C趣味程序百例(19)由8個整數(shù)形成奇特的立方體

62.由8個整數(shù)形成奇特的立方體
     任意給出8個整數(shù)，將這8個整數(shù)分別放在一個立方體的八個頂點(diǎn)上，要求每個面上的四個數(shù)之和相等。
    *問題分析與算法設(shè)計
     簡化問題：將8個頂點(diǎn)對應(yīng)數(shù)組中的8個元素，將“每個面上的四個數(shù)之和皆相等”轉(zhuǎn)換為數(shù)組無素之間和的相等關(guān)系。這里的關(guān)鍵在于正確地將立方體的8個頂點(diǎn)與數(shù)組的8個元素對應(yīng)。
     可以利用簡單的窮舉方法建立8個數(shù)的全部排列。
    *程序與程序注釋
    #include
    #include
    void main()
    {
     int a[9],ii=0,i,a1,a2,a3,a4,b1,b2,b3,b4,flag;
     for(i=1;i<=8;i++) /*輸入個數(shù)*/
     {
     printf("Please enter [%d]number:",i);
     scanf("%d",&a[i]);
     ii+=a[i];
     }
     printf("******************************************\n");
     if(ii%2) /*和為奇數(shù)則輸入的8個數(shù)不可用*/
     {
     printf("Sorry they can't be constructed required cube!\n");
     exit(0);
     }
     for(flag=0,a1=1;a1<=8;a1++) /*flag:完成標(biāo)記.flag=1;表示完成*/
     for(a2=1;a2<=8;a2++) /*采用八重循環(huán)建立八個整數(shù)的全排列*/
     if(a2!=a1) /*前兩個數(shù)不能相同*/
     for(a3=1;a3<=8;a3++)
     if(a3!=a2&&a3!=a1) /*前三個數(shù)不能相同*/
     for(a4=1;a4<=8;a4++)
     if(a4!=a3&&a4!=a2&&a4!=a1) /*前四個數(shù)不能相同*/
     for(b1=1;b1<=8;b1++)
     if(b1!=a4&&b1!=a3&&b1!=a2&&b1!=a1) /*不能相同*/
     for(b2=1;b2<=8;b2++)
     if(b2!=b1&&b2!=a4&&b2!=a3&&b2!=a2&&b2!=a1)
     for(b3=1;b3<=8;b3++)
     if(b3!=b2&&b3!=b1&&b3!=a4&&b3!=a3&&b3!=a2&&b3!=a1)
     /*不能取相同的數(shù)*/
     for(b4=1;b4<=8;b4++)
     if(b4!=b2&&b4!=b1&&b4!=b3&&b4!=a4&&b4!=a3&&b4!=a2&&b4!=a1)
     if(a[b1]+a[b2]+a[b3]+a[b4]==ii/2
     &&a[a1]+a[a2]+a[b1]+a[b2]==ii/2
     &&a[a1]+a[a4]+a[b1]+a[b4]==ii/2)
     {
     flag=1;goto out; /*滿足條件則將flag置1后退出*/
     }
     out:
     if(flag)
     {
     printf("They can be constructed required cube as follow:\n");
     printf(" /%2d............/%2d\n",a[a4],a[a3]);
     printf(" %2d/............%2d/|\n",a[a1],a[a2]);
     printf(" | | | |\n");
     printf(" | | | |\n");
     printf(" | %2d| | |%2d\n",a[b4],a[b3]);
     printf(" /................/\n");
     printf(" %2d/.............%2d/\n",a[b1],a[b2]);
     }
     else printf("Sorry they can't be constructed required cube!\n");
    }
    *運(yùn)行結(jié)果
     Please enter [1] number:20
     Please enter [2] number:45
     Please enter [3] number:39
     Please enter [4] number:25
     Please enter [5] number:29
     Please enter [6] number:7
     Please enter [7] number:3
     Please enter [8] number:2
     Sorry they can't be constructed required cube!