TAOCP Vol 3: Sorting and Searching · Week 86
TAOCP 5.4.2 The Polyphase Merge: reading guide
A way to merge runs using a limited number of tapes without wasting passes, where the ideal initial run distribution follows generalized Fibonacci numbers.
Time About 5 hours this week
Why it matters
Honest note: the tape-merging sections describe hardware nobody uses anymore. Knuth himself says much of 5.4 is historical. The ideas (run generation, merge patterns, minimizing passes over slow storage) still apply to external sorting on disks and SSDs, database sort operators and big-data shuffles, so read for those ideas and skim the tape mechanics.
Before you start
- 5.4.1 Multiway Merging
- 1.2.8 Fibonacci Numbers
How to approach it
Simulate a 3-tape polyphase merge by hand to see the Fibonacci pattern. Skim the detailed tape-handling algorithms.
Exercises
This is a light section. Skim the exercises, do the ones rated 10 or under in your head, and spend the spare time catching up on earlier exercises you skipped.
Traps
- Spending a lot of time on tape rewind details.