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

Practice - 5 Tasks

1fill in blank

easy

Complete the code to define the TreeNode class constructor.

DSA Python

class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = [1]
        self.left = left
        self.right = right

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

Aval

Bleft

Cright

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Assigning self.val to left or right instead of val.

The constructor sets the node's value to the given val parameter.

2fill in blank

medium

Complete the code to update the global maximum path sum inside the helper function.

DSA Python

def maxPathSum(root):
    max_sum = float('-inf')
    def helper(node):
        nonlocal max_sum
        if not node:
            return 0
        left = max(helper(node.left), 0)
        right = max(helper(node.right), 0)
        max_sum = max(max_sum, node.val + left + [1])
        return node.val + max(left, right)
    helper(root)
    return max_sum

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

Aleft

Bnode.val

Cmax_sum

Dright

Attempts:

3 left

💡 Hint

Common Mistakes

Adding node.val twice or using max_sum in the sum incorrectly.

The maximum path sum at the current node includes the node's value plus the left and right path sums. Here, we add right to node.val + left.

3fill in blank

hard

Fix the error in the return statement of the helper function to correctly return the max path sum for one side.

DSA Python

def helper(node):
    if not node:
        return 0
    left = max(helper(node.left), 0)
    right = max(helper(node.right), 0)
    max_sum = max(max_sum, node.val + left + right)
    return node.val + [1]

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

Amax(left, right)

Bleft + right

Cmin(left, right)

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Returning sum of left and right which is invalid for path continuation.

The helper returns the node's value plus the maximum of left or right path sums because the path can only continue in one direction.

4fill in blank

hard

Fill both blanks to complete the maxPathSum function that uses a helper to find the maximum path sum.

DSA Python

def maxPathSum(root):
    max_sum = float('-inf')
    def helper(node):
        nonlocal max_sum
        if not node:
            return 0
        left = max(helper(node.left), 0)
        right = max(helper(node.right), 0)
        max_sum = max(max_sum, node.val + left + right)
        return node.val + [1]
    return [2]

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

Amax(left, right)

Bmin(left, right)

Chelper(root)

Dmax_sum

Attempts:

3 left

💡 Hint

Common Mistakes

Returning helper(root) instead of max_sum.

Returning min(left, right) instead of max(left, right).

The helper returns node.val plus the maximum of left or right path sums. The main function returns the global max_sum found.

5fill in blank

hard

Fill all three blanks to complete the helper function that calculates max path sums and updates max_sum.

DSA Python

def maxPathSum(root):
    max_sum = float('-inf')
    def helper(node):
        nonlocal max_sum
        if not node:
            return 0
        left = max(helper(node.left), 0)
        right = max(helper(node.right), 0)
        max_sum = max(max_sum, [1])
        return [2] + max(left, right)
    return [3]

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

Anode.val + left + right

Bnode.val

Cmax_sum

Dhelper(root)

Attempts:

3 left

💡 Hint

Common Mistakes

Returning helper(root) instead of max_sum.

Incorrect max_sum update expression.

Update max_sum with node.val plus left and right sums. Return node.val plus max of left or right. Finally, return max_sum.

Practice

1. What does the "maximum path sum" in a binary tree represent?

easy

A. The sum of values from root to the deepest leaf

B. The largest sum of values along any path between two nodes

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

D. The sum of all node values in the tree

Solution

1. Step 1: Understand the path definition

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

2. Step 2: Define maximum path sum

   It is the highest sum of node values along any such path in the tree.

3. Final Answer:

   The largest sum of values along any path between two nodes -> Option B

4. Quick Check:

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

Hint: Remember path can start/end anywhere, not just root or leaf [OK]

Common Mistakes:

• Thinking path must start at root
• Confusing max node value with max path sum
• Summing all nodes instead of a path

2. Which of the following Python function signatures is correct for a recursive helper to find maximum path sum in a binary tree node root?

easy

A. def maxPathSum(root: TreeNode) -> int:

B. def maxPathSum(root: int) -> TreeNode:

C. def maxPathSum(root: TreeNode) -> TreeNode:

D. def maxPathSum(root: int) -> int:

Solution

1. Step 1: Identify input type

   The function takes a TreeNode object representing the root of the tree.

2. Step 2: Identify return type

   The function returns an integer representing the maximum path sum.

3. Final Answer:

   def maxPathSum(root: TreeNode) -> int: -> Option A

4. Quick Check:

   Input=TreeNode, Output=int [OK]

Hint: Input is tree node, output is integer sum [OK]

Common Mistakes:

• Using int as input instead of TreeNode
• Returning TreeNode instead of int
• Mixing input and output types

3. Given the following binary tree and code snippet, what is the output?

class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

def maxPathSum(root):
    max_sum = float('-inf')
    def helper(node):
        nonlocal max_sum
        if not node:
            return 0
        left = max(helper(node.left), 0)
        right = max(helper(node.right), 0)
        max_sum = max(max_sum, node.val + left + right)
        return node.val + max(left, right)
    helper(root)
    return max_sum

root = TreeNode(-10, TreeNode(9), TreeNode(20, TreeNode(15), TreeNode(7)))
print(maxPathSum(root))

medium

A. 35

B. 27

C. 42

D. 20

Solution

1. Step 1: Trace left and right subtree sums

   Left subtree max path sum is 9, right subtree max path sum is 20 + 15 + 7 = 42.

2. Step 2: Calculate max path sum including root

   Root (-10) + left (9) + right (20 + 15 + 7) = -10 + 9 + 22 = 21, but max path sum is updated at right subtree as 42.

3. Step 3: Identify maximum path sum

   The maximum path sum is 42, but the path that includes root is less than 42.

4. Final Answer:

   42 -> Option C

5. Quick Check:

   Max path sum = 42 [OK]

Hint: Add max(0, left/right) to avoid negative sums [OK]

Common Mistakes:

• Including negative sums from subtrees
• Confusing return value with max_sum
• Not using nonlocal for max_sum

4. Find the error in the following code snippet for maximum path sum in a binary tree:

def maxPathSum(root):
    max_sum = float('-inf')
    def helper(node):
        if not node:
            return 0
        left = helper(node.left)
        right = helper(node.right)
        max_sum = max(max_sum, node.val + left + right)
        return node.val + max(left, right)
    helper(root)
    return max_sum

medium

A. max_sum should be declared as nonlocal inside helper

B. Return statement should be outside helper function

C. Base case should return None instead of 0

D. max_sum should be initialized to 0 instead of -inf

Solution

1. Step 1: Identify variable scope issue

   max_sum is assigned inside helper but declared outside, so Python treats it as local inside helper.

2. Step 2: Fix scope with nonlocal keyword

   Adding 'nonlocal max_sum' inside helper allows updating the outer max_sum variable.

3. Final Answer:

   max_sum should be declared as nonlocal inside helper -> Option A

4. Quick Check:

   Use nonlocal to update outer variable [OK]

Hint: Use nonlocal to modify outer variables inside nested functions [OK]

Common Mistakes:

• Forgetting nonlocal causes UnboundLocalError
• Changing base case return value incorrectly
• Initializing max_sum to 0 misses negative sums

5. You want to find the maximum path sum in a binary tree where some nodes have negative values. Which approach correctly handles negative values to find the maximum path sum?

hard

A. Only consider paths starting at root to leaf

B. Add all child sums regardless of sign to current node value

C. Replace negative node values with zero before calculation

D. Ignore negative child sums by taking max(child_sum, 0) before adding to current node

Solution

1. Step 1: Understand impact of negative values

   Negative sums reduce total path sum, so ignoring them improves max sum.

2. Step 2: Use max(child_sum, 0) to ignore negatives

   This ensures only positive contributions add to current node's path sum.

3. Step 3: Avoid altering original node values

   Replacing negatives with zero changes tree data and is incorrect.

4. Final Answer:

   Ignore negative child sums by taking max(child_sum, 0) before adding to current node -> Option D

5. Quick Check:

   Ignore negatives with max(child_sum, 0) [OK]

Hint: Use max(child_sum, 0) to skip negative paths [OK]

Common Mistakes:

• Adding negative sums reduces max path sum
• Modifying node values instead of sums
• Restricting paths to root-leaf only