Improved Combinations with the BigInteger Data Type: Listing 4.

Improved mth lexicographical element of a combination.

public Combination Element(BigInteger m)
{
  BigInteger maxM = Choose(this.n, this.k) - 1;

  if (m > maxM)
    throw new Exception("m value is too large in Element");

  int[] ans = new int[this.k];

  int a = this.n;
  int b = this.k;
  BigInteger x = maxM - m; // x is the "dual" of m

  for (int i = 0; i < this.k; ++i)
  {
    ans[i] = LargestV(a, b, x); // see helper below    
    x = x - Choose(ans[i], b);
    a = ans[i];
    b = b - 1;
  }

  for (int i = 0; i < this.k; ++i)
    ans[i] = (n - 1) - ans[i];

  Combination result = new Combination(this.n, this.k);
  ans.CopyTo(result.data, 0);
  return result;
}

About the Author

Dr. James McCaffrey works for Microsoft Research in Redmond, WA. James has worked on several key Microsoft products such as Internet Explorer and Bing. James can be reached at jamccaff@microsoft.com.