Algorithms Foundations

All Articles (3 articles)

• K-Crystal Balls Problem: Jump Search Pattern

  Programming & Patterns / Algorithms Foundations 10 min read

  The K-crystal balls (or K-egg drop) problem demonstrates how constrained resources fundamentally change optimal search strategy. With unlimited test resources, binary search achieves O(log n). With exactly k resources that are consumed on failure, the optimal worst-case complexity becomes O(n^(1/k))—a jump search pattern where each resource enables one level of hierarchical partitioning.

• Sorting Algorithms: Complexity, Stability, and Use Cases

  Programming & Patterns / Algorithms Foundations 25 min read

  A comprehensive guide to sorting algorithms covering fundamental concepts, implementation details, performance characteristics, and real-world applications. Learn when to use each algorithm and understand the engineering trade-offs behind production sorting implementations.

• Search Algorithms: Linear, Binary, and Graph Traversal

  Programming & Patterns / Algorithms Foundations 34 min read

  A comprehensive guide to search algorithms covering fundamental concepts, implementation details, performance characteristics, and real-world applications. Learn when to use each algorithm and understand the engineering trade-offs behind production search implementations.