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##Version 3.0.0

New implementation of the combinatorics library for Java 8. The previous version of the library can be found here

1. Simple combinations
2. Combinations with repetitions
3. Simple permutations
4. Permutations with repetitions

###1. Simple combinations A simple k-combination of a finite set S is a subset of k distinct elements of S. Specifying a subset does not arrange them in a particular order. As an example, a poker hand can be described as a 5-combination of cards from a 52-card deck: the 5 cards of the hand are all distinct, and the order of the cards in the hand does not matter.

Let's generate all 3-combination of the set of 5 colors (red, black, white, green, blue).

   List<List<String>> combinations = Generator.combination("red", "black", "white", "green", "blue")
       .simple(3)
       .stream()
       .collect(Collectors.<List<String>>toList());
   combinations.stream().forEach(System.out::println);

And the result of 10 combinations

   [red, black, white]
   [red, black, green]
   [red, black, blue]
   [red, white, green]
   [red, white, blue]
   [red, green, blue]
   [black, white, green]
   [black, white, blue]
   [black, green, blue]
   [white, green, blue]

###2. Combinations with repetitions A k-multicombination or k-combination with repetition of a finite set S is given by a sequence of k not necessarily distinct elements of S, where order is not taken into account.

As an example. Suppose there are 2 types of fruits (apple and orange) at a grocery store, and you want to buy 3 pieces of fruit. You could select

• (apple, apple, apple)
• (apple, apple, orange)
• (apple, orange, orange)
• (orange, orange, orange)

Example. Generate 3-combinations with repetitions of the set (apple, orange). You can pass an array as the parameter in the function.

   Generator.combination(new String[] { "apple", "orange" })
       .multi(3)
       .stream()
       .forEach(System.out::println);

And the result of 4 multi-combinations

   [apple, apple, apple]
   [apple, apple, orange]
   [apple, orange, orange]
   [orange, orange, orange]

###3. Simple permutations A permutation is an ordering of a set in the context of all possible orderings. For example, the set containing the first three digits, 123, has six permutations: 123, 132, 213, 231, 312, and 321.

This is an example of the permutations of the 3 string items (apple, orange, cherry):

   Generator.permutation("apple", "orange", "cherry")
       .simple()
       .stream()
       .forEach(System.out::println);

The result of 6 permutations

   [apple, orange, cherry]
   [apple, cherry, orange]
   [cherry, apple, orange]
   [cherry, orange, apple]
   [orange, cherry, apple]
   [orange, apple, cherry]

This generator can produce the permutations even if an initial vector has duplicates. For example, all permutations of (1, 1, 2, 2):

   Generator.permutation(1, 1, 2, 2)
       .simple()
       .stream()
       .forEach(System.out::println);

The result of all possible permutations (with duplicates)

   [1, 1, 2, 2]
   [1, 2, 1, 2]
   [1, 2, 2, 1]
   [2, 1, 1, 2]
   [2, 1, 2, 1]
   [2, 2, 1, 1]

###4. Permutations with repetitions Permutation may have more elements than slots. For example, all possible permutation of '12' in three slots are: 111, 211, 121, 221, 112, 212, 122, and 222.

Let's generate all possible permutations with repetitions of 3 elements from the set of apple and orange.

   List<List<String>> permutations = Generator
        .permutation("apple", "orange")
        .withRepetitions(3)
        .stream()
        .collect(Collectors.<List<String>>toList());
        
   permutations.stream().forEach(System.out::println);

And the result of 8 permutations

   [apple, apple, apple]
   [orange, apple, apple]
   [apple, orange, apple]
   [orange, orange, apple]
   [apple, apple, orange]
   [orange, apple, orange]
   [apple, orange, orange]
   [orange, orange, orange]