TAOCP Vol 3: Sorting and Searching · Week 83
TAOCP 5.3.3 Minimum-Comparison Selection: reading guide
Finding the k-th smallest element with as few comparisons as possible, including finding the second largest and the linear-time worst-case selection result.
Time About 5 hours this week
Why it matters
Selection (median, percentiles, top-k) is a common real need. The linear-time median-of-medians idea is a classic.
Before you start
- 5.3.1 Minimum-Comparison Sorting
How to approach it
Work out why finding the second largest takes about n + lg n comparisons using a tournament. Implement quickselect and median of medians and compare their speed.
Exercises
Do every exercise rated 00 to 20 in your head or on paper; they are quick and they check you actually absorbed the definitions. Then pick two or three rated 20 to 25 (M or not) and grind them out fully. Attempt one M25 to M30 and give yourself a hard 90-minute cap before reading the answer. Always read the answer to every exercise you attempted, even the ones you got, because Knuth's answers often teach a second technique.
Traps
- Median of medians is linear but has a big constant; quickselect usually wins in practice.