初级系列1.百钱百鸡问题

百钱百鸡问题

问题描述

一只公鸡值五钱，一只母鸡值三钱，三只小鸡值一钱，现在要用百钱买百鸡，请问公鸡，母鸡，小鸡各多少只？

问题分析
|--公鸡的数量应该在0 - 20之间
|--同理母鸡的数量应该在0 - 33之间
|--将公鸡，母鸡，小鸡的数量分别设为
cock,hen,chicken
则cock + hen + chicken = 100 将问题转化为解不定方程组的问题
不定方程组：
cock + hen + chicken = 100
5cock + 3hen + chicken/3 = 100
算法设计
穷举法,三重循环 时间复杂度 (n^3)

#include <stdio.h>

int main(void)
{
	int cock, hen, chicken;

	for (cock = 0; cock <= 20; cock++) {    /* !<外层循环控制公鸡数量取值范围0~20 */
		for (hen = 0; hen <= 33; hen++) {   /* !<内层循环控制母鸡数量取值范围0~33 */
			for (chicken = 0; chicken <= 100; chicken++) {  
                /* !<内层循环控制小鸡数量取值访问0-100 */
				if ((5*cock + 3*hen + chicken/3.0 == 100) && 
                    (cock + hen + chicken == 100)) {
					printf("cock = %2d, hen = %2d, chicken = %2d\n", cock, hen, chicken);
				}
			}
		}
	}
}

/* !< output */
cock, hen, chicken = 0 25 75
cock, hen, chicken = 4 18 78
cock, hen, chicken = 8 11 81
cock, hen, chicken = 12 4 84

#!/bin/python3
cocks = 20
hens = 33
chickens = 100
for cock in range(cocks):
	for hen in range(hens):
		for chicken in range(chickens):
			if cock + hen + chicken == 100 and cock * 5 + hen *3 + chicken / 3.0 == 100:
				print("cock, hen, chicken =", cock, hen, chicken)
/* !< output */
cock, hen, chicken = 0 25 75
cock, hen, chicken = 4 18 78
cock, hen, chicken = 8 11 81
cock, hen, chicken = 12 4 84