public static void TestMaxSubMatrixWithAllOnes()
{
MaxSubMatrixWithAllOnes maxSubMat = new MaxSubMatrixWithAllOnes();
int[,] mat = new int[, ] {
{ 0, 1, 1, 0, 1 }, { 1, 1, 0, 1, 0 }, { 0, 1, 1, 1, 0 }, { 1, 1, 1, 1, 0 }, { 1, 1, 1, 1, 1 }, { 0, 0, 0, 0, 0 }
};
MaxtrixOutline matOutline = maxSubMat.GetMaxMatrix(mat);
Console.WriteLine("The matrix outline of the max matrix is {0},{1} and the size is {2}", matOutline.RightmostRow, matOutline.RightmostCol, matOutline.SizeOfMatrix);
mat = new int[, ] {
{ 1, 1, 1, 1, 1 }, { 1, 1, 1, 1, 1 }, { 1, 1, 1, 1, 1 }, { 1, 1, 1, 1, 1 }, { 1, 1, 1, 1, 1 }, { 1, 1, 1, 1, 1 }
};
matOutline = maxSubMat.GetMaxMatrix(mat);
Console.WriteLine("The matrix outline of the max matrix is {0},{1} and the size is {2}", matOutline.RightmostRow, matOutline.RightmostCol, matOutline.SizeOfMatrix);
}
/// <summary>
/// We can solve this problem using dynamic programming
/// we need to create a new matrix maxSubMatrix
///
/// the dynamic programming equation is as follows:
/// intialize the maxSubMatrix[0,j] and maxSubMatrix[i,0] to mat[0,j] and mat[i,0] respectively
/// maxSubMatrix[i,j] = min{maxSubMatrix[i-1,j], maxSubMatrix[i,j-1], maxSubMatrix[i-1,j-1]} +1 if mat[i,j] ==1
/// 0 if mat[i,j] == 0
/// </summary>
/// <param name="mat"></param>
/// <returns></returns>
public MaxtrixOutline GetMaxMatrix(int[,] mat)
{
int[,] maxSubMatrix = new int[mat.GetLength(0), mat.GetLength(1)];
// initialization
for (int i = 0; i < mat.GetLength(0); i++)
{
maxSubMatrix[i, 0] = mat[i, 0];
}
for (int j = 0; j < mat.GetLength(1); j++)
{
maxSubMatrix[0, j] = mat[0, j];
}
int maxMatrixSize = 0;
MaxtrixOutline matOutline = null;
for (int i = 1; i < mat.GetLength(0); i++)
{
for (int j = 1; j < mat.GetLength(1); j++)
{
if (mat[i, j] == 1)
{
maxSubMatrix[i, j] = Math.Min(Math.Min(maxSubMatrix[i - 1, j], maxSubMatrix[i, j - 1]), maxSubMatrix[i - 1, j - 1]) + 1;
if (maxMatrixSize < maxSubMatrix[i, j])
{
// this is the rightmost corner of the matrix with maxSize
matOutline = new MaxtrixOutline(i, j, maxSubMatrix[i, j]);
maxMatrixSize = maxSubMatrix[i, j];
}
}
else
{
maxSubMatrix[i, j] = 0;
}
}
}
return(matOutline);
}
