combinations : Java Glossary

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combinations

If you have a set of objects and select some of them, that selection without regard to their order is called a combination. If you have n objects there are 2ⁿ (2 to the nth power) possible combinations ranging from none present to all present. If you consider all the binary numbers ranging from 0 to 2ⁿ-1, and look at the individual bits, they map the possible combinations, 1=present 0=absent. So to generate all possible 16 bit quantities just use a for loop, for ( int i=0; i < 65535; i++).

Example

Sample Code

Links

Example

E.g what are the possible combinations of three objects a b c:

0	000	_
1	001	c
2	010	b
3	011	bc
4	100	a
5	101	ac
6	110	ab
7	111	abc

Sample Code

Here is an implementation of the Dijkstra algorithm for permutations and also a combinations algorithm: view

knapsack problem
Merriam Park Combinations algorithm
permutation
pseudo-random numbers
Uncommon Maths: a library of combination generators

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