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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Implement Dijkstra's algorithm in Python to compute shortest path distances from a source node to all nodes in a directed graph with non-negative weights given as adjacency lists graph = {u: [(v,w), ...]}. Return a dict of distances and explain time complexity using a binary heap vs Fibonacci heap and the practical trade-offs for sparse graphs.

MediumTechnical

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Design an algorithm in Python to maintain the top-k largest elements from a stream using O(k) memory and O(log k) time per update. Explain tie-breaking, merging top-k results from multiple partitions, and how to adapt when k is small compared to stream volume.

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Explain the role of convexity in optimization and how it affects convergence guarantees for gradient descent. Provide convergence rate bounds for L-smooth convex functions and μ-strongly convex functions, discuss step-size selection and the effect of condition number, and explain practical consequences for training convex surrogate models.

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.

MediumTechnical

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Implement an N-Queens solver in Python that returns all distinct board configurations for placing N queens so that no two attack each other. Use backtracking with pruning using sets for occupied columns and diagonals. Explain pruning optimizations, symmetry-breaking to reduce work, and analyze worst-case search complexity.

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