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

Recall & Review

beginner

What is the diameter of a tree?

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

intermediate

How can dynamic programming help in finding the diameter of a tree?

Dynamic programming helps by storing the longest path from each node to its descendants, avoiding repeated calculations and efficiently computing the diameter.

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 in its subtree.

intermediate

Why do we consider the two longest heights among children when computing the diameter at a node?

Because the longest path through that node can be formed by joining the two longest paths from its children, passing through the node itself.

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 and edge is visited once during DFS traversal.

What does the diameter of a tree represent?

A Longest path between any two nodes

B Number of nodes in the tree

C Height of the tree

D Number of leaves in the tree

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 Number of edges in the tree

B Number of children of the node

C Distance from root to the node

D Longest path from node to a leaf in its subtree

Height is the longest path from the node down to a leaf in its subtree.

Why do we use two longest heights from children to compute diameter at a node?

A To count the number of children

B To find the shortest path

C To find the longest path passing through the node

D To calculate the node's degree

The longest path through the node is formed by joining the two longest child paths.

What traversal method is commonly used to compute diameter using DP on trees?

A Breadth-first search

B Depth-first search

C Level order traversal

D Inorder traversal

Depth-first search is used to compute heights and diameters efficiently.

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

A O(N)

B O(N^2)

C O(N log N)

D O(log N)

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

Explain how dynamic programming is applied to find the diameter of a tree.

Think about how to combine child heights to find longest path through a node.

Describe the steps to compute the diameter of a tree using a single DFS traversal.

Focus on how to gather information bottom-up during DFS.