一个正整数的阶乘（英语：factorial）是所有小于及等于该数的正整数的积，并且定义0的阶乘为1。自然数n的阶乘写作n!。即n!=1×2×3×…×n。阶乘亦可以递归方式定义：0!=1，n!=(n-1)!×n。

一、 实现代码

#include <stdio.h>

// result数组的最大长度
#define MAX_LEN 4096
// result数组，存放阶乘结果
int result[MAX_LEN];
// result数组的有效长度
int len = 0;

// factorial函数的功能是计算阶乘，结果存在result数组中
// 返回值：成功为0，失败为1
int factorial(int n)
{
	int value = 0;

	// 初始化result数组及有效长度长度
	result[0] = 1;
	len = 1;

	for(int i=1; i<=n; i++)
	{
		for(int j=len-1; j>=0; j--)
		{
			value = i * result[j];
			result[j] = value % 10;
			value = value / 10;

			int k = j + 1;

			// 考虑进位，不增加result数组长度的情况
			while(value > 0 && k < len)
			{
				value = value + result[k];
				result[k] = value % 10;
				value = value / 10;
				k++;
			}

			// 考虑进位，增加result数组长度的情况
			while(value > 0)
			{
				result[len] = value % 10;
				value = value / 10;
				len++;

				if(len > MAX_LEN)
				{
					return 1;
				}
			}
		}
	}

	return 0;
}

int main(void)
{
	for(int i=0; i<=50; i++)
	{
		// 计算阶乘
		int ret = factorial(i);

		// 计算失败
		if(ret == 1)
		{
			printf("Error! Tooooooo long!!\n");
			break;
		}

		// 打印阶乘结果
		printf("%d! = ", i);
		for(int j=len-1; j>=0; j--)
			printf("%d", result[j]);
		printf("\n");
	}

	return 0;
}

二、 运行结果

[ycxie@fedora Workspace]$ gcc factorial.c -o factorial -Wall
[ycxie@fedora Workspace]$ ./factorial
0! = 1
1! = 1
2! = 2
3! = 6
4! = 24
5! = 120
6! = 720
7! = 5040
8! = 40320
9! = 362880
10! = 3628800
11! = 39916800
12! = 479001600
13! = 6227020800
14! = 87178291200
15! = 1307674368000
16! = 20922789888000
17! = 355687428096000
18! = 6402373705728000
19! = 121645100408832000
20! = 2432902008176640000
21! = 51090942171709440000
22! = 1124000727777607680000
23! = 25852016738884976640000
24! = 620448401733239439360000
25! = 15511210043330985984000000
26! = 403291461126605635584000000
27! = 10888869450418352160768000000
28! = 304888344611713860501504000000
29! = 8841761993739701954543616000000
30! = 265252859812191058636308480000000
31! = 8222838654177922817725562880000000
32! = 263130836933693530167218012160000000
33! = 8683317618811886495518194401280000000
34! = 295232799039604140847618609643520000000
35! = 10333147966386144929666651337523200000000
36! = 371993326789901217467999448150835200000000
37! = 13763753091226345046315979581580902400000000
38! = 523022617466601111760007224100074291200000000
39! = 20397882081197443358640281739902897356800000000
40! = 815915283247897734345611269596115894272000000000
41! = 33452526613163807108170062053440751665152000000000
42! = 1405006117752879898543142606244511569936384000000000
43! = 60415263063373835637355132068513997507264512000000000
44! = 2658271574788448768043625811014615890319638528000000000
45! = 119622220865480194561963161495657715064383733760000000000
46! = 5502622159812088949850305428800254892961651752960000000000
47! = 258623241511168180642964355153611979969197632389120000000000
48! = 12413915592536072670862289047373375038521486354677760000000000
49! = 608281864034267560872252163321295376887552831379210240000000000
50! = 30414093201713378043612608166064768844377641568960512000000000000