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

Recall & Review

beginner

What is the Maximum Path Sum in a binary tree?

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

beginner

In the Maximum Path Sum problem, must the path go through the root?

No. The path can start and end at any nodes in the tree, not necessarily including the root.

intermediate

Why do we use a helper function that returns the maximum gain from a node in the Maximum Path Sum problem?

Because we want to find the best path sum that can be extended upwards to the parent. The helper returns the maximum sum of a path starting at the current node and going down one side.

intermediate

What does it mean if the maximum gain from a child node is negative in the Maximum Path Sum problem?

We ignore that child's path by taking zero instead, because adding a negative sum would reduce the total path sum.

intermediate

How do we update the global maximum path sum during recursion in the Maximum Path Sum problem?

At each node, we consider the sum of the node's value plus maximum gains from left and right children. If this sum is greater than the current global maximum, we update it.

In the Maximum Path Sum problem, what does the helper function return?

A Maximum path sum including both left and right children

B Sum of all nodes in the tree

C Minimum path sum from root to leaf

D Maximum gain from the current node to one child path

The helper returns the maximum gain from the current node to one child path, which can be extended upwards.

If a child node's maximum gain is negative, what should we do?

A Add it to the path sum

B Ignore it by taking zero

C Subtract it from the path sum

D Stop recursion

Negative gains reduce the path sum, so we ignore them by taking zero.

Can the maximum path sum path pass through the root node?

A Sometimes, if it gives the maximum sum

B Yes, always

C No, never

D Only if the tree is balanced

The path can pass through the root if it yields the maximum sum, but it is not required.

What is the time complexity of the Maximum Path Sum algorithm using recursion?

A O(n)

B O(n log n)

C O(n^2)

D O(log n)

Each node is visited once, so the time complexity is O(n), where n is the number of nodes.

What does the global variable track in the Maximum Path Sum problem?

A Number of nodes visited

B Maximum gain from a single child

C Maximum path sum found so far

D Minimum path sum

The global variable keeps track of the maximum path sum found anywhere in the tree.

Explain how recursion helps find the Maximum Path Sum in a binary tree.

Think about how each node contributes to the path sum and how you combine left and right child results.

Describe the difference between the maximum gain returned by the helper and the global maximum path sum.

One is local to a node's single path, the other is overall best path.