Algorithm Design and Analysis Questions

Covers algorithmic problem solving and analysis fundamentals required in technical interviews. Topics include common data structures, sorting and searching, recursion and divide and conquer, dynamic programming, greedy strategies, backtracking, graph algorithms such as breadth first search and depth first search, shortest path and topological sort, string algorithms, and techniques for deriving correct and efficient solutions. Candidates should demonstrate ability to reason about correctness, derive time and space complexity bounds using Big O notation, and discuss scalability and optimization trade offs for large inputs.

MediumTechnical

94 practiced

Describe Bloom filters and their probabilistic trade-offs for set membership. For storing billions of user IDs under a strict memory budget and a target false positive rate p, show how to compute required bit array size m and optimal number of hash functions k. Explain how deletions can be supported and how to merge filters across shards.

HardTechnical

89 practiced

Implement Bellman-Ford in Python to compute shortest paths from a source node in graphs that may have negative edge weights. Show how to detect negative cycles reachable from the source and return nodes involved in a negative cycle. Explain why Bellman-Ford is O(VE) and when it is preferred over Dijkstra.

HardTechnical

78 practiced

Given a tree where each node has a weight, compute the maximum-weight independent set (no two adjacent nodes both selected). Provide an O(N) dynamic programming solution that computes include and exclude values per node, explain root selection and recursion, and outline how to reconstruct the chosen set in Python.

HardTechnical

83 practiced

Explain the Aho-Corasick algorithm for multiple-pattern string matching: describe building the trie of patterns, computing failure links using BFS, and traversing the automaton over the text to report matches in O(text_length + total_pattern_length + number_of_matches). Discuss memory trade-offs and when Aho-Corasick outperforms repeated KMP/regex searches.

MediumTechnical

98 practiced

You are given k sorted singly linked lists. Merge them into one sorted singly linked list and return its head. Implement an efficient Python solution, compare the min-heap approach vs divide-and-conquer pairwise merging, and analyze time and space complexity assuming total N nodes across all lists.

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