Croot.Val

Dright

Attempts:

3 left

💡 Hint

Common Mistakes

Adding left twice instead of left and right.

Adding root.Val twice.

The max path sum through the current node includes root.Val plus left and right max sums.

4fill in blank

hard

Fill both blanks to complete the main function that initializes maxSum and calls the helper.

DSA Go

func maxPathSum(root *TreeNode) int {
    maxSum := [1]
    maxPathSumHelper(root, &[2])
    return maxSum
}

Drag options to blanks, or click blank then click option'

Amath.MinInt32

BmaxSum

C0

D-100000

Attempts:

3 left

💡 Hint

Common Mistakes

Initializing maxSum to 0 which fails for all negative nodes.

Passing maxSum instead of its address.

Initialize maxSum to the smallest integer to handle negative values. Pass its address to helper.

5fill in blank

hard

Fill all three blanks to complete the max function and import statement.

DSA Go

import (
    "fmt"
    "[1]"
)

func max(a, b int) int {
    if a [2] b {
        return a
    }
    return [3]
}

func main() {
    fmt.Println(max(10, 20))
}

Drag options to blanks, or click blank then click option'

Amath

B>

Cb

Dfmt

Attempts:

3 left

💡 Hint

Common Mistakes

Importing wrong package.

Using wrong comparison operator.

Returning a instead of b.

Import math package. Use '>' to compare a and b. Return b if a is not greater.

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