大数值阶乘计算函数

      阶乘往往由于数值巨大而无法用一个long int或者double类型数据保存。近日无聊写了个大数值阶乘的计算函数，理论上只要内存足够，能够计算出任何数值的阶乘，但实际上100万以上的阶乘计算不管是时间消耗还是内存消耗都是极为惊人的，建议使用该函数计算100万以下的阶乘。

      为了有足够的空间保存结果，用一个vector<unsigned long int>保存，每个unsigned long int保存8位结果，vector大小由结果位数决定。本程序主体主要包含两个函数，阶乘计算函数和结果显示函数，定义在Factorial.h中。

      代码如下：

#pragma once#include <vector>#include <math.h>using namespace std;#define MAX_FIGURE 8 //定义每个unsigned long int保存的最大十进制位数#define MAX_NUMBER 100000000 //定义每个unsigned long int保存的最大十进制数上限（不能等于）//该函数计算任意位阶乘//num：输入，阶乘的阶；result：输出阶乘的结果，可能会很长void ComputeFactorial(const unsigned int num, vector<unsigned long int> &result ){result.clear(); result.push_back(1);if ( num == 0 || num == 1 || num >= MAX_NUMBER ){return;}unsigned long int nFigure = 1; //位数vector<unsigned long int> result0 = result;vector<unsigned long int> result1;for ( unsigned int k = 2; k <= num; k++ ){nFigure = (int) log10(1.0*k) + 1;unsigned int n = k;unsigned int multi = 1;result1.clear();for ( unsigned int i = 1; i <= nFigure; i++ ){unsigned int m = n%10;result0 = result;unsigned int size = result0.size();unsigned long int stemp = 0;for ( unsigned int j = 0; j < size; j++ ){unsigned long int temp = result[j]*m + stemp;stemp = temp / MAX_NUMBER;result0[j] = temp % MAX_NUMBER;}if ( stemp != 0 ){result0.push_back(stemp);}size = result0.size();stemp = 0;for ( unsigned int j = 0; j < size; j++ ){unsigned long int temp = MAX_NUMBER / multi;unsigned long int temp2 = result0[j];result0[j] = (result0[j] % temp) * multi + stemp;stemp = temp2 / temp;}if ( stemp != 0 ){result0.push_back(stemp);}unsigned int n0 = result0.size(), n1 = result1.size(), m0 = 0;size = min(n0, n1);stemp = 0;for ( unsigned int j = 0; j < size; j++ ){unsigned int temp = result0[j] + result1[j] + stemp;result1[j] = temp % MAX_NUMBER;stemp = temp / MAX_NUMBER;m0 = j+1;}if ( n0 == n1 && stemp != 0 ){result1.push_back(stemp);}if ( n0 > n1 ){for ( unsigned int j = m0; j < n0; j++ ){unsigned int temp = result0[j] + stemp;result1.push_back( temp % MAX_NUMBER );stemp = temp / MAX_NUMBER;}if ( stemp != 0 ){result1.push_back(stemp);}}if ( n0 < n1 ){for ( unsigned int j = m0; j < n1; j++ ){unsigned int temp = result1[j] + stemp;result1[j] = temp % MAX_NUMBER;stemp = temp / MAX_NUMBER;}if ( stemp != 0 ){result1.push_back(stemp);}}multi = multi*10;n = n / 10;}result = result1;}}//输出计算结果void DisplayTheResult(const vector<unsigned long int> &result){int size = result.size();if ( size < 4 ){for ( int i = (size-1); i >= 0; i-- ){cout << result[i] << " ";}}else{unsigned long int nFigure = 0;unsigned long int temp1, temp2;bool start = true;temp1 = MAX_NUMBER / 10, temp2 = result[size-1];for ( int j = 0; j < MAX_FIGURE; j++ ){unsigned long int temp = temp2 / temp1;if ( temp == 0 ){if ( start ) cout << " ";else {nFigure++;cout << temp;}}else{start = false;nFigure++;cout << temp;}temp2 = temp2 % temp1;temp1 = temp1 / 10;}cout << " ";int p = 1;double nb = pow( 10.0, 1.0*(nFigure-1) );for ( int i = (size-2); i >= 0; i-- ){if ( (p%10) == 0 ) cout << endl;temp1 = MAX_NUMBER / 10, temp2 = result[i];for ( int j = 0; j < MAX_FIGURE; j++ ){unsigned long int temp = temp2 / temp1;nFigure++;cout << temp;temp2 = temp2 % temp1;temp1 = temp1 / 10;}cout << " " ;p++;}//以科学计数方式输出cout << endl << " = " ;double dresult = result[size-1] / nb;cout << dresult;for ( int i = (size-2); i >= max(0, size - 6); i-- ){nb = nb*MAX_NUMBER;dresult = dresult + result[i] / nb;cout << result[i];}cout << "E+" << nFigure-1 << endl;}cout << endl;}

 

        测试代码main.cpp：

#include <iostream>#include <iomanip>#include <Windows.h>#include <time.h>#include "Factorial.h"using namespace std;void main(){HANDLE hOut = GetStdHandle(STD_OUTPUT_HANDLE); SetConsoleTitle(L"计算大数阶乘");COORD size = {92, 10000};SetConsoleScreenBufferSize(hOut,size); // 重新设置缓冲区大小SMALL_RECT rc = {0,0, 92-1, 50-1}; // 重置窗口位置和大小SetConsoleWindowInfo(hOut, true, &rc);cout << "该程序测试任意数的阶乘。/n/n";char ch = 'y';while ( ch == 'y' || ch == 'Y' ){cout << "请输入阶乘的阶（大于或等于0的正整数）：";unsigned int num = 0;cin >> num;vector<unsigned long int> result;clock_t start, end;start = clock();ComputeFactorial(num, result);end = clock();cout << num << "! = " << endl;DisplayTheResult(result); //输出结果unsigned long int temp = (unsigned long int) end - start, hour, min, sec;cout << "计算共用时：" << temp ;temp = temp / CLOCKS_PER_SEC;hour = temp / 3600;temp = temp % 3600;min = temp / 60;temp = temp % 60;sec = temp;cout << "ms，即" << hour << "小时" << min << "分钟" << sec << "秒。" << endl;cout << "/n是否继续计算其它值，是请输入Y或者y，否则输入其它字母：" ;cin >> ch;cout << endl << endl;}}

 

        经过测试，10万的阶乘计算时间为274489ms，即4分34秒。这个速度受电脑配置影响，这是在E5300，2G DDRII 800的硬件条件下测试出来的。

        下面是测试结果图：

         小数阶乘：

 

         1000阶乘：

         下面是系统计算机计算1000!的阶乘结果：

 

         1万大数阶乘，耗时1529毫秒：

 

         10万大数阶乘：

 

      该函数计算阶乘速度不算很快，还有很大的改进空间。