Initial data commit

Task/Combinations-and-permutations/Java/combinations-and-permutations.java

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+import java.math.BigInteger;
+
+public class CombinationsAndPermutations {
+
+    public static void main(String[] args) {
+        System.out.println(Double.MAX_VALUE);
+        System.out.println("A sample of permutations from 1 to 12 with exact Integer arithmetic:");
+        for ( int n = 1 ; n <= 12 ; n++ ) {
+            int k = n / 2;
+            System.out.printf("%d P %d = %s%n", n, k, permutation(n, k));
+        }
+
+        System.out.println();
+        System.out.println("A sample of combinations from 10 to 60 with exact Integer arithmetic:");
+        for ( int n = 10 ; n <= 60 ; n += 5 ) {
+            int k = n / 2;
+            System.out.printf("%d C %d = %s%n", n, k, combination(n, k));
+        }
+
+        System.out.println();
+        System.out.println("A sample of permutations from 5 to 15000 displayed in floating point arithmetic:");
+        System.out.printf("%d P %d = %s%n", 5, 2, display(permutation(5, 2), 50));
+        for ( int n = 1000 ; n <= 15000 ; n += 1000 ) {
+            int k = n / 2;
+            System.out.printf("%d P %d = %s%n", n, k, display(permutation(n, k), 50));
+        }
+
+        System.out.println();
+        System.out.println("A sample of combinations from 100 to 1000 displayed in floating point arithmetic:");
+        for ( int n = 100 ; n <= 1000 ; n += 100 ) {
+            int k = n / 2;
+            System.out.printf("%d C %d = %s%n", n, k, display(combination(n, k), 50));
+        }
+
+    }
+
+    private static String display(BigInteger val, int precision) {
+        String s = val.toString();
+        precision = Math.min(precision, s.length());
+        StringBuilder sb = new StringBuilder();
+        sb.append(s.substring(0, 1));
+        sb.append(".");
+        sb.append(s.substring(1, precision));
+        sb.append(" * 10^");
+        sb.append(s.length()-1);
+        return sb.toString();
+    }
+
+    public static BigInteger combination(int n, int k) {
+        //  Select value with smallest intermediate results
+        //    combination(n, k) = combination(n, n-k)
+        if ( n-k < k ) {
+            k = n-k;
+        }
+        BigInteger result = permutation(n, k);
+        while ( k > 0 ) {
+            result = result.divide(BigInteger.valueOf(k));
+            k--;
+        }
+        return result;
+    }
+
+    public static BigInteger permutation(int n, int k) {
+        BigInteger result = BigInteger.ONE;
+        for ( int i = n ; i >= n-k+1 ; i-- ) {
+            result = result.multiply(BigInteger.valueOf(i));
+        }
+        return result;
+    }
+
+}