Maximum Path Sum in Binary Tree in DSA C++ - 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 recursion to solve Maximum Path Sum in a binary tree?

Recursion helps explore all paths from each node down to its children, calculating sums and choosing the best path easily by combining results from subtrees.

intermediate

In the Maximum Path Sum problem, why do we ignore negative sums from child paths?

Negative sums reduce the total path sum, so we treat them as zero to avoid lowering the maximum sum.

intermediate

What does the helper function return in the Maximum Path Sum algorithm?

It returns the maximum sum of a path starting from the current node and extending downwards to one child, used to build larger paths.

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 best left and right child paths. If this sum is greater than the current global max, we update it.

What does the Maximum Path Sum in a binary tree represent?

A The sum of all node values in the tree

B The largest sum of values along any path in the tree

C The longest path length in the tree

D The smallest value in the tree

The maximum path sum is the largest sum of node values along any path in the tree.

Why do we treat negative child path sums as zero in the algorithm?

A Because negative sums increase the total path sum

B Because negative sums are not allowed in trees

C Because negative sums reduce the total path sum

D Because zero is always greater than any sum

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

What does the helper function return in the Maximum Path Sum algorithm?

A Minimum value in the subtree

B Maximum sum of the entire tree

C Number of nodes in the path

D Maximum sum of a path starting at the current node and going down one child

The helper returns the max sum path starting at the current node going down one child.

How is the global maximum path sum updated during recursion?

A By comparing sum of node value plus left and right child paths

B By adding all node values in the tree

C By comparing current node value only

D By counting the number of nodes

We update global max by comparing sum of node value plus best left and right child paths.

Can the maximum path in the tree start and end at any nodes?

A Yes, it can start and end anywhere following parent-child links

B No, it must start at the root

C No, it must end at a leaf node

D No, it must be a path from leftmost to rightmost node

The path can start and end at any nodes as long as it follows parent-child connections.

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

Think about how you visit each node and use results from children.

Describe the role of ignoring negative sums in the Maximum Path Sum algorithm.

Why would adding a negative number hurt your total?