net.zomis.minesweeper.analyze

Class Combinatorics

java.lang.Object

net.zomis.minesweeper.analyze.Combinatorics

public class Combinatorics
extends Object

Static methods for combinatorics

Author:

Simon Forsberg

Method Summary

Modifier and Type	Method and Description
static List<Integer>	indexCombinations(double x, int size, int elements) Deprecated.
static <T> List<T>	listCombination(double combination, int size, List<T> elementList)
static <T> List<T>	multiListCombination(List<FieldRule<T>> rules, double combinationNumber)
static double	nCr(int n, int r) Calculates the Binomial Coefficient
static BigInteger	nCrBigInt(int n, int r) Calculates the Binomial Coefficient
static double	NNKK(int N, int n, int K, int k) Calculates the combinations for the hypergeometric probability distribution, that is, it does not divide by N nCr n.
static int[]	specificCombination(int elements, int size, BigInteger combinationNumber) You have x elements and want to pick a specific combination them which will contain y elements.
static int[]	specificCombination(int elements, int size, double combination) You have x elements and want to pick a specific combination them which will contain y elements.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

NNKK

public static double NNKK(int N,
                          int n,
                          int K,
                          int k)

Calculates the combinations for the hypergeometric probability distribution, that is, it does not divide by N nCr n.

Example: There are 6 fields, 3 of them contains a mine. You have the possibility to take 2 of these at once.
NNKK(6, 3, 2, 0) will return the number of combinations where 0 of the 2 you are taking contains a mine.

Parameters:

N - All elements

n - All elements containing what we are looking for

K - How many elements are we looking in

k - How many elements we are looking in that contains what we are looking for

Returns:

The number of combinations of k interesting elements in K areas when there are n interesting elements in N areas.

See Also:

Hypergeometric Distribution on Wikipedia

listCombination

public static <T> List<T> listCombination(double combination,
                                          int size,
                                          List<T> elementList)

multiListCombination

public static <T> List<T> multiListCombination(List<FieldRule<T>> rules,
                                               double combinationNumber)

indexCombinations

@Deprecated
public static List<Integer> indexCombinations(double x,
                                                           int size,
                                                           int elements)

Deprecated.

nCr

public static double nCr(int n,
                         int r)

Calculates the Binomial Coefficient

Parameters:

n - number of elements you have

r - number of elements you want to pick

Returns:

number of combinations when you have n elements and want r of them

See Also:

Binomial Coefficient on Wikipedia

nCrBigInt

public static BigInteger nCrBigInt(int n,
                                   int r)

Calculates the Binomial Coefficient

Parameters:

n - number of elements you have

r - number of elements you want to pick

Returns:

number of combinations when you have n elements and want r of them

See Also:

Binomial Coefficient on Wikipedia

specificCombination

public static int[] specificCombination(int elements,
                                        int size,
                                        BigInteger combinationNumber)

You have x elements and want to pick a specific combination them which will contain y elements.

For example, you have 5 elements and want 3 of them. There are 10 combinations for this. The exact combinations can be ordered as: 012, 013, 014, 023, 024, 034, 123, 124, 134, 234. Combination number 4 is then 023, so specificCombination(5, 3, BigInteger.valueOf(4)) will return the array { 0, 2, 3 }

Parameters:

elements - number of elements you have

size - number of elements you want to pick

combinationNumber - the combination number you want to pick. 1 <= combinationNumber <= nCr(elements, size)

Returns:

the specific elements that you picked, each element is 0 <= value < elements

Throws:

IllegalArgumentException - if combinationNumber is out of range

IllegalArgumentException - if elements or size is negative

specificCombination

public static int[] specificCombination(int elements,
                                        int size,
                                        double combination)

You have x elements and want to pick a specific combination them which will contain y elements.

For example, you have 5 elements and want 3 of them. There are 10 combinations for this. The exact combinations can be ordered as: 012, 013, 014, 023, 024, 034, 123, 124, 134, 234. Combination number 4 is then 023, so specificCombination(5, 3, 4) will return the array { 0, 2, 3 }

Parameters:

elements - number of elements you have

size - number of elements you want to pick

combination - the combination number you want to pick. 1 <= combinationNumber <= nCr(elements, size)

Returns:

the specific elements that you picked, each element is 0 <= value < elements

Throws:

IllegalArgumentException - if combinationNumber is out of range

IllegalArgumentException - if elements or size is negative