DP on Trees Diameter of Tree in DSA Typescript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the diameter of a tree?

The diameter of a tree is the longest path between any two nodes in the tree. This path may or may not pass through the root.

intermediate

Why do we use dynamic programming (DP) on trees to find the diameter?

DP helps by storing results of subproblems (like longest paths from children) to avoid repeated calculations, making the diameter calculation efficient.

beginner

In the DP approach for tree diameter, what does the 'height' of a node represent?

The height of a node is the length of the longest path from that node down to a leaf node.

intermediate

How do you update the diameter while doing a DFS traversal in the DP approach?

At each node, calculate the sum of the two largest heights from its children. Update the diameter if this sum is greater than the current diameter.

beginner

What is the time complexity of finding the diameter of a tree using DP?

The time complexity is O(N), where N is the number of nodes, because each node is visited once during DFS.

What does the diameter of a tree represent?

A Shortest path between root and leaf

B Longest path between any two nodes

C Number of nodes in the tree

D Height of the root node

The diameter is the longest path between any two nodes in the tree.

In DP on trees, what is the 'height' of a node?

A Longest path from the node to a leaf

B Number of children of the node

C Distance from root to the node

D Number of nodes in the subtree

Height is the longest path from the node down to any leaf node.

How do you find the diameter during DFS traversal?

A Maximum height of a single child

B Sum of the two smallest heights of children

C Sum of the two largest heights of children

D Number of children of the node

Diameter is updated by summing the two largest heights from children at each node.

What is the time complexity of the DP approach to find tree diameter?

A O(N^2)

B O(log N)

C O(1)

D O(N)

Each node is visited once, so the time complexity is O(N).

Why is DP useful in finding the diameter of a tree?

A It avoids repeated calculations by storing subproblem results

B It sorts the nodes

C It removes cycles from the tree

D It increases the height of the tree

DP stores results like heights of subtrees to avoid recalculating them.

Explain how to find the diameter of a tree using dynamic programming and DFS.

Think about longest paths and how heights help.

Describe why the diameter path might not pass through the root node in a tree.

Consider a tree shaped like a long chain on one side.