Trees, Graphs & Hash Tables

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Question 1

Which of the following is a required property of a Binary Search Tree (BST)?

Accepted Answer

The BST property: for any node N, every key in its left subtree is less than N.key, and every key in its right subtree is greater. This allows O(log n) search, insert, and delete in a balanced BST. An unbalanced BST degrades to O(n) in the worst case (a linked list).

Question 2

What is the main difference between AVL trees and Red-Black trees?

Accepted Answer

AVL trees enforce a stricter balance invariant (the heights of left and right subtrees differ by at most 1), making lookups slightly faster. Red-Black trees allow more imbalance but require fewer rotations on insertion/deletion, making them faster for write-heavy workloads. Java TreeMap and C++ std::map use Red-Black trees.

Question 3

In a min-heap, what is the value at the root node?

Accepted Answer

A min-heap satisfies the heap property: every parent node is less than or equal to its children. Therefore, the root always contains the minimum element. This makes `getMin()` an O(1) operation. A max-heap is the opposite — the root is the maximum.

Question 4

What is the key difference between Depth-First Search (DFS) and Breadth-First Search (BFS) in graphs?

Accepted Answer

DFS goes deep along one path before backtracking (uses a stack, either explicit or via recursion). BFS explores all nodes at distance k before any at distance k+1 (uses a queue). BFS finds the shortest path in unweighted graphs. Both have O(V + E) time complexity for adjacency list representations.

Question 5

What distinguishes a directed graph from an undirected graph?

Accepted Answer

In a directed graph (digraph), each edge has a direction — an edge from A to B does not imply an edge from B to A. In an undirected graph, edges are bidirectional. Social media "follows" (Twitter) are directed; Facebook "friendships" are undirected.

Question 6

Which technique is commonly used to handle hash collisions in a hash table?

Accepted Answer

Two main collision resolution strategies: (1) Chaining — each bucket is a linked list of all entries that hash to that bucket. (2) Open addressing — when a collision occurs, probe for the next available slot (linear probing, quadratic probing, or double hashing). Python dict uses open addressing; Java HashMap uses chaining.

Question 7

What data structure is a trie (prefix tree) most suited for?

Accepted Answer

A trie stores strings character by character in a tree structure. Each path from root to a terminal node represents a word. This enables O(m) lookup, insertion, and prefix search where m is the key length — independent of the number of stored strings. Used in autocomplete systems, spell checkers, and IP routing.

Question 8

What is a priority queue, and what data structure typically implements it?

Accepted Answer

A priority queue dequeues elements in order of priority (not insertion order). Heaps are the most common implementation: a binary heap provides O(log n) insert and O(log n) extract-min/max. Priority queues are used in Dijkstra's shortest path algorithm, A* search, and job scheduling.

Question 9

When should you prefer an adjacency list over an adjacency matrix to represent a graph?

Accepted Answer

An adjacency matrix uses O(V²) memory regardless of edge count. An adjacency list uses O(V + E) memory. For sparse graphs (E << V²), an adjacency list is far more memory-efficient. Adjacency matrices are preferred when the graph is dense or when O(1) edge lookup is critical.

Question 10

What is the result of an in-order traversal of a valid Binary Search Tree?

Accepted Answer

In-order traversal visits nodes in the sequence: left subtree → root → right subtree. Applied to a BST, this visits nodes in ascending sorted order. This property makes BSTs useful for range queries and sorted output. Pre-order visits root first; post-order visits root last.

Trees, Graphs & Hash Tables

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Trees, Graphs & Hash Tables

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