原始数字魔方(3*3的二维矩阵) 旋转后 得到目标数字魔方(3*3的二维矩阵)

问题描述：原始数字魔方是个3*3的数字矩阵，内部元素从1到9，如下：

1	2	3
4	5	6
7	8	9

它有如下的子魔方


每个子魔方可以进行的旋转操作



现在给定一个目标魔方，问原始魔方最少经过多少次旋转可以得到目标魔方？例如，若目标魔方为

5	4	1
6	2	3
7	8	9

则程序输出应当为3.
程序如下：
1. 输入二维矩阵initArr，其第block[ii]子魔方旋转α度后得到的矩阵rotatedArr。void MagicCubeRotation(int **initArr, int **rotatedArr, int row, int col, int block, int n)
{
int rowBorderLeft = 0, rowBorderRight = 0, colBorderLeft = 0, colBorderRight = 0;
if (block == 1)
{
rowBorderLeft = 0; rowBorderRight = 1; colBorderLeft = 0;colBorderRight = 1;
}
else if(block == 2)
{
rowBorderLeft = 0; rowBorderRight = 1; colBorderLeft = 1;colBorderRight = 2;
}
else if (block == 3)
{
rowBorderLeft = 1; rowBorderRight = 2; colBorderLeft = 0;colBorderRight = 1;
}
else if (block == 4)
{
rowBorderLeft = 1; rowBorderRight = 2; colBorderLeft = 1;colBorderRight = 2;
}
else
{
cout << "Error input block." << endl;
return;
}

for (int ii=0; ii<row; ++ii)
memcpy(&rotatedArr[ii][0], &initArr[ii][0], col*sizeof(int));

switch(n)
{
case 0:
break;
case 90:
rotatedArr[rowBorderLeft][colBorderRight] = initArr[rowBorderLeft][colBorderLe
4000
ft];
rotatedArr[rowBorderRight][colBorderRight] = initArr[rowBorderLeft][colBorderRight];
rotatedArr[rowBorderLeft][colBorderLeft] = initArr[rowBorderRight][colBorderLeft];
rotatedArr[rowBorderRight][colBorderLeft] = initArr[rowBorderRight][colBorderRight];
break;
case 180:
rotatedArr[rowBorderRight][colBorderRight] = initArr[rowBorderLeft][colBorderLeft];
rotatedArr[rowBorderRight][colBorderLeft] = initArr[rowBorderLeft][colBorderRight];
rotatedArr[rowBorderLeft][colBorderRight] = initArr[rowBorderRight][colBorderLeft];
rotatedArr[rowBorderLeft][colBorderLeft] = initArr[rowBorderRight][colBorderRight];
break;
case 270:
rotatedArr[rowBorderRight][colBorderLeft] = initArr[rowBorderLeft][colBorderLeft];
rotatedArr[rowBorderLeft][colBorderLeft] = initArr[rowBorderLeft][colBorderRight];
rotatedArr[rowBorderRight][colBorderRight] = initArr[rowBorderRight][colBorderLeft];
rotatedArr[rowBorderLeft][colBorderRight] = initArr[rowBorderRight][colBorderRight];
break;
default :
cout << "Error input parameter. " << endl; break;
}
}2. 判断两个二维矩阵是否相等。bool IsEqual2DMatrix(int **tarArr, int **rotatedArr, int row, int col)
{
for(int ii=0; ii<row; ++ii)
{
for (int jj=0; jj<col; ++jj)
{
if (tarArr[ii][jj] != rotatedArr[ii][jj])
return false;
}
}

return true;
}3. 判断block[ii]块旋转α度后是否与目标魔方相等。void GetMagCubeRotatedResult(int **inArr, int **outArr, int **tarArr, int row, int col, int block, int angle, int *flag)
{
if (*flag == 1)
return;

MagicCubeRotation(inArr, outArr, row, col, block, angle);
if (IsEqual2DMatrix(tarArr, outArr, row, col))
{
*flag = 1;
}

return;
}4. 二维数组拷贝。void MatrixCopy2D(int **&arr1, int **arr2, int row, int col)
{
for (int ii=0; ii<row; ++ii)
memcpy(&arr1[ii][0], &arr2[ii][0], col*sizeof(int));
}5. 计算需要旋转的次数。void CalcMagicCubeRotationTimes(int **&initArr, int **&outArr, int **&tarArr, int row, int col,
int *block, int num, int *angRotate, int count, int depth)
{
if ( count > 4 || depth > 4)
return ;

int ** tmp= new int *[row];
int ** tmp2= new int *[row];
int flag = 0, lock1 = 1, lock2 = 1;
for(int ii = 0; ii < row; ii ++)
{
tmp[ii] = new int[col];
tmp2[ii] = new int[col];
}

MatrixCopy2D(tmp, initArr, row, col);
for (int ii=0; ii<4; ++ii)
{
MatrixCopy2D(initArr, tmp, row, col);
GetMagCubeRotatedResult(initArr, outArr, tarArr, row, col, block[num], angRotate[ii], &flag);
MatrixCopy2D(tmp2, outArr, row, col);
// cout << block[num] << "(" << angRotate[ii] << ") ";

if ( angRotate[ii] != 0 && lock1)
{
++(count);
lock1 = 0;
}

if (flag)
{
cout << "一共需要旋转" << count << "次" << endl;
getchar();getchar();break;
}
else
{
if (lock2)
{
++(depth);
lock2 = 0;
}
// cout << depth << "深度时旋转了" << count << "次" << endl;

switch(num)
{
case 0:
CalcMagicCubeRotationTimes(tmp2, outArr, tarArr, row, col, block, 1, angRotate, count, depth);
CalcMagicCubeRotationTimes(tmp2, outArr, tarArr, row, col, block, 2, angRotate, count, depth);
CalcMagicCubeRotationTimes(tmp2, outArr, tarArr, row, col, block, 3, angRotate, count, depth);
break;

case 1:
CalcMagicCubeRotationTimes(tmp2, outArr, tarArr, row, col, block, 0, angRotate, count, depth);
CalcMagicCubeRotationTimes(tmp2, outArr, tarArr, row, col, block, 2, angRotate, count, depth);
CalcMagicCubeRotationTimes(tmp2, outArr, tarArr, row, col, block, 3, angRotate, count, depth);
break;

case 2:
CalcMagicCubeRotationTimes(tmp2, outArr, tarArr, row, col, block, 0, angRotate, count, depth);
CalcMagicCubeRotationTimes(tmp2, outArr, tarArr, row, col, block, 1, angRotate, count, depth);
CalcMagicCubeRotationTimes(tmp2, outArr, tarArr, row, col, block, 3, angRotate, count, depth);
break;

case 3:
CalcMagicCubeRotationTimes(tmp2, outArr, tarArr, row, col, block, 1, angRotate, count, depth);
CalcMagicCubeRotationTimes(tmp2, outArr, tarArr, row, col, block, 2, angRotate, count, depth);
CalcMagicCubeRotationTimes(tmp2, outArr, tarArr, row, col, block, 0, angRotate, count, depth);
break;

default:
cout << "Error" << endl; break;
}

}
}

for(int ii = 0; ii < row; ii ++)
{
delete [] tmp[ii] ;
delete [] tmp2[ii];
}

return;
}6. 主函数。int main(int argc, char **argv)
{
const int row = 3, col = 3;
int mInitArr[][col] = {1,2,3,4,5,6,7,8,9};
//int mTarArr[][col] = {4, 1, 3, 5, 2, 6, 7, 8, 9}; //1
//int mTarArr[][col] = {2, 5, 3, 1, 4, 6, 7, 8, 9}; //1
//int mTarArr[][col] = {2, 4, 5, 1, 6, 3, 7, 8, 9}; //2
int mTarArr[][col] = {5, 4, 1, 6, 2, 3, 7, 8, 9}; //3
//int mTarArr[][col] = {4, 2, 1, 5, 8, 6, 7, 9, 3};

int block[] = {1, 2, 3, 4};
int angRotate[] = {0, 90, 180, 270};
int rotateCnt = 0;
int minCnt = 100;
int judgeContinueFlag = 1;
int flag = 0;
int count = 0;
int depth = 0;

int ** initArr= new int *[row];
for(int i = 0; i < row; i ++)
initArr[i] = new int[col];

int ** tarArr= new int *[row];
for(int i = 0; i < row; i ++)
tarArr[i] = new int[col];

int ** outArr= new int *[row];
for(int i = 0; i < row; i ++)
outArr[i] = new int[col];

for (int ii=0; ii<row; ++ii)
{
for (int jj=0; jj<col; ++jj)
{
initArr[ii][jj] = mInitArr[ii][jj];
tarArr[ii][jj] = mTarArr[ii][jj];
outArr[ii][jj] = 0;
}
}

cout << "原始矩阵：" << endl;
for (int ii=0; ii<row; ++ii)
{
for (int jj=0; jj<col; ++jj)
cout <<ii*col+jj+1 << " ";
cout << endl;
}
cout << endl;

cout << "目标矩阵：" << endl;
for (int ii=0; ii<row; ++ii)
{
for (int jj=0; jj<col; ++jj)
cout <<mTarArr[ii][jj] << " ";
cout << endl;
}
cout << endl;

CalcMagicCubeRotationTimes(initArr, outArr, tarArr, row, col,
block, 0, angRotate, count, depth);

getchar();getchar();
return 0;
}7. 输出结果：