Binary Search and Heaps

Binary search and heaps solve different kinds of order problems. Use binary search when values are sorted or when a yes-no feasibility predicate changes monotonically over an answer range. Maintain a closed or half-open interval invariant and avoid discarding a possible boundary candidate. Use a min-heap or max-heap when the task repeatedly asks for the smallest or largest currently available item while inserts or updates occur. A heap does not support arbitrary search in O(log n); finding a specific value is generally O(n). For top-k values, maintain a min-heap of size k and replace its root when a larger candidate arrives. For merge-k sorted lists, push each current head and pop the next output. Heap construction is O(n), each push or pop is O(log n), and binary search takes O(log n) predicate evaluations. Test duplicates, empty heap, one item, and boundary answers.