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Task/Permutations-Rank-of-a-permutation/Java/permutations-rank-of-a-permutation.java

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+import java.math.BigInteger;
+import java.util.*;
+
+class RankPermutation
+{
+  public static BigInteger getRank(int[] permutation)
+  {
+    int n = permutation.length;
+    BitSet usedDigits = new BitSet();
+    BigInteger rank = BigInteger.ZERO;
+    for (int i = 0; i < n; i++)
+    {
+      rank = rank.multiply(BigInteger.valueOf(n - i));
+      int digit = 0;
+      int v = -1;
+      while ((v = usedDigits.nextClearBit(v + 1)) < permutation[i])
+        digit++;
+      usedDigits.set(v);
+      rank = rank.add(BigInteger.valueOf(digit));
+    }
+    return rank;
+  }
+
+  public static int[] getPermutation(int n, BigInteger rank)
+  {
+    int[] digits = new int[n];
+    for (int digit = 2; digit <= n; digit++)
+    {
+      BigInteger divisor = BigInteger.valueOf(digit);
+      digits[n - digit] = rank.mod(divisor).intValue();
+      if (digit < n)
+        rank = rank.divide(divisor);
+    }
+    BitSet usedDigits = new BitSet();
+    int[] permutation = new int[n];
+    for (int i = 0; i < n; i++)
+    {
+      int v = usedDigits.nextClearBit(0);
+      for (int j = 0; j < digits[i]; j++)
+        v = usedDigits.nextClearBit(v + 1);
+      permutation[i] = v;
+      usedDigits.set(v);
+    }
+    return permutation;
+  }
+
+  public static void main(String[] args)
+  {
+    for (int i = 0; i < 6; i++)
+    {
+      int[] permutation = getPermutation(3, BigInteger.valueOf(i));
+      System.out.println(String.valueOf(i) + " --> " + Arrays.toString(permutation) + " --> " + getRank(permutation));
+    }
+    Random rnd = new Random();
+    for (int n : new int[] { 12, 144 })
+    {
+      BigInteger factorial = BigInteger.ONE;
+      for (int i = 2; i <= n; i++)
+        factorial = factorial.multiply(BigInteger.valueOf(i));
+      // Create 5 random samples
+      System.out.println("n = " + n);
+      for (int i = 0; i < 5; i++)
+      {
+        BigInteger rank = new BigInteger((factorial.bitLength() + 1) << 1, rnd);
+        rank = rank.mod(factorial);
+        int[] permutation = getPermutation(n, rank);
+        System.out.println("  " + rank + " --> " + Arrays.toString(permutation) + " --> " + getRank(permutation));
+      }
+    }
+  }
+
+}