Question 1

What is the difference between BFS and DFS graph traversal?

Accepted Answer

BFS explores level by level using a queue (shortest path in unweighted graphs); DFS explores depth-first using a stack or recursion. BFS: visit all neighbors before going deeper — finds shortest path in unweighted graphs. DFS: go as deep as possible before backtracking — used for cycle detection, topological sort, connected components.

Question 2

What is a min-heap and what is its key property?

Accepted Answer

A complete binary tree where each node's value is smaller than or equal to its children — so the minimum is always at the root. Min-heap supports: getMin() O(1), insert O(log n), deleteMin O(log n). Used in Dijkstra's algorithm, Prim's MST, and priority queues. Python's heapq module implements a min-heap.

Question 3

What is a trie (prefix tree) and what is it best used for?

Accepted Answer

Efficient string storage and prefix-based search — used in autocomplete, spell checkers, and IP routing tables. A trie stores strings character by character. Searching for a string of length m takes O(m) — independent of the number of strings. Prefix search (autocomplete) is a natural fit.

Question 4

What is Dijkstra's algorithm used for?

Accepted Answer

Finding the shortest path from a source node to all other nodes in a graph with non-negative edge weights. Dijkstra's uses a min-heap: always relax the closest unvisited node. Time: O((V+E) log V) with a heap. Does NOT work with negative weights — use Bellman-Ford for those.

Question 5

What is the sliding window technique in algorithm design?

Accepted Answer

Maintaining a window of elements over an array/string that expands/shrinks to find subarrays satisfying a condition in O(n). Instead of recomputing from scratch for each subarray, slide two pointers to maintain a window. Solves: longest substring without repeating characters, max sum subarray of size k. Reduces O(n²) to O(n).

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