搬山

设有n座山，计算机与人作为比赛的双方，轮流搬山。规定每次搬山数不能超过k座，谁搬最后一座淮输。游戏开始时，计算机请人输入山的总数n和每次允许搬山的最大数k，然后请人开始，等人输入了需要搬走的山的数目后，计算机马上打印出它搬多少座山，并提示尚余多少座山。双方轮流搬山直到最后一座山搬完为止。计算机会显示谁是赢家，并问人是否要继续比赛。如果人不想玩了，计算机便会统计出共玩了几局，双方胜负如何。

问题分析

程序中先输入山的座数，要求每次搬山的最大数，从而找出最佳的搬山座数以获得游戏的胜利。

程序在若干次游戏结束后还记录了电脑跟人的胜负次数。程序中应用了条件语句、循环语句和逻辑判断语句来实现功能。

在有n座山的情况下，计算机为了将最后一座山留给人，而且又要控制每次搬山的数目不超过最大数k，应搬山的数目要满足关系：(n-1)%(k+1)。

算法设计

计算机参加游戏时应遵循下列原则：

(1) 当剩余山的数目-1≤可移动的最大数k时，计算机要移（剩余山数目-1）座，以便将最后一座山留给人。

(2) 对于任意正整数x，y，一定有：

0≤x%(y+1)≤y

在有n座山的情况下，计算机为了将最后一座山留给人，而且又要控制每次搬山的数目不超过最大数k，则它应搬山的数目要满足下列关系：

(n-1)%(k+1)

如果算出结果为0，即整除无余数，则规定只搬一座山，以防止冒进后发生问题。

#include<stdio.h>int main(){    int n, k, x, y, cc, pc, g;    printf("More Mountain Game\n");    printf("Game Begin\n");    pc=cc=0;    g=1;    for( ; ; )    {        printf("No.%2d game \n", g++);        printf("-------------\n");        printf("How many mountains are there?");        scanf("%d", &n);  /*读入山的总数*/        if(!n)            break;        printf("How many mountains are allowed to each time?");        do        {            scanf("%d", &k);  /*读入允许的搬山数*/            if(k>n || k<1)  /*判断搬山数*/                printf("Repeat again!\n");        }        while(k>n || k<1);        do        {            printf("How many mountains do you wish move away?");            scanf("%d",&x);            if(x<1 || x>k || x>n)  /*判断搬山数是否符合要求*/            {                printf("IIIegal,again please!\n");                continue;            }            n-=x;            printf("There are %d mountains left now.\n", n);            if(!n)            {                printf("……………I win. You are failure……………\n\n");                cc++;            }            else            {                y=(n-1)%(k+1);  /*求出最佳搬山数*/                if(!y)                    y=1;                n-=y;                printf("Copmputer move %d mountains away.\n", y);                if(n)                    printf(" There are %d mountains left now.\n", n);                else                {                    printf("……………I am failure. You win………………\n\n");                    pc++;                }            }        }        while(n);    }    /*打印结果*/    printf("Games in total have been played %d.\n", cc+pc);    printf("You score is win %d,lose %d.\n", pc, cc);    printf("My score is win %d,lose %d.\n", cc, pc);    return 0;}

运行结果：
More Mountain Game
Game Begin
No. 1 game
-------------
How many mountains are there?10↙︎
How many mountains are allowed to each time?3↙︎
How many mountains do you wish move away?5↙︎
IIIegal,again please!
How many mountains do you wish move away?2↙︎
There are 8 mountains left now.
Copmputer move 3 mountains away.
There are 5 mountains left now.
How many mountains do you wish move away?3↙︎
There are 2 mountains left now.
Copmputer move 1 mountains away.
There are 1 mountains left now.
How many mountains do you wish move away?1↙︎
There are 0 mountains left now.
……………I win. You are failure……………