DP on Trees Maximum Path Sum in DSA Typescript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the "Maximum Path Sum" problem in trees?

It is the problem of finding the highest sum of node values along any path in a tree. The path can start and end at any nodes, and must follow parent-child connections.

intermediate

Why do we use Dynamic Programming (DP) on trees for Maximum Path Sum?

Because the problem involves overlapping subproblems on tree nodes, DP helps by storing results of subtrees to avoid repeated calculations and efficiently find the max path sum.

intermediate

In DP on trees for Maximum Path Sum, what does the recursive function usually return?

It returns the maximum path sum starting from the current node and extending down to one of its children, which can be used by its parent to form larger paths.

intermediate

How do we handle negative node values in Maximum Path Sum on trees?

We compare the node's value with sums including children and choose the maximum. If children sums are negative, we ignore them by taking zero instead, ensuring the path sum doesn't decrease.

intermediate

What is the role of a global variable in the DP solution for Maximum Path Sum on trees?

It keeps track of the overall maximum path sum found so far during recursion, since the best path may not pass through the root or be returned by the recursive calls.

In the Maximum Path Sum problem on trees, what does a path consist of?

A Any sequence of nodes connected by edges, without repeating nodes

B Only paths from root to leaf nodes

C Only paths that include the root node

D Only paths that include leaf nodes

A path can start and end at any nodes, as long as nodes are connected and not repeated.

What does the recursive DP function return in Maximum Path Sum on trees?

A Minimum path sum from root to current node

B Maximum path sum including both children and current node

C Sum of all nodes in the subtree

D Maximum path sum starting at current node and extending down one child

It returns the max sum path starting at current node and going down one child to help build larger paths.

How do we treat negative sums from children in Maximum Path Sum DP?

A Add them anyway to the current node value

B Ignore them by taking zero instead

C Subtract them from the current node value

D Stop recursion when negative sums appear

Negative sums reduce the path sum, so we ignore them by considering zero instead.

Why do we need a global variable in the DP solution for Maximum Path Sum?

A To store the maximum path sum found anywhere in the tree

B To count the number of nodes visited

C To store the sum of all nodes in the tree

D To keep track of the current node value

Because the best path may be anywhere in the tree, not just along the returned paths.

Which of these is NOT true about Maximum Path Sum in trees?

A The path can start and end at any nodes

B The path must be simple (no repeated nodes)

C The path must include the root node

D The path follows parent-child connections

The path does not have to include the root node.

Explain how dynamic programming helps solve the Maximum Path Sum problem on trees.

Think about how results from children help solve parent's problem.

Describe how to handle negative node values when finding the Maximum Path Sum in a tree.

Negative sums can reduce total path sum, so consider skipping them.