Maximum Path Sum in Binary Tree in DSA Javascript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the Maximum Path Sum in a binary tree?

It is the largest sum of values from any path in the tree. The path can start and end at any nodes, but must follow parent-child connections.

beginner

Why do we use a recursive approach to find the maximum path sum in a binary tree?

Because each node's maximum path sum depends on the maximum sums of its left and right children, recursion helps break down the problem into smaller parts.

intermediate

In the maximum path sum problem, what does the helper function usually return?

It returns the maximum sum of a path starting from the current node and extending down to one child or none, to be used by its parent.

intermediate

How do we update the global maximum path sum during recursion?

At each node, we calculate the sum of the node's value plus the maximum sums from left and right children (if positive). If this sum is greater than the current global max, we update it.

beginner

What is the time complexity of the maximum path sum algorithm in a binary tree?

It is O(n), where n is the number of nodes, because we visit each node once during the recursion.

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

A The sum of values from root to leaf only

B The sum of all node values in the tree

C The largest sum of values along any path between two nodes

D The maximum value of a single node

The maximum path sum is the largest sum along any path connecting two nodes, not necessarily from root to leaf.

In the recursive solution, what do we do if the left or right child's maximum path sum is negative?

A Ignore it by treating it as zero

B Subtract it from the current node's value

C Include it anyway

D Stop recursion

Negative sums reduce the total, so we ignore them by treating negative sums as zero.

What is the role of the global variable in the maximum path sum algorithm?

A To count the number of nodes

B To store the maximum path sum found so far

C To store the current node's value

D To keep track of recursion depth

The global variable keeps track of the highest path sum found during the traversal.

Which traversal method is naturally used in the maximum path sum recursive solution?

A Level-order

B In-order

C Pre-order

D Post-order

Post-order traversal is used because we need results from left and right children before processing the current node.

What is the space complexity of the maximum path sum algorithm in a balanced binary tree?

A O(log n)

B O(1)

C O(n)

D O(n log n)

The space complexity is O(log n) due to the recursion stack in a balanced tree.

Explain how recursion helps find the maximum path sum in a binary tree.

Think about how each node depends on its children.

Describe the steps to update the global maximum path sum during traversal.

Focus on what happens at each node.