// given two matrices, a and b, determine if they are equal in size, equal in size and number, transposed, or none
// a transposed matrix is one in which the rows of one matrix are the columns of the other as in:
//   1 2 3
//   4 5 6
// and
//   1 4
//   2 5
//   3 6
 
public class MatrixComparison
{
	public static void main(String[] args)
	{
		int[][] a = {{1, 2, 3}, {4, 5, 6}};				// assign the two matrices and their rows and columns, adjust these 3 lines to change the outcome of the progrma
		int[][] b = {{1, 2, 3}, {4, 5, 6}};
		int aRows = 2, aColumns = 3, bRows = 2, bColumns = 3;
		if(equal(a, b, aRows, aColumns, bRows, bColumns)) System.out.println("The two matrices are equal");			// test for equal
		else if(equalSize(aRows, aColumns, bRows, bColumns)) System.out.println("The two matrices are equal size but not equal content");	// test for equal size (we know they won't equal in content or the previous if would have been true)
		else if(transpose(a, b, aRows, aColumns, bRows, bColumns)) System.out.println("The two matrices are transpositions of each other");	// test for transpositions
		else System.out.println("The two matrices have nothing to do with each other");								// default when none of the others are true
	}
	
	public static boolean equal(int[][] a, int[][] b, int c, int d, int e, int f)		// do the contents of a and b match precisely?  a has dimensions [c][d] and b has dimensions [e][f]
	{
		if(c!=e||d!=f) return false;			// if not equal size, then no, not equal
		else {
			for(int i=0;i<c;i++)				// note:  c==e and d==f or we would not reach here, so we have no danger of a subscript out of range exception
				for(int j=0;j<d;j++)
					else if(a[i][j]!=b[i][j]) return false;  // if any element a[i][j] does not match b[i][j] then we have a mismatch
		}
		return true;
	}
	
	public static boolean equalSize(int a, int b, int c, int d)			// are the two matrices of equal size? we are only testing their dimensions here, aRows/aColumns to bRows/bColumns
	{
		if(a==c&&b==d) return true;
		else return false;
	}
	
	public static boolean transpose(int[][] a, int[][] b, int c, int d, int e, int f)  // same as equal method except that we are comparing each a[i][j] to b[j][i]
	{
		if(c!=f||d!=e) return false;
		else {
			for(int i=0;i<c;i++)
				for(int j=0;j<d;j++)
					else if(a[i][j]!=b[j][i]) return false;
		}
		return true;
	}
}