张丘建《算经》中提出“百鸡问题”：鸡翁一值钱五，鸡母一值钱三，鸡雏三值钱一。百钱买百鸡，问鸡翁、母、雏各几何？分析：公鸡-cocks ,母鸡-hens,小鸡-chicks cocks+hens+chicks=100 5*cocks+3*hens+chicks/3=100★ 关键: 受百钱买百鸡的约束有 0≤cocks≤19, 0≤hens≤33, 0≤chicks≤100★ 思路: 累试法(枚举法) 依次取cocks值域中的值,然后求其余两数,看是否满足题意算法描述:cocks=0 当cocks≤19时 { 找满足题意的hens,chicks数 cocks加1 }细化:cocks=0 当cocks≤19时 { hens=0 当hens≤33时 { 找满足题意的chicks数 hens加1 } cocks加1 }再细化:cocks=0 当cocks≤19时 { hens=0 当hens≤33时 { chicks=100-cocks-hens 如果 (5*cocks+3*hens+chicks/3=100) 则输出 hens加1 } cocks加1 }编写代码如下: #include "stdio.h"void main(){ int cocks, hens, chicks; printf ("cocks hens chicks\n"); printf ("-------------------\n"); cocks=0; while (cocks <= 19) { hens=0; while (hens <= 33) { chicks = 100 - cocks - hens; if ( cocks * 5 + hens * 3 + chicks / 3 == 100 ) printf ("%5d %5d %5d\n", cocks, hens, chicks); hens++; } cocks++; } printf ("-------------------\n");} 运行结果:===========================cocks hens chicks------------------- 0 25 75 3 20 77 4 18 78 7 13 80 8 11 81 11 6 83 12 4 84-------------------===========================######################################更正########################################经热心人评论指点, 做如下改正:小鸡数必须为3的倍数:算法描述:cocks=0 当cocks≤19时 { hens=0 当hens≤33时 { chicks=100-cocks-hens 如果 (5*cocks+3*hens+chicks/3=100 且 小鸡数为3的倍数) 则输出 hens加1 } cocks加1 }代码: #include "stdio.h"void main(){ int cocks, hens, chicks; printf ("cocks hens chicks\n"); printf ("-------------------\n"); cocks=0; while (cocks <= 19) { hens=0; while (hens <= 33) { chicks = 100 - cocks - hens; if ( cocks * 5 + hens * 3 + chicks / 3 == 100 && chicks % 3 == 0) printf ("%5d %5d %5d\n", cocks, hens, chicks); hens++; } cocks++; } printf ("-------------------\n");} 运行结果:===========================cocks hens chicks------------------- 0 25 75 4 18 78 8 11 81 12 4 84-------------------===========================
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