Algorithms

“Find the k largest elements in this array.” Most candidates reach for Arrays.sort() and stop. It works. It’s O(n log n). A stronger answer reaches for the heap: sorting processes all n elements in O(n log n) time, while a bounded heap takes O(n log k) and maintains only k candidates — preferable when k is small relative to n, or when the input arrives as a stream. For 1 ≤ k ≤ n, the heap uses O(k) auxiliary space, and the returned result uses O(k) output space. This post builds four common heap patterns that cover a wide range of top-k questions asked in Java interviews, with working code, the complexity math, and the PriorityQueue traps that quietly sink candidates. ...

“Design a distributed cache.” You say hash(key) % N. The interviewer nods, then asks: “A node dies at 3 AM. What happens?” If your answer is “we rehash everything,” you’ve just told them your cache has a planned outage every time the cluster changes shape. This post builds the real answer — a working consistent hash ring in Java, with virtual nodes and tests — and the lineage and follow-ups that turn it into a senior-level answer. ...

Undirected Graphs Some problems Path Shortest path Cycle Ehler tour: A cycle that uses each edge excatly once. Hamilton tour: A cycle that uses each vertex exactly once classical NP-complete problem. Connectivity MST: Biconnectivity: A vertex whose removal disconnects the graph Planarity Graph isomorphism: Are two graphs identical? No one knows so far. A lonstanding open problem Representations Real-world graphs tend to be sparse (huge number of vertices, small average vertex degree). ...