package com.mattrixwv.matrix;


import java.util.Arrays;
import java.util.StringJoiner;

import com.mattrixwv.matrix.exceptions.InvalidCoordinatesException;
import com.mattrixwv.matrix.exceptions.InvalidGeometryException;
import com.mattrixwv.matrix.exceptions.InvalidRowSizeException;
import com.mattrixwv.matrix.exceptions.InvalidScalarException;
import com.mattrixwv.matrix.exceptions.NullMatrixException;


/**
 * Represents a matrix of integers and provides various matrix operations.
 */
public class IntegerMatrix{
	/**
	 * The grid that represents the matrix
	 */
	protected int[][] grid;

	//?Helper functions
	/**
	 * Validates that all rows in the grid are of equal length.
	 *
	 * @param grid The 2D array to validate.
	 * @throws InvalidRowSizeException If the rows of the matrix are not all the same length.
	 */
	private int[][] validateGrid(int[][] grid){
		if(grid.length == 0){
			return new int[0][0];
		}
		else if(grid[0].length == 0){
			return new int[grid.length][0];
		}
		else{
			//Make sure all rows are the same length
			int length = grid[0].length;
			for(int cnt = 1;cnt < grid.length;++cnt){
				if(grid[cnt].length != length){
					throw new InvalidRowSizeException("All rows in a matrix must be the same size");
				}
			}

			//Copy every element over to a new grid
			int[][] newGrid = new int[grid.length][grid[0].length];
			for(int rowCnt = 0;rowCnt < grid.length;++rowCnt){
				newGrid[rowCnt] = Arrays.copyOf(grid[rowCnt], grid[rowCnt].length);
			}

			//Save the new grid
			return newGrid;
		}
	}
	/**
	 * Sets the matrix grid to the specified 2D array. Validates the input to ensure
	 * all rows are of equal length.
	 *
	 * @param grid The 2D array to set as the matrix grid.
	 * @throws InvalidRowSizeException If the rows of the matrix are not all the same length.
	 */
	protected void setGrid(int[][] grid){
		this.grid = validateGrid(grid);
	}
	/**
	 * Creates a deep copy of the matrix grid.
	 *
	 * @return A new IntegerMatrix instance containing the copied grid.
	 */
	protected int[][] copyGrid(){
		if(getNumCols() == 0){
			return new int[grid.length][0];
		}

		//Allocate memory for the new grid
		int[][] newGrid = new int[grid.length][grid[0].length];

		//Copy every element from the current grid to the new one
		for(int row = 0;row < grid.length;++row){
			newGrid[row] = Arrays.copyOf(grid[row], grid[row].length);
		}

		//Return the new grid
		return newGrid;
	}
	/**
	 * Checks if the matrix is a square matrix (i.e., the number of rows equals the number of columns).
	 *
	 * @return {@code true} if the matrix is square, {@code false} otherwise.
	 */
	public boolean isSquare(){
		if(getNumRows() == 0){
			return false;
		}
		else{
			return getNumRows() == getNumCols();
		}
	}
	/**
	 * Creates a new matrix with the specified row and column removed.
	 * This matrix is smaller by one row and one column than the current matrix.
	 *
	 * @param row The index of the row to remove.
	 * @param col The index of the column to remove.
	 * @return A new IntegerMatrix instance with the specified row and column removed.
	 * @throws InvalidGeometryException If the matrix is not square or too small for Laplace expansion.
	 * @throws InvalidCoordinatesException If the row or column index is out of bounds.
	 */
	protected IntegerMatrix laplaceExpansionHelper(int row, int col){
		//Make sure the matrix is large enough to have this operation performed
		if((getNumRows() <= 1) || (getNumCols() <= 1)){
			throw new InvalidGeometryException("A matrix must be at least 2x2 for you to perform Laplace Expansion: " + getNumRows() + "x" + getNumCols());
		}
		//Make sure the matrix is square
		if(!isSquare()){
			throw new InvalidGeometryException("A matrix must be square for you to perform Laplace Expansion");
		}
		//Make sure the row is valid
		if((row < 0) || (row >= getNumRows())){
			throw new InvalidCoordinatesException("An invalid row number was supplied: " + row + ". The matrix contains " + getNumRows() + " rows");
		}
		//Make sure the col is valid
		if((col < 0) || (col >= getNumCols())){
			throw new InvalidCoordinatesException("An invalid column number was supplied: " + col + ". The matrix contains " + getNumCols() + " columns");
		}


		//Create a new matrix that is one row and column smaller than the existing row
		int[][] newGrid = new int[getNumRows() - 1][getNumCols() - 1];
		//Traverse the matrix and set the values in the new matrix, skipping elements in the given row and col
		for(int workingRow = 0, newRow = 0;workingRow < getNumRows();++workingRow){
			//Skip the row we are expanding
			if(workingRow == row){
				continue;
			}
			for(int workingCol = 0, newCol = 0;workingCol < getNumCols();++workingCol){
				//Skip the column we are expanding
				if(workingCol == col){
					continue;
				}
				newGrid[newRow][newCol] = grid[workingRow][workingCol];
				++newCol;
			}
			++newRow;
		}


		//Return the new matrix
		return new IntegerMatrix(newGrid);
	}

	//?Constructors
	/**
	 * Constructs an empty matrix (0x0).
	 */
	public IntegerMatrix(){
		grid = new int[0][0];
	}
	/**
	 * Constructs a matrix with the specified grid.
	 *
	 * @param grid The 2D array to initialize the matrix with.
	 */
	public IntegerMatrix(int[][] grid){
		this.grid = validateGrid(grid);
	}
	/**
	 * Constructs a copy of the specified matrix.
	 *
	 * @param matrix The matrix to copy.
	 */
	public IntegerMatrix(IntegerMatrix matrix){
		this.grid = validateGrid(matrix.grid);
	}
	/**
	 * Constructs a matrix with the specified number of rows and columns, filled with the specified value.
	 *
	 * @param rows The number of rows.
	 * @param cols The number of columns.
	 * @param fill The value to fill the matrix with.
	 * @throws InvalidGeometryException If the number of rows or columns is less than or equal to zero.
	 */
	public IntegerMatrix(int rows, int cols, int fill){
		if(rows <= 0){
			throw new InvalidGeometryException("A filled matrix must have at least 1 row");
		}
		else if(cols <= 0){
			throw new InvalidGeometryException("A filled matrix must have at least 1 column");
		}
		else{
			grid = new int[rows][cols];
			for(int row = 0;row < rows;++row){
				for(int col = 0;col < cols;++col){
					grid[row][col] = fill;
				}
			}
		}
	}

	//?Gets
	/**
	 * Gets the value at the specified row and column.
	 *
	 * @param row The row index.
	 * @param col The column index.
	 * @return The value at the specified row and column.
	 * @throws InvalidCoordinatesException If the row or column index is out of bounds.
	 */
	public int get(int row, int col){
		//Make sure the row and column are valid
		if(row >= grid.length){
			throw new InvalidCoordinatesException("Row cannot be greater than the number of rows");
		}
		else if(row < 0){
			throw new InvalidCoordinatesException("Row cannot be less than 0");
		}
		else if(col >= grid[row].length){
			throw new InvalidCoordinatesException("Column cannot be greater than the number of columns");
		}
		else if(col < 0){
			throw new InvalidCoordinatesException("Column cannot be less than 0");
		}

		//Return the location in the grid
		return grid[row][col];
	}
	/**
	 * Returns a new matrix that is a copy of the specified row.
	 *
	 * @param row The index of the row to retrieve.
	 * @return A new IntegerMatrix instance containing the specified row.
	 * @throws InvalidCoordinatesException If the row index is out of bounds.
	 */
	public IntegerMatrix getRow(int row){
		//Make sure the row number is valid
		if((row < 0) || (row >= grid.length)){
			throw new InvalidCoordinatesException("The row number " + row + " is not valid");
		}

		//Generate a copy of the row
		int[][] newRow = new int[1][grid[row].length];
		newRow[0] = Arrays.copyOf(grid[row], grid[row].length);

		//Return the new matrix
		return new IntegerMatrix(newRow);
	}
	/**
	 * Returns the number of rows in the matrix.
	 *
	 * @return The number of rows.
	 */
	public int getNumRows(){
		return grid.length;
	}
	/**
	 * Returns a new matrix that is a copy of the specified column.
	 *
	 * @param col The index of the column to retrieve.
	 * @return A new IntegerMatrix instance containing the specified column.
	 * @throws InvalidCoordinatesException If the column index is out of bounds.
	 */
	public IntegerMatrix getCol(int col){
		//Make sure the column number is valid
		if((col < 0) || (grid.length == 0) || (col >= grid[0].length)){
			throw new InvalidCoordinatesException("The column number " + col + " is not valid");
		}

		//Generate a copy of the col
		int[][] newColumn = new int[grid.length][1];
		for(int row = 0;row < grid.length;++row){
			newColumn[row][0] = grid[row][col];
		}

		//Return the new matrix
		return new IntegerMatrix(newColumn);
	}
	/**
	 * Returns the number of columns in the matrix.
	 *
	 * @return The number of columns.
	 */
	public int getNumCols(){
		if(grid.length > 0){
			return grid[0].length;
		}
		else{
			return 0;
		}
	}

	//?Sets
	/**
	 * Sets the value at the specified row and column.
	 *
	 * @param row   The row index.
	 * @param col   The column index.
	 * @param value The value to set.
	 * @throws InvalidCoordinatesException If the row or column index is out of bounds.
	 */
	public void set(int row, int col, int value){
		//Make sure the row number is valid
		if((row < 0) || (row >= grid.length)){
			throw new InvalidCoordinatesException("Invalid row number " + row);
		}
		//Make sure the column number is valid
		if((col < 0) || (col >= getNumCols())){
			throw new InvalidCoordinatesException("Invalid column number " + col);
		}

		//Save the element
		grid[row][col] = value;
	}
	/**
	 * Sets the specified row with the given array of elements.
	 *
	 * @param row	 The row index.
	 * @param elements The array of elements to set.
	 * @throws InvalidCoordinatesException If the row index is out of bounds.
	 * @throws InvalidGeometryException	 If the length of the elements array does not match the number of columns.
	 */
	public void setRow(int row, int[] elements){
		//Make sure the row number is valid
		if((row < 0) || (row >= grid.length)){
			throw new InvalidCoordinatesException("Invalid row number " + row);
		}
		//Make sure the number of elements is valid
		if(elements == null){
			throw new InvalidGeometryException("Row cannot be null");
		}
		else if(elements.length != getNumCols()){
			throw new InvalidGeometryException(elements.length, getNumCols());
		}

		//Save the elements
		grid[row] = Arrays.copyOf(elements, elements.length);
	}
	/**
	 * Sets the specified row with the given matrix containing a single row.
	 *
	 * @param row	 The row index.
	 * @param matrix  The matrix containing a single row to set.
	 * @throws NullMatrixException		   If the matrix is null.
	 * @throws InvalidGeometryException	  If the matrix does not contain a single row.
	 */
	public void setRow(int row, IntegerMatrix matrix){
		//Make sure the matrix isn't null
		if(matrix == null){
			throw new NullMatrixException();
		}
		//Make sure the matrix has a single row
		if(matrix.getNumRows() != 1){
			throw new InvalidGeometryException("Setting a row by Matrix requires the matrix contain a single row");
		}

		//Set the row
		setRow(row, matrix.grid[0]);
	}
	/**
	 * Sets the specified column with the given array of elements.
	 *
	 * @param col	 The column index.
	 * @param elements The array of elements to set.
	 * @throws InvalidCoordinatesException If the column index is out of bounds.
	 * @throws InvalidGeometryException	 If the length of the elements array does not match the number of rows.
	 */
	public void setCol(int col, int[] elements){
		//Make sure the column number is valid
		if((col < 0) || (col >= getNumCols())){
			throw new InvalidCoordinatesException("Invalid column number " + col);
		}
		//Make sure the number of elements is valid
		if(elements == null){
			throw new InvalidGeometryException("Column cannot be null");
		}
		else if(elements.length != grid.length){
			throw new InvalidGeometryException(elements.length, grid.length);
		}

		//Save the elements
		for(int row = 0;row < elements.length;++row){
			grid[row][col] = elements[row];
		}
	}
	/**
	 * Sets the specified column with the given matrix containing a single column.
	 *
	 * @param col	 The column index.
	 * @param matrix  The matrix containing a single column to set.
	 * @throws NullMatrixException		   If the matrix is null.
	 * @throws InvalidGeometryException	  If the matrix does not contain a single column.
	 */
	public void setCol(int col, IntegerMatrix matrix){
		//Make sure the matrix isn't null
		if(matrix == null){
			throw new NullMatrixException();
		}
		//Make sure the matrix has a single column
		else if(matrix.getNumCols() != 1){
			throw new InvalidGeometryException("Setting a column by Matrix requires the matrix contain a single column");
		}

		int[] vector = new int[matrix.getNumRows()];
		for(int cnt = 0;cnt < matrix.getNumRows();++cnt){
			vector[cnt] = matrix.grid[cnt][0];
		}

		//Set the column
		setCol(col, vector);
	}

	//?Adds
	/**
	 * Adds a new row with the specified array of elements to the matrix.
	 *
	 * @param elements The array of elements to add as a new row.
	 * @throws NullMatrixException		   If the elements array is null.
	 * @throws InvalidGeometryException	  If the length of the elements array does not match the number of columns.
	 */
	public void addRow(int[] elements){
		//Make sure the matrix isn't null
		if(elements == null){
			throw new NullMatrixException();
		}
		//Make sure the number of columns is valid
		else if((grid.length == 0) || (getNumCols() == elements.length)){
			int[][] newGrid = new int[grid.length + 1][elements.length];
			//Copy all existing data into the new grid
			for(int row = 0;row < grid.length;++row){
				newGrid[row] = Arrays.copyOf(grid[row], grid[row].length);
			}
			grid = newGrid;
		}
		else{
			throw new InvalidGeometryException(elements.length, getNumCols());
		}

		//Add all elements to the grid
		grid[grid.length - 1] = Arrays.copyOf(elements, elements.length);
	}
	/**
	 * Adds a new row with the given matrix containing a single row to the matrix.
	 *
	 * @param matrix The matrix containing a single row to add.
	 * @throws NullMatrixException		   If the matrix is null.
	 * @throws InvalidGeometryException	  If the matrix does not contain a single row.
	 */
	public void addRow(IntegerMatrix matrix){
		//Make sure the matrix isn't null
		if(matrix == null){
			throw new NullMatrixException();
		}
		//Make sure the matrix has a single row
		else if(matrix.getNumRows() != 1){
			throw new InvalidGeometryException("Adding a row by Matrix requires the matrix contain a single row");
		}

		//Add the row
		addRow(matrix.grid[0]);
	}
	/**
	 * Adds a new column with the specified array of elements to the matrix.
	 *
	 * @param elements The array of elements to add as a new column.
	 * @throws NullMatrixException		   If the elements array is null.
	 * @throws InvalidGeometryException	  If the length of the elements array does not match the number of rows.
	 */
	public void addCol(int[] elements){
		//Make sure the matrix isn't null
		if(elements == null){
			throw new NullMatrixException();
		}
		//Make sure the number of rows is valid
		if(grid.length == 0){
			grid = new int[elements.length][1];
			for(int row = 0;row < grid.length;++row){
				grid[row][0] = elements[row];
			}
		}
		else if(grid.length == elements.length){
			//Copy all existing data into the new grid
			for(int row = 0;row < grid.length;++row){
				grid[row] = Arrays.copyOf(grid[row], grid[row].length + 1);
				grid[row][grid[row].length - 1] = elements[row];
			}
		}
		else{
			throw new InvalidGeometryException(elements.length, getNumCols());
		}
	}
	/**
	 * Adds a new column with the given matrix containing a single column to the matrix.
	 *
	 * @param matrix The matrix containing a single column to add.
	 * @throws NullMatrixException		   If the matrix is null.
	 * @throws InvalidGeometryException	  If the matrix does not contain a single column.
	 */
	public void addCol(IntegerMatrix matrix){
		//Make sure the matrix isn't null
		if(matrix == null){
			throw new NullMatrixException();
		}
		//Make sure the matrix has a single column
		else if(matrix.getNumCols() != 1){
			throw new InvalidGeometryException("Adding a column by Matrix requires the matrix contain a single column");
		}

		int[] vector = new int[matrix.getNumRows()];
		for(int cnt = 0;cnt < matrix.getNumRows();++cnt){
			vector[cnt] = matrix.get(cnt, 0);
		}

		//Add the column
		addCol(vector);
	}
	/**
	 * Appends the specified matrix to the right side of the current matrix.
	 *
	 * @param rightSide The matrix to append to the right side.
	 * @return A new IntegerMatrix instance with the right-side matrix appended.
	 * @throws NullMatrixException		   If the right-side matrix is null.
	 * @throws InvalidGeometryException	  If the number of rows does not match.
	 */
	public IntegerMatrix appendRight(IntegerMatrix rightSide){
		//Make sure the matrix isn't null
		if(rightSide == null){
			throw new NullMatrixException();
		}
		//Make sure the matrices have the same number of rows
		else if(getNumRows() != rightSide.getNumRows()){
			throw new InvalidGeometryException("Invalid number of rows. " + rightSide.getNumRows() + " must be " + getNumRows());
		}

		//Traverse both matrices and set their values in the new matrix
		int[][] newGrid = new int[getNumRows()][getNumCols() + rightSide.getNumCols()];
		for(int row = 0;row < getNumRows();++row){
			//Set all elements from the current grid's row
			newGrid[row] = Arrays.copyOf(grid[row], grid[row].length + rightSide.grid[row].length);

			//Set all elements from the right side grid's row
			for(int col = 0;col < rightSide.getNumCols();++col){
				newGrid[row][getNumCols() + col] = rightSide.grid[row][col];
			}
		}

		//Return the new matrix
		return new IntegerMatrix(newGrid);
	}
	/**
	 * Appends the specified matrix to the bottom of the current matrix.
	 *
	 * @param bottomSide The matrix to append to the bottom.
	 * @return A new IntegerMatrix instance with the bottom matrix appended.
	 * @throws NullMatrixException		   If the bottom matrix is null.
	 * @throws InvalidGeometryException	  If the number of columns does not match.
	 */
	public IntegerMatrix appendBottom(IntegerMatrix bottomSide){
		//Make sure the matrix isn't null
		if(bottomSide == null){
			throw new NullMatrixException();
		}
		//Make sure the matrices have the same number of columns
		else if(getNumCols() != bottomSide.getNumCols()){
			throw new InvalidGeometryException("Invalid number of columns. " + bottomSide.getNumCols() + " must be " + getNumCols());
		}

		//Traverse both matrices and set their values in the new matrix
		int[][] newGrid = new int[getNumRows() + bottomSide.getNumRows()][getNumCols()];
		for(int col = 0;col < getNumCols();++col){
			//Set all elements from the current grid's column
			for(int row = 0;row < getNumRows();++row){
				newGrid[row][col] = grid[row][col];
			}
			//Set all elements from the right side grid's column
			for(int row = 0;row < bottomSide.getNumRows();++row){
				newGrid[getNumRows() + row][col] = bottomSide.grid[row][col];
			}
		}

		//Return the new matrix
		return new IntegerMatrix(newGrid);
	}

	//?Simple operations
	/**
	 * Generates an identity matrix of the given size.
	 *
	 * @param size The size of the identity matrix.
	 * @return A new IntegerMatrix instance representing the identity matrix.
	 * @throws InvalidGeometryException If the size is less than or equal to zero.
	 */
	public static IntegerMatrix generateIdentity(int size){
		//Make sure the size is valid
		if(size > 0){
			//Create a grid with the correct size
			int[][] newGrid = new int[size][size];

			//Go through every element and make sure it is set correctly
			for(int row = 0;row < size;++row){
				for(int col = 0;col < size;++col){
					if(col == row){
						newGrid[row][col] = 1;
					}
					else{
						newGrid[row][col] = 0;
					}
				}
			}

			//Return the new matrix
			return new IntegerMatrix(newGrid);
		}
		else{
			throw new InvalidGeometryException("An identity matrix must have a size > 0");
		}
	}
	/**
	 * Adds the specified matrix to the current matrix.
	 *
	 * @param rightSide The matrix to add.
	 * @return A new IntegerMatrix instance with the result of the addition.
	 * @throws InvalidGeometryException If the matrices do not have the same dimensions.
	 */
	public IntegerMatrix add(IntegerMatrix rightSide){
		//Make sure the matrix isn't null
		if(rightSide == null){
			throw new NullMatrixException();
		}

		//Make sure the matrices have compatible geometry
		if((getNumRows() != rightSide.getNumRows()) || (getNumCols() != rightSide.getNumCols())){
			throw new InvalidGeometryException("Both matrices must have the same number of rows and columns: " + getNumRows() + "x" + getNumCols() + " + " + rightSide.getNumRows() + "x" + rightSide.getNumCols());
		}

		//Create a new grid with the same elements as the current grid
		int[][] newGrid = copyGrid();

		//Add each element in the right matrix to the corresponding element in the left matrix
		for(int row = 0;row < newGrid.length;++row){
			for(int col = 0;col < newGrid[0].length;++col){
				newGrid[row][col] += rightSide.grid[row][col];
			}
		}

		//Return the new matrix
		return new IntegerMatrix(newGrid);
	}
	/**
	 * Adds the scalar to every element in the matrix.
	 *
	 * @param scalar The scalar to add.
	 * @return A new IntegerMatrix instance with the result of the addition.
	 */
	public IntegerMatrix add(int scalar){
		//Create a new grid with the same elements as the current grid
		int[][] newGrid = copyGrid();

		//Add the scalar to each element in the grid
		for(int row = 0;row < newGrid.length;++row){
			for(int col = 0;col < newGrid[0].length;++col){
				newGrid[row][col] += scalar;
			}
		}

		//Return the new matrix
		return new IntegerMatrix(newGrid);
	}
	/**
	 * Subtracts the specified matrix from the current matrix.
	 *
	 * @param rightSide The matrix to subtract.
	 * @return A new IntegerMatrix instance with the result of the subtraction.
	 * @throws InvalidGeometryException If the matrices do not have the same dimensions.
	 */
	public IntegerMatrix subtract(IntegerMatrix rightSide){
		//Make sure the matrix isn't null
		if(rightSide == null){
			throw new NullMatrixException();
		}

		//Make sure the matrices have compatible geometry
		if((getNumRows() != rightSide.getNumRows()) || (getNumCols() != rightSide.getNumCols())){
			throw new InvalidGeometryException("Both matrices must have the same number of rows and columns: " + getNumRows() + "x" + getNumCols() + " + " + rightSide.getNumRows() + "x" + rightSide.getNumCols());
		}

		//Create a new grid with the same elements as the current gird
		int[][] newGrid = copyGrid();

		//Subtract each element in the right matrix from the corresponding element in the left matrix
		for(int row = 0;row < newGrid.length;++row){
			for(int col = 0;col < newGrid[0].length;++col){
				newGrid[row][col] -= rightSide.grid[row][col];
			}
		}

		//Return the new matrix
		return new IntegerMatrix(newGrid);
	}
	/**
	 * Subtracts the scalar from every element in the matrix.
	 *
	 * @param scalar The scalar to subtract.
	 * @return A new IntegerMatrix instance with the result of the subtraction.
	 */
	public IntegerMatrix subtract(int scalar){
		//Create a new grid with the same elements as the current grid
		int[][] newGrid = copyGrid();

		//Subtract the scalar from each element in the grid
		for(int row = 0;row < newGrid.length;++row){
			for(int col = 0;col < newGrid[0].length;++col){
				newGrid[row][col] -= scalar;
			}
		}

		//Return the new matrix
		return new IntegerMatrix(newGrid);
	}
	/**
	 * Multiplies the current matrix by the specified matrix.
	 *
	 * @param rightSide The matrix to multiply by.
	 * @return A new IntegerMatrix instance with the result of the multiplication.
	 * @throws InvalidGeometryException If the number of columns in the current matrix does not match the number of rows in the right-side matrix.
	 */
	public IntegerMatrix multiply(IntegerMatrix rightSide){
		//Make sure the matrix isn't null
		if(rightSide == null){
			throw new NullMatrixException();
		}

		//Make sure the matrices have compatible geometry
		if(getNumCols() != rightSide.getNumRows()){
			throw new InvalidGeometryException("The left matrix must have the same number of columns as the right matrix has rows: " + getNumRows() + "x" + getNumCols() + " + " + rightSide.getNumRows() + "x" + rightSide.getNumCols());
		}

		//Create a new grid with the same elements as the current grid
		int[][] newGrid = new int[getNumRows()][rightSide.getNumCols()];

		//Multiply each row in the left matrix with each column int he right matrix to come up with the current element
		for(int leftRow = 0;leftRow < grid.length;++leftRow){
			for(int rightCol = 0;rightCol < rightSide.getNumCols();++rightCol){
				//Get a sum of the product of each column in the current row (left) and each row in the current column (right)
				int elementProductSum = 0;
				for(int incrementCounter = 0;incrementCounter < grid.length;++incrementCounter){
					elementProductSum += grid[leftRow][incrementCounter] * rightSide.grid[incrementCounter][rightCol];
				}
				newGrid[leftRow][rightCol] = elementProductSum;
			}
		}

		//Return the new matrix
		return new IntegerMatrix(newGrid);
	}
	/**
	 * Multiplies every element in the matrix by the scalar.
	 *
	 * @param scalar the scalar to multiply
	 * @return A new IntegerMatrix instance with the result of the multiplication
	 */
	public IntegerMatrix multiply(int scalar){
		//Create a new grid with the same elements as the current grid
		int[][] newGrid = copyGrid();

		//Multiply every element in the grid by the scalar
		for(int row = 0;row < grid.length;++row){
			for(int col = 0;col < grid[0].length;++col){
				newGrid[row][col] *= scalar;
			}
		}

		//Return the new matrix
		return new IntegerMatrix(newGrid);
	}
	/**
	 * Multiplies the current matrix by itself the given number of times.
	 *
	 * @param power The number of times to multiply the matrix by itself
	 * @return A new IntegerMatrix instance with the result of the multiplication
	 * @throws InvalidScalarException If the power is negative
	 * @throws InvalidGeometryException If the matrix is not square
	 */
	public IntegerMatrix pow(int power){
		//Make sure the matrix is square so it can be multiplied
		if(!isSquare()){
			throw new InvalidGeometryException("The matrix must be square to raise it to a power");
		}
		//Make sure the power is positive
		if(power < 0){
			throw new InvalidScalarException("The power must be >= 0");
		}
		else if(power == 0){
			return new IntegerMatrix(getNumRows(), getNumCols(), 1);
		}

		//Create a new matrix for the product
		IntegerMatrix newMatrix = new IntegerMatrix(this);
		//Multiply the current grid power times
		for(int currentPower = 1;currentPower < power;++currentPower){
			newMatrix = newMatrix.multiply(this);
		}

		//Return the new grid
		return newMatrix;
	}
	/**
	 * Calculates the dot product of the two matrices.
	 *
	 * @param rightSide The matrix to use on the right side of the calculation
	 * @return The dot product of the two matrices
	 * @throws NullMatrixException If the right matrix is null
	 * @throws InvalidGeometryException If the matrices do not have compatible dimensions
	 */
	public int dotProduct(IntegerMatrix rightSide){
		//Make sure the matrix isn't null
		if(rightSide == null){
			throw new NullMatrixException();
		}

		//Make sure the matrices have compatible geometry
		if(getNumCols() != rightSide.getNumRows()){
			throw new InvalidGeometryException("The left matrix must have the same number of columns as the right matrix has rows: " + getNumRows() + "x" + getNumCols() + " + " + rightSide.getNumRows() + "x" + rightSide.getNumCols());
		}

		//Multiply each row in the left matrix with each column in the right matrix to come up with the current element
		//?Would be simpler, but slower, to get the product matrix to come up with the current element
		int sum = 0;
		for(int leftRow = 0;leftRow < grid.length;++leftRow){
			for(int rightCol = 0;rightCol < rightSide.getNumCols();++rightCol){
				for(int incrementCounter = 0;incrementCounter < grid.length;++incrementCounter){
					sum += grid[leftRow][incrementCounter] * rightSide.grid[incrementCounter][rightCol];
				}
			}
		}

		//Return the sum
		return sum;
	}
	/**
	 * Calculates the Hadamard product of the two matrices.
	 *
	 * @param rightSide The matrix to use on the right side of the calculation
	 * @return The Hadamard product of the two matrices
	 * @throws NullMatrixException If the right matrix is null
	 * @throws InvalidGeometryException If the matrices do not have compatible dimensions
	 */
	public IntegerMatrix hadamardProduct(IntegerMatrix rightSide){
		//Make sure the matrix isn't null
		if(rightSide == null){
			throw new NullMatrixException();
		}

		//Make sure the matrices have compatible geometry
		if((getNumRows() != rightSide.getNumRows()) || (getNumCols() != rightSide.getNumCols())){
			throw new InvalidGeometryException("Both matrices must have the same number of rows and columns: " + getNumRows() + "x" + getNumCols() + " + " + rightSide.getNumRows() + "x" + rightSide.getNumCols());
		}

		//Create a new grid with the same element as the current grid
		int[][] newGrid = copyGrid();

		//Multiply each element in the right matrix to the corresponding element in the left matrix
		for(int row = 0;row < newGrid.length;++row){
			for(int col = 0;col < newGrid[0].length;++col){
				newGrid[row][col] *= rightSide.grid[row][col];
			}
		}

		//Return the new matrix
		return new IntegerMatrix(newGrid);
	}

	//?Complex operations
	/**
	 * Transposes the current matrix (i.e., swaps rows and columns).
	 *
	 * @return A new IntegerMatrix instance representing the transposed matrix.
	 */
	public IntegerMatrix transpose(){
		//Create a new grid
		int[][] newGrid = new int[getNumCols()][getNumRows()];

		//Traverse every element in the existing grid and add each column to the new grid as a row
		for(int col = 0;col < getNumCols();++col){
			for(int row = 0;row < getNumRows();++row){
				newGrid[col][row] = grid[row][col];
			}
		}

		//Return the new matrix
		return new IntegerMatrix(newGrid);
	}
	/**
	 * Calculates the determinant of the matrix. For matrices 4x4 or larger, a recursive approach is used.
	 *
	 * @return The determinant of the matrix.
	 * @throws InvalidGeometryException If the matrix is not square.
	 * @see #determinant()
	 */
	public int det(){
		return determinant();
	}
	/**
	 * Calculates the determinant of a 2x2 matrix.
	 *
	 * @return The determinant of the matrix.
	 * @throws InvalidGeometryException If the matrix is not 2x2.
	 */
	private int det2(){
		return (grid[0][0] * grid[1][1]) - (grid[0][1] * grid[1][0]);
	}
	/**
	 * Calculates the determinant of a 3x3 matrix.
	 *
	 * @return The determinant of the matrix.
	 * @throws InvalidGeometryException If the matrix is not 3x3.
	 */
	private int det3(){
		return (grid[0][0] * grid[1][1] * grid[2][2]) + (grid[0][1] * grid[1][2] * grid[2][0]) + (grid[0][2] * grid[1][0] * grid[2][1]) -
						(grid[2][0] * grid[1][1] * grid[0][2]) - (grid[2][1] * grid[1][2] * grid[0][0]) - (grid[2][2] * grid[1][0] * grid[0][1]);
	}
	/**
	 * Calculates the determinant of a 4x4 or larger matrix.
	 *
	 * @return The determinant of the matrix.
	 * @throws InvalidGeometryException If the matrix is not 4x4.
	 */
	private int det4(){
		int det = 0;

		//Find the row/column with the largest number of 0's
		int zerosLocation = 0;
		int maxNumZeros = 0;
		boolean zerosRow = true;
		//Check the rows
		for(int row = 0;row < getNumRows();++row){
			int numZeros = 0;
			for(int col = 0;col < getNumCols();++col){
				if(grid[row][col] == 0){
					++numZeros;
				}
			}
			if(numZeros > maxNumZeros){
				maxNumZeros = numZeros;
				zerosLocation = row;
				zerosRow = true;
			}
		}
		//Check the columns
		for(int col = 0;col < getNumCols();++col){
			int numZeros = 0;
			for(int row = 0;row < getNumRows();++row){
				if(grid[row][col] == 0){
					++numZeros;
				}
			}
			if(numZeros > maxNumZeros){
				maxNumZeros = numZeros;
				zerosLocation = col;
				zerosRow = false;
			}
		}

		//If the largest number of zeros were found in a row
		if(zerosRow){
			//Set a variable to make sure the appropriate + or - is applied to the scalar
			int multiplier = 1;
			if((zerosLocation % 2) == 1){
				multiplier = -1;
			}
			//Go through every column in the optimal row using the formula
			for(int col = 0;col < getNumCols();++col){
				if(grid[zerosLocation][col] != 0){
					det += (multiplier * grid[zerosLocation][col] * laplaceExpansionHelper(zerosLocation, col).determinant());
				}
				multiplier = -multiplier;
			}
		}
		//If the largest number of zeros were found in a column
		else{
			//Set a variable to make sure the appropriate + or - is applied to the scalar
			int multiplier = 1;
			if((zerosLocation % 2) == 1){
				multiplier = -1;
			}
			//Go through every row in the coptimal column using the formula
			for(int row = 0;row < getNumRows();++row){
				if(grid[row][zerosLocation] != 0){
					det += (multiplier * grid[row][zerosLocation] * laplaceExpansionHelper(row, zerosLocation).determinant());
				}
				multiplier = -multiplier;
			}
		}

		return det;
	}
	/**
	 * Calculates the determinant of the matrix. For matrices 4x4 or larger, a recursive approach is used.
	 *
	 * @return The determinant of the matrix.
	 * @throws InvalidGeometryException If the matrix is not square.
	 */
	public int determinant(){
		//Make sure the matrix is square
		if(!isSquare()){
			throw new InvalidGeometryException("A matrix must be square for it to have a determinant");
		}
		//?Don't have to worry about a matrix existing. isSquare takes care of 0x0 matrix

		//Determine the formula do use for the determinant
		int det = 0;
		switch(getNumRows()){
			//If the matrix is 1x1 return the number
			case 1 : det = grid[0][0]; break;
			//If the matrix is 2x2 use the formula
			case 2 : det = det2(); break;
			//If the matrix is 3x3 use the formula
			case 3 : det = det3(); break;
			//If the matrix is larger break it down and try again
			default : det = det4();
		}

		//Return the determinant
		return det;
	}
	/**
	 * Calculates the cofactor matrix of the current matrix.
	 *
	 * @return A new IntegerMatrix instance representing the cofactor matrix.
	 * @throws InvalidGeometryException If the matrix is not square.
	 * @see #cofactor()
	 */
	public IntegerMatrix cof(){
		return cofactor();
	}
	/**
	 * Calculates the cofactor matrix of the current matrix.
	 *
	 * @return A new IntegerMatrix instance representing the cofactor matrix.
	 * @throws InvalidGeometryException If the matrix is not square.
	 */
	public IntegerMatrix cofactor(){
		//Make sure the matrix is square
		if(!isSquare()){
			throw new InvalidGeometryException("A matrix must be square to find the cofactor matrix");
		}

		//Create a new grid
		int[][] newGrid = new int[getNumRows()][getNumCols()];
		//If the grid is 1x1 return the grid
		if(getNumRows() == 1){
			newGrid[0][0] = 1;
		}
		//Use the formula to find the cofactor matrix
		else{
			for(int row = 0;row < getNumRows();++row){
				int multiplier = ((row % 2) == 0) ? 1 : -1;
				for(int col = 0;col < getNumCols();++col){
					newGrid[row][col] = multiplier * laplaceExpansionHelper(row, col).determinant();
					multiplier = -multiplier;
				}
			}
		}

		//Return the new matrix
		return new IntegerMatrix(newGrid);
	}
	/**
	 * Calculates the adjoint matrix of the current matrix.
	 *
	 * @return A new IntegerMatrix instance representing the adjoint matrix.
	 * @throws InvalidGeometryException If the matrix is not square.
	 * @see #adjoint()
	 */
	public IntegerMatrix adj(){
		return adjoint();
	}
	/**
	 * Calculates the adjoint matrix of the current matrix.
	 *
	 * @return A new IntegerMatrix instance representing the adjoint matrix.
	 * @throws InvalidGeometryException If the matrix is not square.
	 */
	public IntegerMatrix adjoint(){
		return cofactor().transpose();
	}
	/**
	 * Calculates the inverse of the current matrix.
	 *
	 * @return A new IntegerMatrix instance representing the inverse matrix.
	 * @throws InvalidGeometryException If the matrix is not square or if the determinant is 0.
	 */
	public IntegerMatrix inverse(){
		//Make sure the matrix is square
		if(!isSquare()){
			throw new InvalidGeometryException("A matrix must be square for it to have an inverse");
		}

		//Make sure the determinant is not 0
		int determinant = determinant();
		if(determinant == 0){
			throw new InvalidScalarException("The determinant cannot be 0");
		}

		//Return the new matrix
		return adjoint().multiply(1 / determinant);
	}

	//?Object functions
	/**
	 * Determines whether the given object is equal to the current matrix.
	 * Can determine equality using IntegerMatrix or int[][].
	 *
	 * @param rightSide The object to compare to the current matrix.
	 * @return True if the objects are equal, false otherwise.
	 * @see #equals(IntegerMatrix)
	 */
	@Override
	public boolean equals(Object rightSide){
		if(rightSide == null){
			return false;
		}
		if(rightSide.getClass().equals(this.getClass())){
			return equals((IntegerMatrix)rightSide);
		}
		else if(rightSide.getClass().equals(int[][].class)){
			int[][] rightMatrix = (int[][])rightSide;
			return equals(new IntegerMatrix(rightMatrix));
		}
		else{
			return false;
		}
	}
	/**
	 * Determines whether the given IntegerMatrix is equal to the current matrix.
	 *
	 * @param rightMatrix The IntegerMatrix to compare to the current matrix.
	 * @return True if the matrices are equal, false otherwise.
	 */
	private boolean equals(IntegerMatrix rightMatrix){
		//Make sure they have the same number of elements
		if((getNumRows() != rightMatrix.getNumRows()) || (getNumCols() != rightMatrix.getNumCols())){
			return false;
		}

		//Check every element
		for(int row = 0;row < getNumRows();++row){
			for(int col = 0;col < getNumCols();++col){
				if(grid[row][col] != rightMatrix.grid[row][col]){
					return false;
				}
			}
		}

		//If false hasn't been returned yet then they are equal
		return true;
	}
	/**
	 * Calculates a hash code for the current matrix.
	 *
	 * @return The hash code for the current matrix.
	 */
	@Override
	public int hashCode(){
		return Arrays.hashCode(grid);
	}
	/**
	 * Returns a string representation of the matrix, with rows and columns formatted for readability.
	 *
	 * @return A string representation of the matrix.
	 */
	@Override
	public String toString(){
		StringJoiner matrix = new StringJoiner("\n").setEmptyValue("[]");
		for(int rowCnt = 0;rowCnt < getNumRows();++rowCnt){
			StringJoiner row = new StringJoiner(", ", "[", "]");

			for(int colCnt = 0;colCnt < getNumCols();++colCnt){
				row.add(Integer.toString(grid[rowCnt][colCnt]));
			}

			matrix.add(row.toString());
		}
		return matrix.toString();
	}
}