C#，《小白学程序》第二十五课：大数乘法（BigInteger Multiply）的Karatsuba算法及源代码

1 文本格式

/// <summary>
/// 《小白学程序》第二十五课：大数（BigInteger）的Karatsuba乘法
/// Multiplies two bit strings X and Y and returns result as long integer
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <returns></returns>
public static string karatsuba_multiply(string a, string b)
{
    // Find the maximum of lengths of x and Y and make
    // length of smaller string same as that of larger string
    int n = Math.Max(a.Length, b.Length);
    if (a.Length != n) a = a.PadLeft(n, '0');
    if (b.Length != n) b = b.PadLeft(n, '0');

    // Base cases
    if (n == 0)
    {
        return "0";
    }
    else if (n == 1)
    {
        return ((a[0] - '0') * (b[0] - '0')).ToString();
    }
    else if (n <= 9)
    {
        // int max 21474 83647
        // long max 9223 37203 68547 75807
        return (ulong.Parse(a) * ulong.Parse(b)).ToString();
    }

    int fh = n / 2;  // First half of string
    int sh = n - fh; // Second half of string

    // Find the first half and second half of first string.
    string x1 = a.Substring(0, fh);
    string x2 = a.Substring(fh);

    // Find the first half and second half of second string
    string y1 = b.Substring(0, fh);
    string y2 = b.Substring(fh);

    // Recursively calculate the three products of
    // inputs of size n/2
    string p1 = karatsuba_multiply(x1, y1);
    string p2 = karatsuba_multiply(x2, y2);
    //string P3 = Karatsuba(AddBitStrings(Xl, Xr), AddBitStrings(Yl, Yr));
    string p3 = karatsuba_multiply(big_integer_plus(x1, x2), big_integer_plus(y1, y2));

    // Combine the three products to get the final result.
    //return P1 * (1L << (2 * sh)) + (P3 - P1 - P2) * (1L << sh) + P2;
    int[] t1 = new int[sh];
    string w1 = String.Join("", t1);
    string v1 = p1 + w1 + w1;
    string v2 = big_integer_subtract(p3, big_integer_plus(p1, p2)) + w1;
    return big_integer_plus(v1, big_integer_plus(v2, p2));
}
 

2 代码格式

/// <summary>
/// 《小白学程序》第二十五课：大数（BigInteger）的Karatsuba乘法
/// Multiplies two bit strings X and Y and returns result as long integer
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <returns></returns>
public static string karatsuba_multiply(string a, string b)
{
    // Find the maximum of lengths of x and Y and make
    // length of smaller string same as that of larger string
    int n = Math.Max(a.Length, b.Length);
    if (a.Length != n) a = a.PadLeft(n, '0');
    if (b.Length != n) b = b.PadLeft(n, '0');

    // Base cases
    if (n == 0)
    {
        return "0";
    }
    else if (n == 1)
    {
        return ((a[0] - '0') * (b[0] - '0')).ToString();
    }
    else if (n <= 9)
    {
        // int max 21474 83647
        // long max 9223 37203 68547 75807
        return (ulong.Parse(a) * ulong.Parse(b)).ToString();
    }

    int fh = n / 2;  // First half of string
    int sh = n - fh; // Second half of string

    // Find the first half and second half of first string.
    string x1 = a.Substring(0, fh);
    string x2 = a.Substring(fh);

    // Find the first half and second half of second string
    string y1 = b.Substring(0, fh);
    string y2 = b.Substring(fh);

    // Recursively calculate the three products of
    // inputs of size n/2
    string p1 = karatsuba_multiply(x1, y1);
    string p2 = karatsuba_multiply(x2, y2);
    //string P3 = Karatsuba(AddBitStrings(Xl, Xr), AddBitStrings(Yl, Yr));
    string p3 = karatsuba_multiply(big_integer_plus(x1, x2), big_integer_plus(y1, y2));

    // Combine the three products to get the final result.
    //return P1 * (1L << (2 * sh)) + (P3 - P1 - P2) * (1L << sh) + P2;
    int[] t1 = new int[sh];
    string w1 = String.Join("", t1);
    string v1 = p1 + w1 + w1;
    string v2 = big_integer_subtract(p3, big_integer_plus(p1, p2)) + w1;
    return big_integer_plus(v1, big_integer_plus(v2, p2));
}