Set Matrix Zeroes

Given a m x n matrix, if an element is 0, set its entire row and column to 0. Do it in place. Try to use constant space.

Use first row and first column to record if the current row or column has 0 value element.

    public void setZeroes(int[][] matrix) {
        if (matrix==null||matrix.length==0) {
            return;
        }
        boolean isFirstRowZero = false;
        boolean isFirstColumnZero = false;

        //check if first row should be zero
        for (int j=0; j<matrix[0].length; j++) {
            if (matrix[0][j]==0) {
                isFirstRowZero = true;
                break;
            }
        }

        //check if first column should be zero
        for (int i=0; i<matrix.length; i++) {
            if (matrix[i][0]==0) {
                isFirstColumnZero = true;
                break;
            }
        }

        //check if the element is zero, if so set the corresponding first row and first column to zero
        for (int i=1; i<matrix.length; i++) {
            for (int j=1; j<matrix[i].length; j++) {
                if (matrix[i][j]==0) {
                    matrix[i][0]=0;
                    matrix[0][j]=0;
                }
            }
        }

        //set matrix to zero
        for (int i=1; i<matrix.length; i++) {
            for (int j=1;j<matrix[0].length; j++) {
                if (matrix[i][0]==0||matrix[0][j]==0) {
                    matrix[i][j]=0;
                }
            }
        }

        //set first row
        if (isFirstColumnZero) {
            for (int i=0; i<matrix.length; i++) {
                matrix[i][0]=0;
            }
        }

        //set first column
        if (isFirstRowZero) {
            for (int j=0; j<matrix[0].length; j++) {
                matrix[0][j]=0;
            }
        }
    }