#include <stdio.h>
#define MAXMATRIXSIZE 100
int MatrixPrint(int nMatrixSize);
void ClearMartix(int Martrix[MAXMATRIXSIZE][MAXMATRIXSIZE]);
int MatrixCau(int Martrix[MAXMATRIXSIZE][MAXMATRIXSIZE],
int xPoint,int yPoint,int nMatrixSize );
bool CanEqualTo(int Martrix[MAXMATRIXSIZE][MAXMATRIXSIZE],
int xPoint,int yPoint,int nValue);
void PrintMatrix(int Martrix[MAXMATRIXSIZE][MAXMATRIXSIZE],int nMatrixSize);
int main(int argc ,char * argv[])
{
int nMatrixSize=1;
printf("请输入拉丁方阵的大小:\n");
if(scanf("%d",&nMatrixSize) == 0 ||
nMatrixSize <= 0)
{
printf("你输入的不是一个大于零的整数!\n");
return 1;
}
else if(nMatrixSize > MAXMATRIXSIZE)
{
printf("你输入数超出了设定的最大值!\n");
return 1;
}
int nSize = MatrixPrint(nMatrixSize);
printf("拉丁方阵的总数:%d\n",nSize);
return 0;
}
int MatrixPrint(int nMatrixSize)
{
int nSize = 0;
int MATRIX[MAXMATRIXSIZE][MAXMATRIXSIZE];
ClearMartix(MATRIX);
return MatrixCau(MATRIX,0,0,nMatrixSize);
}
void ClearMartix(int Martrix[MAXMATRIXSIZE][MAXMATRIXSIZE])
{
for(int i=0 ; i<MAXMATRIXSIZE ; i++)
{
for(int j=0 ; j<MAXMATRIXSIZE ; j++)
{
Martrix[i][j] = 0;
}
}
}
void PrintMatrix(int Martrix[MAXMATRIXSIZE][MAXMATRIXSIZE],int nMatrixSize)
{
for(int i=0 ; i<nMatrixSize ; i++)
{
for(int j=0 ; j<nMatrixSize ; j++)
{
printf("%3d",Martrix[i][j]);
}
printf("\n");
}
printf("\n");
}
bool CanEqualTo(int Martrix[MAXMATRIXSIZE][MAXMATRIXSIZE],
int xPoint,int yPoint,int nValue)
{
for(int i=0 ; i<xPoint ; i++)
{
if(Martrix[yPoint][i] == nValue)
{
return false;
}
}
for(int j=0 ; j<yPoint ; j++)
{
if(Martrix[j][xPoint] == nValue)
{
return false;
}
}
return true;
}
int MatrixCau(int Martrix[MAXMATRIXSIZE][MAXMATRIXSIZE],
int xPoint,int yPoint,int nMatrixSize )
{
int nSize = 0;
for(int i = 1 ; i <= nMatrixSize ; i++ )
{
if(CanEqualTo(Martrix,xPoint,yPoint,i))
{
Martrix[yPoint][xPoint] = i;
if(xPoint ==nMatrixSize-1 && yPoint == nMatrixSize-1)
{
PrintMatrix(Martrix,nMatrixSize);
nSize += 1;
continue;
}
if(xPoint == nMatrixSize-1 )
{
nSize += MatrixCau(Martrix,0,yPoint+1,nMatrixSize);
}
else
{
nSize += MatrixCau(Martrix,xPoint+1,yPoint,nMatrixSize);
}
}
}
return nSize;
}
