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

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Describe the Count-Min Sketch data structure for approximate frequency counting in high-volume streams. Explain the update and query operations, how to choose parameters (width and depth) to bound the error and failure probability, how to merge sketches from shards, and trade-offs vs exact counting when memory is constrained.

HardTechnical

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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

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Explain the max-flow min-cut theorem and implement the Edmonds-Karp algorithm (BFS-based Ford-Fulkerson) in Python to compute maximum flow in a directed graph with non-negative capacities. Describe residual graph maintenance, runtime O(VE^2), and when to use Dinic's algorithm instead. Provide a practical use-case such as bipartite matching.

MediumTechnical

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For dataset size N, D features, and K classes, provide time and memory complexity estimates per training epoch for logistic regression (batch gradient descent), decision tree (CART), random forest with T trees, and kernel SVM. Discuss practical scaling strategies—feature hashing, subsampling, sparse data handling, and distributed training—when N or D is large.

HardTechnical

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Given N ≤ 40 integers (possibly negative), design and implement a meet-in-the-middle algorithm in Python to find a subset whose sum is closest to a target T faster than O(2^N). Explain splitting the array, enumerating half-sums, sorting, binary searching complements, and analyze time and memory complexity.

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