写一个算法思路可以利用32位计算机计算一下两个数之间的乘积

[incompletewild]

b=42423408908534590893423408590820480923840928095829482342398402480234
a=14234235634298490859038409583058093485093850983095830509385038503805
c=a*b
c是多少

[wuyi8808]

BigInteger Class

[wuyi8808]

http://www.cnblogs.com/skyivben/archive/2008/07/13/1241681.html

[wuyi8808]

using System;
using System.Text;
using System.Collections.Generic;

sealed class BigInteger
{
  static readonly int Len = 9; // int.MaxValue = 2,147,483,647
  static readonly int Base = (int)Math.Pow(10, Len);

  int sign;
  List<int> data;

  BigInteger(long x)
  {
    sign = (x == 0) ? 0 : ((x > 0) ? 1 : -1);
    data = new List<int>();
    for (ulong z = Abs(x); z != 0; z /= (ulong)Base) data.Add((int)(z % (ulong)Base));
  }

  BigInteger(BigInteger x)
  {
    sign = x.sign;  // x != null
    data = new List<int>(x.data);
  }

  public static implicit operator BigInteger(long x)
  {
    return new BigInteger(x);
  }

  public static BigInteger Parse(string s)
  {
    if (s == null) return null;
    s = s.Trim().Replace(",", null);
    if (s.Length == 0) return 0;
    BigInteger z = 0;
    z.sign = (s[0] == '-') ? -1 : 1;
    if (s[0] == '-' || s[0] == '+') s = s.Substring(1);
    int r = s.Length % Len;
    z.data = new List<int>(new int[s.Length / Len + ((r != 0) ? 1 : 0)]);
    int i = z.data.Count - 1;
    if (r != 0) z.data[i--] = int.Parse(s.Substring(0, r));
    for (; i >= 0; i--, r += Len) z.data[i] = int.Parse(s.Substring(r, Len));
    z.Shrink();
    return z;
  }

  public static void Swap(ref BigInteger x, ref BigInteger y)
  {
    BigInteger z = x;
    x = y;
    y = z;
  }

  public static ulong Abs(long x)
  {
    return (x < 0) ? (ulong)-x : (ulong)x;
  }

  public static BigInteger Abs(BigInteger x)
  {
    if (x == null) return null;
    BigInteger z = new BigInteger(x);
    z.sign = Math.Abs(x.sign);
    return z;
  }

  public static BigInteger Pow(BigInteger x, int y)
  {
    if (x == null) return null;
    BigInteger z = 1, n = x;
    for (; y > 0; y >>= 1, n *= n) if ((y & 1) != 0) z *= n;
    return z;
  }

  public static BigInteger operator +(BigInteger x)
  {
    if (x == null) return null;
    return new BigInteger(x);
  }

  public static BigInteger operator -(BigInteger x)
  {
    if (x == null) return null;
    BigInteger z = new BigInteger(x);
    z.sign = -x.sign;
    return z;
  }

  public static BigInteger operator +(BigInteger x, BigInteger y)
  {
    if (x == null || y == null) return null;
    if (x.AbsCompareTo(y) < 0) Swap(ref x, ref y);
    BigInteger z = new BigInteger(x);
    if (x.sign * y.sign == -1) z.AbsSubtract(y);
    else z.AbsAdd(y);
    return z;
  }

  public static BigInteger operator -(BigInteger x, BigInteger y)
  {
    if (x == null || y == null) return null;
    return x + (-y);
  }

  public static BigInteger operator *(BigInteger x, BigInteger y)
  {
    if (x == null || y == null) return null;
    BigInteger z = 0;
    z.sign = x.sign * y.sign;
    z.data = new List<int>(new int[x.data.Count + y.data.Count]);
    for (int i = x.data.Count - 1; i >= 0; i--)
      for (int j = y.data.Count - 1; j >= 0; j--)
      {
        long n = Math.BigMul(x.data[i], y.data[j]);
        z.data[i + j] += (int)(n % Base);
        z.CarryUp(i + j);
        z.data[i + j + 1] += (int)(n / Base);
        z.CarryUp(i + j + 1);
      }
    z.Shrink();
    return z;
  }

  public static BigInteger operator /(BigInteger dividend, BigInteger divisor)
  {
    BigInteger remainder;
    return DivRem(dividend, divisor, out remainder);
  }

  public static BigInteger operator %(BigInteger dividend, BigInteger divisor)
  {
    BigInteger remainder;
    DivRem(dividend, divisor, out remainder);
    return remainder;
  }

  public static BigInteger DivRem(BigInteger dividend, BigInteger divisor, out BigInteger remainder)
  {
    remainder = null;
    if (dividend == null || divisor == null) return null;
    if (divisor.sign == 0) throw new Exception("division by zero");
    if (dividend.AbsCompareTo(divisor) < 0)
    {
      remainder = new BigInteger(dividend);
      return 0;
    }
    remainder = 0;
    BigInteger quotient = 0;
    quotient.sign = dividend.sign * divisor.sign;
    quotient.data = new List<int>(new int[dividend.data.Count]);
    divisor = Abs(divisor); // NOT: divisor.sign = Math.Abs(divisor.sign);
    for (int i = dividend.data.Count - 1; i >= 0; i--)
    {
      remainder = remainder * Base + dividend.data[i];
      int iQuotient = remainder.BinarySearch(divisor, -1);
      quotient.data[i] = iQuotient;
      remainder -= divisor * iQuotient;
    }
    quotient.Shrink();
    if (remainder.sign != 0) remainder.sign = dividend.sign;
    return quotient;
  }

  public static BigInteger Sqrt(BigInteger x)
  {
    if (x == null || x.sign < 0) return null;
    BigInteger root = 0;
    root.sign = 1;
    root.data = new List<int>(new int[x.data.Count / 2 + 1]);
    for (int i = root.data.Count - 1; i >= 0; i--) root.data[i] = x.BinarySearch(root, i);
    root.Shrink();
    return root;
  }

  int BinarySearch(BigInteger divisor, int i)
  {
    int low = 0, high = Base - 1, mid = 0, cmp = 0;
    while (low <= high)
    {
      mid = (low + high) / 2;
      cmp = CompareTo(divisor, mid, i);
      if (cmp > 0) low = mid + 1;
      else if (cmp < 0) high = mid - 1;
      else return mid;
    }
    return (cmp < 0) ? (mid - 1) : mid;
  }

  int CompareTo(BigInteger divisor, int mid, int i)
  {
    if (i >= 0) divisor.data[i] = mid;
    return AbsCompareTo(divisor * ((i >= 0) ? divisor : mid));
  }

  void AbsAdd(BigInteger x)
  {
    for (int i = 0; i < x.data.Count; i++)
    {
      data[i] += x.data[i];
      CarryUp(i);
    }
  }

  void AbsSubtract(BigInteger x)
  {
    for (int i = 0; i < x.data.Count; i++)
    {
      data[i] -= x.data[i];
      CarryDown(i);
    }
    Shrink();
  }

  void CarryUp(int n)
  {
    for (; data[n] >= Base; n++)
    {
      if (n == data.Count - 1) data.Add(data[n] / Base);
      else data[n + 1] += data[n] / Base;
      data[n] %= Base;
    }
  }

  void CarryDown(int n)
  {
    for (; data[n] < 0; n++)
    {
      data[n + 1]--;
      data[n] += Base;
    }
    Shrink();
  }

  void Shrink()
  {
    for (int i = data.Count - 1; i >= 0 && data[i] == 0; i--) data.RemoveAt(i);
    if (data.Count == 0) sign = 0;
  }

  public override string ToString()
  {
    StringBuilder sb = new StringBuilder();
    if (sign < 0) sb.Append('-');
    sb.Append((data.Count == 0) ? 0 : data[data.Count - 1]);
    for (int i = data.Count - 2; i >= 0; i--) sb.Append(data[i].ToString("D" + Len));
    return sb.ToString();
  }

  public int CompareTo(BigInteger other)
  {
    if (object.ReferenceEquals(other, null)) return 1;
    if (sign < other.sign) return -1;
    if (sign > other.sign) return 1;
    if (sign == 0) return 0;
    return sign * AbsCompareTo(other);
  }

  int AbsCompareTo(BigInteger other)
  {
    if (data.Count < other.data.Count) return -1;
    if (data.Count > other.data.Count) return 1;
    for (int i = data.Count - 1; i >= 0; i--)
      if (data[i] != other.data[i])
        return (data[i] < other.data[i]) ? -1 : 1;
    return 0;
  }
}
  
class Program
{
  static void Main()
  {
    BigInteger b = BigInteger.Parse("42423408908534590893423408590820480923840928095829482342398402480234");
    BigInteger a = BigInteger.Parse("14234235634298490859038409583058093485093850983095830509385038503805");
    BigInteger c = a * b;
    Console.WriteLine(c);
    // 603864798814279120185225586728269967994486053541840823568791676976796892171207357745308923065868664503808921702014434265317500446290370
  }
}

[polarissky]

向空军学习

[諾临風]

不错~

[incompletewild]

谢谢！

[jianke917]

利用求高精度数据之积，将两数据转换为数组，利用数字进位法则计算！

public void GetAmass()
        {

            //Console.WriteLine("请输入第一个数！");
            //string a = Console.ReadLine();
            //Console.WriteLine("请输入第二个数！");
            //string b = Console.ReadLine();
            string a = "42423408908534590893423408590820480923840928095829482342398402480234";
            string b = "14234235634298490859038409583058093485093850983095830509385038503805";
            int[] num1 = new int[a.Length+1];
            int[] num2 = new int[b.Length+1];
            int[] c= new int[a.Length+b.Length+1];
            for (int i = 1; i <= a.Length; i++)
            {
                num1[i] = Convert.ToInt32(a.Substring(a.Length - i, 1));
            }
            for (int j = 1; j <= b.Length; j++)
            {

                num2[j] = Convert.ToInt32(b.Substring(b.Length - j, 1));
            }
            for (int i = 1; i <=a.Length; i++)
            {
                for (int j = 1; j <=b.Length; j++)
                {
                    int x = num1[i] * num2[j];
                    int y = x / 10;//进位
                    int z = x % 10;//本位数
                    int w = i + j - 1;
                    c[w] += z;
                    c[w + 1] = c[w + 1] + y + c[w] / 10;
                    c[w] = c[w] % 10;
                }
            }
          
          string s = null;
          int l = a.Length + b.Length + 1;
          while (c[l - 1] == 0)
          {
              l -= 1;
          }
          for (int i = l-1; i >=1 ; i--)
          {
              s += c[i].ToString();
          }        
          Console.WriteLine(s);
          Console.ReadLine();
        }

[jianke917]

结果：603864798814279120185225586728269967994486053541840823568791676976796892171207357745308923065868664503808921702014434265317500446290370