Algorithm Analysis and Optimization Questions

Assess the ability to analyze, compare, and optimize algorithmic solutions with respect to time and space resources. Candidates should be fluent in Big O notation and able to identify dominant operations, reason about worst case, average case, and amortized complexity, and calculate precise time and space bounds for algorithms and data structure operations. The topic includes recognizing complexity classes such as constant time, logarithmic time, linear time, linearithmic time, quadratic time, and exponential time, and understanding when constant factors and lower order terms affect practical performance. Candidates should know and apply common algorithmic patterns and techniques, including two pointers, sliding window, divide and conquer, recursion, binary search, dynamic programming, greedy strategies, and common graph algorithms, and demonstrate how to transform brute force approaches into efficient implementations. Coverage also includes trade offs between time and space and when to trade memory for speed, amortized analysis, optimization tactics such as memoization, caching, pruning, iterative versus recursive approaches, and data layout considerations. Candidates must be able to reason about correctness, invariants, and edge cases, identify performance bottlenecks, and explain practical implications such as cache behavior and memory access patterns. For senior roles, be prepared to justify precise complexity claims and discuss optimization choices in system level and constrained environment contexts.