C语言三阶幻方求解

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1、//三阶幻方.cpp:Definestheentrypointfortheconsoleapplication./******************************************************操作系统：WindowsXP**编译环境：MicrosoftVisualC++6.0****程序编写：万传华**联系邮箱：wanchuanhua@sina.com******************************************************///求解幻方//abc

2、//def//ghi//a+e+i=15//b+e+h=15//c+e+g=15//d+e+f=15//->(a+b+c+d)+(i+h+g+f)+4*e=60//->(a+b+c+d+e+f+g+h+i)+3*e=60//->3*15+3*e=60//->e=5//f=15-e-d=10-d,g=15-e-c=10-c=10-(15-a-b)=a+b-5,//h=15-e-b=10-b,i=15-e-a=10-a,//a+d+g=15//a+d+(15-c-e)=15//a+d+(15-(15-a-b)-5)

3、=15//2*a+b+d=20//同理2*c+b+f=20,2*g+d+h=20,2*i+f+h=20//用a、b两个未知数可解其它//ab15-a-b//20-2*a-b52*a+b-10//a+b-510-b10-a//需要检验//1.数字是否重复//2.数字范围[1,9]//a,b,5,(15-a-b),(20-2*a-b),(2*a+b-10),(a+b-5),(10-b),(10-a)两两不等->//a<>b,a<>5,b<>5,a+b<>10,2*a+b<>15,a+2*b<>15,3*a+b<>2

4、0,3*a+2*b<>25//1<=a<=9,1<=b<=9,1<=15-a-b<=9,1<=20-2*a-b<=9,1<=2*a+b-10<=9,1<=a+b-5<=9,1<=10-b<=9,1<=10-a<=9->//1<=a<=9,1<=b<=9,6<=a+b<=14,11<=2*a+b<=19//假如a=1,根据11<=2*a+b<=19,1<=b<=9,9<=a+b<=14,可得b=9,可是a+b<>10,故b无解//假如a=2,b=7或者9,满足所有条件//......//#include"stda

5、fx.h"#include#include#includevoidtest(){inti,j,count=0;for(i=1;i<10;++i){if(i==5)continue;for(j=1;j<10;++j){if(i==j)continue;if(j==5)continue;if(i+j<6)continue;if(i+j>14)continue;if(2*i+j<11)continue;if(2*i+j>19)continue;if(i+j==1

6、0)continue;if(2*i+j==15)continue;if(i+2*j==15)continue;if(3*i+j==20)continue;if(3*i+2*j==25)continue;printf("第%d解：",++count);printf("t%d,%d,%d",i,j,15-i-j);printf("t%d,%d,%d",20-2*i-j,5,2*i+j-10);printf("t%d,%d,%d",i+j-5,10-j,10-i);}}printf("共

7、找到%d解",count);};voidshow(int*M,unsignedrows,unsignedcols){printf("");for(unsignedi=0;i1，未知数WZS>1，FCS<=WZS//int*M,每行一个表达式(共FCS行)，共WZS+1列(加常数列)intgcd(inta

8、,intb){intc;//处理b>a的情况if(b>a){c=a,a=b,b=c;}do{c=a%b,a=b,b=c;}while(c);returna;};//整数型方程//方程数FCS>1，未知数WZS>1，FCS<=WZS//int*M,每行一个表达式(共FCS行)，共WZS+1列(加常数列)voidEquation(int*M,unsignedFCS,unsignedWZS)