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

Practice - 5 Tasks

1fill in blank

easy

Complete the code to define the TreeNode class with a value property.

DSA Typescript

class TreeNode {
  val: number;
  left: TreeNode | null;
  right: TreeNode | null;
  constructor(val: number) {
    this.val = [1];
    this.left = null;
    this.right = null;
  }
}

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

Aval

Bvalue

CnodeVal

Dnum

Attempts:

3 left

💡 Hint

Common Mistakes

Using a different variable name than the constructor parameter.

Forgetting to assign the value to 'this.val'.

The constructor parameter is named 'val', so we assign 'this.val = val;' to store the node's value.

2fill in blank

medium

Complete the code to return the maximum path sum starting from the current node and going down.

DSA Typescript

function maxGain(node: TreeNode | null): number {
  if (node === null) return 0;
  const leftGain = Math.max(maxGain(node.left), [1]);
  const rightGain = Math.max(maxGain(node.right), 0);
  return node.val + Math.max(leftGain, rightGain);
}

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

A0

Bnode.val

C-Infinity

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Using node.val instead of 0, which can add negative values.

Using 1 or -Infinity which are not correct for ignoring negatives.

We use 0 to ignore negative gains from child nodes, so we only add positive sums.

3fill in blank

hard

Fix the error in updating the global maximum path sum inside the helper function.

DSA Typescript

let maxSum = -Infinity;
function maxGain(node: TreeNode | null): number {
  if (node === null) return 0;
  const leftGain = Math.max(maxGain(node.left), 0);
  const rightGain = Math.max(maxGain(node.right), 0);
  const priceNewpath = node.val + leftGain + rightGain;
  maxSum = Math.max(maxSum, [1]);
  return node.val + Math.max(leftGain, rightGain);
}

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

AmaxGain(node)

BpriceNewpath

Cnode.val

DleftGain + rightGain

Attempts:

3 left

💡 Hint

Common Mistakes

Using node.val alone, missing child gains.

Using maxGain(node) which causes infinite recursion.

Using leftGain + rightGain without node.val.

We update maxSum with the sum of the current node plus left and right gains, stored in priceNewpath.

4fill in blank

hard

Fill both blanks to complete the main function that returns the maximum path sum in the binary tree.

DSA Typescript

function maxPathSum(root: TreeNode | null): number {
  let maxSum = -Infinity;
  function maxGain(node: TreeNode | null): number {
    if (node === null) return 0;
    const leftGain = Math.max(maxGain(node.left), 0);
    const rightGain = Math.max(maxGain(node.right), 0);
    const priceNewpath = node.val + leftGain + rightGain;
    maxSum = Math.max(maxSum, priceNewpath);
    return node.val + Math.max(leftGain, rightGain);
  }
  maxGain([1]);
  return [2];
}

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

Aroot

BmaxSum

Cnull

DmaxGain

Attempts:

3 left

💡 Hint

Common Mistakes

Passing null to maxGain instead of root.

Returning maxGain instead of maxSum.

Returning root instead of maxSum.

We start recursion from root and return the global maxSum after traversal.

5fill in blank

hard

Fill all three blanks to complete the function that calculates the maximum path sum using a helper and global variable.

DSA Typescript

let maxSum = -Infinity;
function maxPathSum(root: TreeNode | null): number {
  function maxGain(node: TreeNode | null): number {
    if (node === null) return 0;
    const leftGain = Math.max(maxGain(node.left), [1]);
    const rightGain = Math.max(maxGain(node.right), [2]);
    const priceNewpath = node.val + leftGain + rightGain;
    maxSum = Math.max(maxSum, priceNewpath);
    return node.val + Math.max(leftGain, rightGain);
  }
  maxGain([3]);
  return maxSum;
}

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

A0

B-Infinity

Croot

Dnull

Attempts:

3 left

💡 Hint

Common Mistakes

Using -Infinity instead of 0 for gains.

Starting recursion from null.

Not ignoring negative gains.

We ignore negative gains by comparing with 0 and start recursion from root.

Practice

1. What does the "Maximum Path Sum in Binary Tree" problem ask you to find?

easy

A. The highest sum of node values along any path in the tree

B. The longest path length in the tree

C. The sum of all node values in the tree

D. The minimum value node in the tree

Solution

1. Step 1: Understand the problem goal

   The problem asks for the maximum sum of values along any path in the binary tree, where a path can start and end at any nodes.

2. Step 2: Differentiate from other tree sums

   This is different from longest path or total sum; it focuses on the maximum sum achievable on any path.

3. Final Answer:

   The highest sum of node values along any path in the tree -> Option A

4. Quick Check:

   Maximum path sum = highest node value sum [OK]

Hint: Focus on sums along paths, not lengths or totals [OK]

Common Mistakes:

• Confusing path sum with longest path length
• Summing all nodes instead of a path
• Looking for minimum instead of maximum

2. Which TypeScript function signature correctly represents a function to find maximum path sum in a binary tree node?

easy

A. function maxPathSum(root: number[]): number

B. function maxPathSum(root: TreeNode | null): number

C. function maxPathSum(root: string): string

D. function maxPathSum(root: TreeNode): void

Solution

1. Step 1: Identify correct parameter type

   The function should accept a binary tree node or null, so TreeNode | null is correct.

2. Step 2: Identify correct return type

   The function returns a number representing the maximum path sum, so return type is number.

3. Final Answer:

   function maxPathSum(root: TreeNode | null): number -> Option B

4. Quick Check:

   Input: TreeNode or null, Output: number [OK]

Hint: Function input is tree node or null, output is number [OK]

Common Mistakes:

• Using array or string instead of TreeNode
• Returning void instead of number
• Not allowing null as input

3. Given the following TypeScript code, what is the output?

class TreeNode {
  val: number;
  left: TreeNode | null;
  right: TreeNode | null;
  constructor(val: number, left: TreeNode | null = null, right: TreeNode | null = null) {
    this.val = val;
    this.left = left;
    this.right = right;
  }
}

function maxPathSum(root: TreeNode | null): number {
  let maxSum = -Infinity;
  function helper(node: TreeNode | null): number {
    if (!node) return 0;
    const left = Math.max(helper(node.left), 0);
    const right = Math.max(helper(node.right), 0);
    maxSum = Math.max(maxSum, node.val + left + right);
    return node.val + Math.max(left, right);
  }
  helper(root);
  return maxSum;
}

const tree = new TreeNode(1, new TreeNode(2), new TreeNode(3));
console.log(maxPathSum(tree));

medium

A. 3

B. 5

C. 1

D. 6

Solution

1. Step 1: Calculate max path sums for each node

   Node 2 and 3 have no children, so max path sums are 2 and 3. For root 1, left=2, right=3, total=1+2+3=6.

2. Step 2: Determine maximum path sum

   Maximum path sum is max of all nodes' sums: max(2,3,6) = 6.

3. Final Answer:

   6 -> Option D

4. Quick Check:

   Sum(1+2+3) = 6 [OK]

Hint: Sum node + max left + max right, ignore negatives [OK]

Common Mistakes:

• Ignoring zero floor for negative sums
• Returning sum of only root and one child
• Confusing return value with maxSum variable

4. Identify the bug in this TypeScript function for maximum path sum:

function maxPathSum(root: TreeNode | null): number {
  let maxSum = 0;
  function helper(node: TreeNode | null): number {
    if (!node) return 0;
    const left = helper(node.left);
    const right = helper(node.right);
    maxSum = Math.max(maxSum, node.val + left + right);
    return node.val + Math.max(left, right);
  }
  helper(root);
  return maxSum;
}

medium

A. Returns node.val + min(left, right) instead of max

B. helper function missing base case

C. maxSum initialized to 0 instead of -Infinity

D. Does not call helper on root

Solution

1. Step 1: Check maxSum initialization

   maxSum initialized to 0 can cause wrong result if all node values are negative.

2. Step 2: Correct initialization for negative values

   Initialize maxSum to -Infinity to handle negative node values correctly.

3. Final Answer:

   maxSum initialized to 0 instead of -Infinity -> Option C

4. Quick Check:

   maxSum must start at -Infinity for negative nodes [OK]

Hint: Initialize maxSum to -Infinity to handle negatives [OK]

Common Mistakes:

• Starting maxSum at 0 causes wrong max for negative trees
• Forgetting base case returns 0
• Using min instead of max for return

5. Given a binary tree with nodes: root= -10, left=9, right=20, right.left=15, right.right=7, what is the maximum path sum?

hard

A. 42

B. 35

C. 27

D. 20

Solution

1. Step 1: Calculate max path sums for subtrees

   Right subtree max path: 15 + 20 + 7 = 42. Left subtree max is 9. Root is -10.

2. Step 2: Determine overall max path sum

   Max path sum is max of 42 (right subtree path), 9 (left), and paths including root. The max is 42.

3. Final Answer:

   42 -> Option A

4. Quick Check:

   Sum(15+20+7) = 42 [OK]

Hint: Check all subtree sums including root, pick max [OK]

Common Mistakes:

• Ignoring path through both children and root
• Choosing sum of root and one child only
• Not considering negative root value impact