24点游戏的一种解法

题目：给你4个正整数，这4个正整数的范围是1到13.问这四个数可否通过加减乘除的不同组合（可以使用括号）得到最终结果24.假如有这样的组合，那么给出这种组合的具体表达式。

 

分析：最简单直接的办法就是穷举每一个组合，及计算每一种组合的结果，看其是否有结果24.

解决方法：可以从原来数组中任意取出两个数，然后依次计算这两个数的加、减、乘、除，将计算结果放入原来的数组，并把取出来的两个数从原来数组中删除。依次规则进行，直到数组中只剩下一个数，这就是这个组合的运算结果。以上步骤中“任意取两个数”其实对应于任意数的组合，并加括号。

 

下面是本题的一个C语言实现：

#include<stdio.h>
#include<math.h>
#include<string.h>

int is_this_right(double* array,char result[][50],int n)
{
       if(n==1)
       {
               if(fabs(array[0]-24.0)<0.001) //因为有除法，所以用实数存结果，并允许有一定误差
               {
                       printf("%s\n",result[0]);
                       return 1;
               }
               else
                       return 0;
       }
       int i,j;
       for(i=0;i<n;i++)
               for(j=i+1;j<n;j++)
               {
                       double a,b,temp;
                       char s_a[50]={},s_b[50]={},s_temp[50]={};
                       a=array[i];
                       strcpy(s_a,result[i]);
                       b=array[j];
                       strcpy(s_b,result[j]);

                       array[j]=array[n-1];
                       strcpy(result[j],result[n-1]);

                       temp=a+b;
                       strcpy(s_temp,"(");
                       strcat(s_temp,s_a);
                       strcat(s_temp,"+");
                       strcat(s_temp,s_b);
                       strcat(s_temp,")");

                       array[i]=temp;
                       strcpy(result[i],s_temp);
                       if(is_this_right(array,result,n-1))
                               return 1;

                       temp=a-b;
                       strcpy(s_temp,"(");
                       strcat(s_temp,s_a);
                       strcat(s_temp,"-");
                       strcat(s_temp,s_b);
                       strcat(s_temp,")");

                       array[i]=temp;
                       strcpy(result[i],s_temp);
                       if(is_this_right(array,result,n-1))
                               return 1;

                       temp=b-a;
                       strcpy(s_temp,"(");
                       strcat(s_temp,s_b);
                       strcat(s_temp,"-");
                       strcat(s_temp,s_a);
                       strcat(s_temp,")");

                       array[i]=temp;
                       strcpy(result[i],s_temp);
                       if(is_this_right(array,result,n-1))
                               return 1;

                       temp=a*b;
                       strcpy(s_temp,"(");
                       strcat(s_temp,s_a);
                       strcat(s_temp,"*");
                       strcat(s_temp,s_b);
                       strcat(s_temp,")");

                       array[i]=temp;
                       strcpy(result[i],s_temp);
                       if(is_this_right(array,result,n-1))
                               return 1;

                       temp=a/b;
                       strcpy(s_temp,"(");
                       strcat(s_temp,s_a);
                       strcat(s_temp,"/");
                       strcat(s_temp,s_b);
                       strcat(s_temp,")");

                       array[i]=temp;
                       strcpy(result[i],s_temp);
                       if(is_this_right(array,result,n-1))
                               return 1;

                       temp=b/a;
                       strcpy(s_temp,"(");
                       strcat(s_temp,s_b);
                       strcat(s_temp,"/");
                       strcat(s_temp,s_a);
                       strcat(s_temp,")");

                       array[i]=temp;
                       strcpy(result[i],s_temp);
                       if(is_this_right(array,result,n-1))
                               return 1;

                       array[i]=a;
                       strcpy(result[i],s_a);
                       array[j]=b;
                       strcpy(result[j],s_b);
               }
       return 0;
}

int main()
{
       int i;
       double array_of_four_numbers[4];
       char result[4][50];
       printf("please input the four numbers:\n");
       scanf("%lf",array_of_four_numbers);
       scanf("%lf",array_of_four_numbers+1);
       scanf("%lf",array_of_four_numbers+2);
       scanf("%lf",array_of_four_numbers+3);
       sprintf(result[0],"%lf",array_of_four_numbers[0]);
       sprintf(result[1],"%lf",array_of_four_numbers[1]);
       sprintf(result[2],"%lf",array_of_four_numbers[2]);
       sprintf(result[3],"%lf",array_of_four_numbers[3]);

       if(!is_this_right(array_of_four_numbers,result,4))
               printf("can not get the result 24 use the four numberinputed.\n");
       return 0;
}