TAOCP 6.2.1 Searching an Ordered Table: reading guide

Binary search and its variants: uniform binary search, Fibonacci search, and interpolation search, with analysis and a careful look at how easy it is to get binary search wrong.

Time About 7 hours this week

Why it matters

Binary search is famously hard to write correctly. Knowing the variants also helps with things like branch-free search and searching on sorted disk pages.

Before you start

6.1 Sequential Searching

How to approach it

Write binary search from memory, then test it exhaustively on all arrays up to size 10 and all targets. Implement interpolation search and test it on uniform and skewed data.

Exercises

Work every exercise rated 10 to 20; most are about tracing the algorithm by hand or tweaking one step, which is exactly the skill you want. Pick one or two rated 20 to 25 that involve modifying the algorithm and implement your modification in a real language with tests. Skip HM exercises unless you enjoy calculus, and treat anything rated 40+ as a research problem, not homework.

Traps

Off-by-one in bounds and infinite loops when lo and hi are adjacent.
Midpoint overflow on very large arrays.