DP on Trees Maximum Path Sum in DSA Go - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to return the maximum of two integers.

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 '>' causes the function to return the smaller number.

Using '==' or '!=' does not compare sizes correctly.

The function returns the larger of a and b, so the condition should be 'a > b'.

2fill in blank

medium

Complete the code to update the global maximum path sum if current sum is greater.

DSA Go

if currentSum [1] maxSum {
    maxSum = currentSum
}

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

A<

B>

C==

D<=

Attempts:

3 left

💡 Hint

Common Mistakes

Using '<' causes maxSum to never update correctly.

Using '==' or '<=' does not cover all cases.

We update maxSum only if currentSum is greater than maxSum.

3fill in blank

hard

Fix the error in the recursive function to return the maximum path sum including the current node.

DSA Go

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

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

Amin

Babs

Csum

Dmax

Attempts:

3 left

💡 Hint

Common Mistakes

Using min returns the smaller sum, which is incorrect.

Using sum or abs are not valid functions here.

We return the node's value plus the maximum of left or right path sums to continue the path upwards.

4fill in blank

hard

Fill both blanks to create a map of node values to their maximum path sums and filter nodes with sums greater than 10.

DSA Go

result := map[int]int{}
for _, node := range nodes {
    sum := [1](node)
    if sum [2] 10 {
        result[node.Val] = sum
    }
}

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

AmaxPathSumHelper

B>

C<

DminPathSumHelper

Attempts:

3 left

💡 Hint

Common Mistakes

Using minPathSumHelper is incorrect as it does not exist or is irrelevant.

Using '<' filters sums less than 10, which is wrong.

We compute max path sums using maxPathSumHelper and select sums greater than 10.

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that maps node values to their max path sums if sums are positive.

DSA Go

result := map[int]int{}
for _, node := range nodes {
    sum := [1](node)
    if sum [2] 0 {
        result[[3]] = sum
    }
}

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

AmaxPathSumHelper

B>

Cnode.Val

DminPathSumHelper

Attempts:

3 left

💡 Hint

Common Mistakes

Using minPathSumHelper is incorrect.

Using sum <= 0 filters out positive sums incorrectly.

Using wrong key instead of node.Val.

We use maxPathSumHelper to get sums, check if sum > 0, and map node.Val to sum.

Practice

1. What does the "Maximum Path Sum" in a tree represent in the context of dynamic programming on trees?

easy

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

B. The number of nodes in the longest path of the tree

C. The sum of all node values in the tree

D. The maximum value of a single node in the tree

Solution

1. Step 1: Understand the problem definition

   The maximum path sum is about finding the path between any two nodes that gives the highest sum of node values.

2. Step 2: Differentiate from other sums

   It is not just the sum of all nodes or the longest path length, but the maximum sum along any path.

3. Final Answer:

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

4. Quick Check:

   Maximum path sum = largest sum on any path [OK]

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

Common Mistakes:

• Confusing maximum path sum with longest path length
• Thinking it is sum of all nodes
• Considering only single node values

2. Which of the following Go function signatures is correct for a recursive function that returns the maximum path sum starting from a given tree node?

easy

A. func maxPathSum(node int) int

B. func maxPathSum(node TreeNode) string

C. func maxPathSum(node *TreeNode) (int, error)

D. func maxPathSum(node *TreeNode) int

Solution

1. Step 1: Identify correct parameter type

   The function should accept a pointer to TreeNode to handle nil nodes and avoid copying.

2. Step 2: Identify correct return type

   The function returns an integer representing the maximum path sum, so return type int is correct.

3. Final Answer:

   func maxPathSum(node *TreeNode) int -> Option D

4. Quick Check:

   Pointer input and int output for max sum [OK]

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

Common Mistakes:

• Passing node by value instead of pointer
• Returning string or error instead of int
• Using wrong parameter type like int

3. Given the following Go code snippet for a binary tree node and a function to compute maximum path sum, what is the output printed?

package main

import "fmt"

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

func maxPathSumUtil(node *TreeNode, maxSum *int) int {
    if node == nil {
        return 0
    }
    left := max(0, maxPathSumUtil(node.Left, maxSum))
    right := max(0, maxPathSumUtil(node.Right, maxSum))
    *maxSum = max(*maxSum, left + right + node.Val)
    return max(left, right) + node.Val
}

func maxPathSum(root *TreeNode) int {
    maxSum := -1000000
    maxPathSumUtil(root, &maxSum)
    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. 35

C. 42

D. 20

Solution

1. Step 1: Calculate max path sums for subtrees

   Left subtree: 9 (updates maxSum to 9). Right subtree: 15 (maxSum=15), 7 (no change), at 20: left=15, right=7, *maxSum = max(15, 15+7+20)=42, returns max(15,7)+20=35.

2. Step 2: Compare and update maxSum

   At root (-10): left=max(0,9)=9, right=max(0,35)=35, *maxSum = max(42, 9+35+(-10))=max(42,34)=42.

3. Final Answer:

   42 -> Option C

4. Quick Check:

   Max path sum = 42 [OK]

Hint: Add max(0, child sums) and update global max [OK]

Common Mistakes:

• Not ignoring negative sums by using max(0, ...)
• Adding node values incorrectly
• Confusing max path sum with max root-to-leaf sum

4. The following Go function is intended to compute the maximum path sum in a binary tree. What is the bug causing incorrect results?

func maxPathSumUtil(node *TreeNode, maxSum *int) int {
    if node == nil {
        return 0
    }
    left := maxPathSumUtil(node.Left, maxSum)
    right := maxPathSumUtil(node.Right, maxSum)
    *maxSum = max(*maxSum, left + right + node.Val)
    return max(left, right) + node.Val
}

medium

A. It does not ignore negative sums from children before adding

B. It returns the sum of both children instead of max child sum

C. It does not update maxSum correctly

D. It does not handle nil nodes

Solution

1. Step 1: Check handling of negative child sums

   The function uses left and right sums directly without ignoring negative values, which can reduce the path sum.

2. Step 2: Identify fix by ignoring negatives

   To fix, use max(0, left) and max(0, right) to ignore negative sums before adding to node.Val.

3. Final Answer:

   It does not ignore negative sums from children before adding -> Option A

4. Quick Check:

   Ignore negative child sums for correct max path [OK]

Hint: Always ignore negative child sums with max(0, child) [OK]

Common Mistakes:

• Not using max(0, child) to ignore negatives
• Returning sum of both children instead of max child
• Not updating maxSum properly

5. You are given a binary tree where some nodes have negative values. How would you modify the standard DP on trees maximum path sum algorithm to correctly handle this case and find the maximum path sum?

hard

A. Ignore all negative nodes completely from the tree

B. Use max(0, child sums) to ignore negative paths and update global max with left + right + node.Val

C. Only consider paths from root to leaf nodes

D. Sum all node values regardless of sign and return the total

Solution

1. Step 1: Handle negative child sums carefully

   Use max(0, child sums) to ignore negative paths that reduce the total sum.

2. Step 2: Update global maximum path sum correctly

   Update the global max with the sum of left + right + current node value to consider paths passing through the node.

3. Final Answer:

   Use max(0, child sums) to ignore negative paths and update global max with left + right + node.Val -> Option B

4. Quick Check:

   Ignore negatives, update max with left+right+node [OK]

Hint: Ignore negative child sums, update max with combined path [OK]

Common Mistakes:

• Summing all nodes including negatives blindly
• Considering only root-to-leaf paths
• Removing negative nodes instead of ignoring sums