Algorithm to Return All Combinations of K Elements from N
I Want to Write a Function That Takes an Array of Letters as an Argument and a Number of Those Letters to Select. Say You Provide an Array of 8 Letters and...
I want to write a function that takes an array of letters as an argument and a number of those letters to select.
Say you provide an array of 8 letters and want to select 3 letters from that. Then you should get:
8! / ((8 - 3)! * 3!) = 56
Arrays (or words) in return consisting of 3 letters each.
77 Answers
Art of Computer Programming Volume 4: Fascicle 3 has a ton of these that might fit your particular situation better than how I describe.
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Gray Codes
An issue that you will come across is of course memory and pretty quickly, you'll have problems by 20 elements in your set -- 20C3 = 1140. And if you want to iterate over the set it's best to use a modified gray code algorithm so you aren't holding all of them in memory. These generate the next combination from the previous and avoid repetitions. There are many of these for different uses. Do we want to maximize the differences between successive combinations? minimize? et cetera.
Some of the original papers describing gray codes:
- Some Hamilton Paths and a Minimal Change Algorithm
- Adjacent Interchange Combination Generation Algorithm
Here are some other papers covering the topic:
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