计算组合数C(m, n)

浅浅的花香味﹌ 2023-01-17 03:23 138阅读 0赞

#include<stdio.h>
    unsigned long f(unsigned short m, unsigned short n);
    unsigned long Fact(unsigned short k);
    int main()
    {
        /* 考虑到用户可能输入负数, 将m、n声明为short类型更稳妥 */
        /* 虽然f函数的两个参数均为unsigned short类型, 但实际最大值 = short类型的最大正数值 */
        short m;
        short n;
        /* 考虑到排列数可能较大, 用unsigned long类型声明更合适 */
        unsigned long result;
        /* 输入容错机制 */
        while(scanf("%hd%hd", &m, &n) != 2 || m < 1 || n < 0)
        {
            while(getchar() != '\n') ;
            printf("请输入合法数据.\n");
        }
        result = f(m, n) / Fact(n);
        if(result != 0)
        {
            printf("C(%hd, %hd) = %lu.\n", m, n, result);
        }
        else
        {
            /* 数据不合法 */
            printf("C(m, n): m >= n!\n");
        }
        /* */
        return 0;
    }
    /* 计算A(m, n) */
    unsigned long f(unsigned short m, unsigned short n)
    {
        /* 数据不合法 */
        if(n > m)
        {
            return 0;
        }
        /* */
        unsigned long S = 1;
        /* S = m * (m - 1) * (m - 2) * ... * (m - n + 1) */
        unsigned short i = m;
        while(i >= m - n + 1)
        {
            S *= i;
            i --;
        }
        /* 有趣的是, 如果n == 0, 那么循环一次都不执行, 最终结果确实也为1 */
        return S;
    }
    /* 计算k的阶乘 */
    unsigned long Fact(unsigned short k)
    {
        unsigned short i = k;
        unsigned long S = 1;
        while(i >= 1)
        {
            S *= i;
            i --;
        }
        /* 有趣的是, 如果k == 0, 那么循环一次都不执行, 最终结果也为1 */
        return S;
    }

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjA0ODQ2Mw_size_16_color_FFFFFF_t_70][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjA0ODQ2Mw_size_16_color_FFFFFF_t_70 1][]

[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjA0ODQ2Mw_size_16_color_FFFFFF_t_70]: /images/20221022/6843ffcf30b348c1a63538aa22fa0629.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjA0ODQ2Mw_size_16_color_FFFFFF_t_70 1]: /images/20221022/2eba886bee2b43aab79e6be8de14729e.png