Oleksii Trekhleb | Javascript algorithms (Permutations)
This is a series of books diving deep into the core mechanisms of the JavaScript language.
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When the order doesn’t matter, it is a Combination.
When the order does matter it is a Permutation.
The combination to the safe is 472. We do care about the order. 724
won’t work, nor will 247
. It has to be exactly 4-7-2
.
Permutations without repetitions
A permutation, also called an arrangement number or order, is a rearrangement of the elements of an ordered list S
into a one-to-one correspondence with S
itself.
Below are the permutations of string ABC
.
ABC ACB BAC BCA CBA CAB
Or for example the first three people in a running race: you can’t be first and second.
Number of combinations
n (n-1) (n -2) … 1 = n!
Permutations with repetitions
When repetition is allowed we have permutations with repetitions. For example the the lock below: it could be 333
.
Number of combinations
n n n… (r times) = n^r
Cheatsheet
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