大整数阶乘的运算（可以计算1000！） .

由于阶乘运算的增长速度特别快（比2^n的增长速度快），对于较小整数的阶乘运算采用简单的递规算法可以实现，但是对于大整数的乘法（比如1000！），则传统的递规算法就失去了作用。

由于本人的水平不高，用下列拙劣的方式实现，请高人多多指教。具体如下：定义一个很长的数组，用数组的每一项表示计算结果的每一位。例如，7！＝5040，a[1000]，则a[0]＝0，a[1]=4,a[2]=0,a[3]=5。

程序源代码：

/**
*计算大数的阶乘，算法的主要思想就是将计算结果的每一位用数组的一位来表示：如要计算5!，那么首先将
*(1) a[0]=1，然后a[0]=a[0]*2，a[0]=2，
*(2) a[0]=a[0]*3，a[0]=6
*(3) a[0]=a[0]*4，a[0]=24，此时a[1]＝2，a[0]＝4
*/
public class Factorial 
{
 static int a[] = new int [10000];
 static void factorial(int n)
 {
   for(int i=2; i< a.length; i++)
   a[i] = 0;   //将数组元素初始化
  a[0] = 1;  //用数组的一项存放计算结果的位数
  a[1] = 1;  //将第一项赋值为一
  for(int j= 2; j <= n; j++)
  {
   int i=1;
   int c = 0; //c表示向高位的进位
   for(; i <= a[0]; i++)
   {
    a[i] = a[i] * j + c;//将来自低位的计算结果和本位的结果相加
    c = a[i] / 10; 
    a[i] = a[i] % 10;
   }
   for(; c != 0; i++)
   {
    a[i] = c%10;
    c = c / 10;
   }
   a[0] = i - 1;
  }
 }
 public static void main(String[] args) 
 {
  String num = args[0];

  int  count = 0;
  int n = Integer.parseInt(num);
  f(n);
  for(int i= a[0]; i>0; i--)
  {
   
    count++;
   System.out.print(/*"a[" + i + "]=" + */a[i]/* + "  "*/);
  }
  System.out.println("/n"+count);
 }
}

 

 

======================================

本文给出Java语言版的计算大数阶乘的程序，本文使用动态数组的存储计算过程的中间结果和最终结果。每个short型数组元素表示4位10进制数。顺便说一下，这是我的第一个Java程序。

import java.util.Scanner;
/**
 *
 * @author liangbch@263.net
 */
public class Fac {
      public Fac() {
    }

    public static void Calc(int n)
    {
        int RAD=10000;
        int buffSize=(int)(n * Math.log10((n+1)/2) / Math.log10(RAD)+1);
        short[] buff = new short[buffSize];
        int len=1;
        buff[0]=1;
        for (int i=1;i<=n;i++)
        {
            int c=0;
            for (int j=0;j<len;j++)
            {
                int prod=(buff[j]*i+c);
                buff[j]=(short)(prod % RAD);
                c=prod / RAD;
            }
            while (c>0)
            {
                buff[len++]= (short)(c % RAD);
                c=c/RAD;
            }
        }

        System.out.printf("%d!=%d", n, buff[len-1]);
        for (int i=len-2;i>=0;i--)
            System.out.printf("%04d",buff[i]);
     }

    public static void main(String[] args) {
       System.out.println("Please input a integer");
       Scanner in=new Scanner(System.in);
       int n=in.nextInt();
       Calc(n);
    }
}

Java中求阶乘的算法

 

1.一般算法：

public class Factorial {
    public static int factorial(int n) {
        if (n < 0 || n > 16) {
            System.err.println("n must be great than 0 and less than 17");
            return -1;
        } else if (n == 0) {
            return 1;
        } else {
            int result = 1;
            for (int i = 1; i <= n; i++) {
                result *= i;
            }
            return result;
        }
    }

    public static void main(String args[]) {
        System.out.println("result = " + factorial(5));
    }
}

public class Factorial {
	public static int factorial(int n) {
		if (n < 0 || n > 16) {
			System.err.println("n must be great than 0 and less than 17");
			return -1;
		} else if (n == 0) {
			return 1;
		} else {
			int result = 1;
			for (int i = 1; i <= n; i++) {
				result *= i;
			}
			return result;
		}
	}

	public static void main(String args[]) {
		System.out.println("result = " + factorial(5));
	}
} 

   运行结果：result = 120

2.递归算法：

public class Factorial {
    public static int recursion(int n) {
        if (n < 0 || n > 16) {
            System.err.println("n must be great than 0 and less than 17");
            return -1;
        } else if (n == 0) {
            return 1;
        } else {
            return n * recursion(n - 1);
        }
    }

    public static void main(String[] args) {
        System.out.println("result = " + recursion(16));
    }
}

public class Factorial {
	public static int recursion(int n) {
		if (n < 0 || n > 16) {
			System.err.println("n must be great than 0 and less than 17");
			return -1;
		} else if (n == 0) {
			return 1;
		} else {
			return n * recursion(n - 1);
		}
	}

	public static void main(String[] args) {
		System.out.println("result = " + recursion(16));
	}
}

 运行结果：result = 2004189184

3.使用BigInteger

import java.math.BigInteger;

public class Factorial {
    public static BigInteger bigInteger(int n) {
        BigInteger result = new BigInteger("1");
        if (n < 0) {
            System.err.println("n must be great than 0");
            return new BigInteger("-1");
        } else if (n == 0) {
            return new BigInteger("1");
        } else {
            for (int i = 1; i <= n; i++) {
                BigInteger num = new BigInteger(String.valueOf(i));
                result = result.multiply(num);
            }
            return result;
        }
    }

    public static void main(String[] args) {
        System.out.println("result = " + bigInteger(100));
    }
}

import java.math.BigInteger;

public class Factorial {
	public static BigInteger bigInteger(int n) {
		BigInteger result = new BigInteger("1");
		if (n < 0) {
			System.err.println("n must be great than 0");
			return new BigInteger("-1");
		} else if (n == 0) {
			return new BigInteger("1");
		} else {
			for (int i = 1; i <= n; i++) {
				BigInteger num = new BigInteger(String.valueOf(i));
				result = result.multiply(num);
			}
			return result;
		}
	}

	public static void main(String[] args) {
		System.out.println("result = " + bigInteger(100));
	}
}

 运行结果：result = 93326215443944152681699238856266700490715968264381621468592963895

217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000