Binary Search Explained
Binary search halves the search space with each comparison, but the real story is memory access: log n probes into an array versus n/2 on average for a linear scan. This video walks the loop step by step and shows the invariant, the midpoint math, and where the classic implementation hides its bugs.
Topics covered:
- The invariant: what must hold before the loop starts
- Midpoint calculation and the off-by-one errors it hides
- Cache behavior: why log n accesses beat n/2
- When binary search loses: small arrays and linked structures
- Lower-bound and upper-bound variants
- Real uses: database indexes, b-trees, and log-structured storage
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