Find the Good Matrix

A simple method is to create a 2-dimensional array to store the changes we need to update in the original matrix to convert the given matrix into the Good matrix.
 

Our approach will be to create a 2-dimensional array answer with N rows and M columns, and we will copy all elements value present in the matrix ARR into the matrix answer. We will iterate the variable row from 0 to N - 1, and in each iteration, we will iterate col from 0 to M - 1.

1. We will check if ARR[row][col] is equal to 0, then we need to set all elements value in the entire row and column of ARR[row][col] to 0. We will iterate index from 0 to N - 1, and set answer[index][col] as 0.
2. We will iterate index from 0 to M - 1, and set answer[row][index] as 0.

In the end, the matrix answer is the Good matrix which we will get after updating the given matrix as described in the question. We will return the matrix answer.

Algorithm:
 

• Create a 2-dimensional array answer with N rows and M columns, which we will use to convert the given matrix into the Good matrix. We will update the changes in the matrix answer.
• Copy all elements value present in the array ARR into the array answer.
• Iterate row from 0 to N - 1.
  • Iterate col from 0 to M - 1.
    • Check if ARR[row][col] is equal to 0.
      • Iterate index from 0 to N - 1, and set answer[index][col] as 0.
      • Iterate index from 0 to M - 1, and set answer[row][index] as 0.
• Return the matrix answer.

The basic idea is to create an array for all rows and an array for all columns in which we will keep the information of those rows and columns whose value we need to set as 0 for the entire row and column.
 

We will create array rows of size N and array columns of size M. The array rows will keep the record of all rows, and the array columns will keep the record for all columns whose value of all elements we need to set to 0. Initially, all elements of rows and columns will contain the value 0. We will set the element’s value to 1 if we need to set all element values present in that particular row or column to 0.

1. We will iterate the variable index from 0 to N - 1, and in each iteration, we will iterate pos from 0 to M - 1. We will check if ARR[index][pos] is equal to 0, then we need to set all elements in the row index and the column pos to 0. We will set rows[index] and columns[pos] as 1.
2. Now, we will update the changes in the original matrix. We will iterate the variable index from 0 to N - 1, and in each iteration, we will iterate pos from 0 to M - 1. We will check either rows[index] or columns[pos] is equal to 1, then we will update ARR[index][pos] with the value 1.

In the end, the matrix ARR is converted into the Good matrix. We will return the matrix ARR.
 

Algorithm:

• Create an array rows of size N and columns of size M. The element of the array rows, and the array columns will contain the value 1 if we need to set all elements value present in that particular row and column to 0.
• Iterate index from 0 to N - 1.
  • Iterate pos from 0 to M - 1.
    • Check if ARR[index][pos] is equal to 0.
      • Update rows[index] with the value 1.
      • Update columns[pos] with the value 1.
• Iterate index from 0 to N-1.
  • Iterate pos from 0 to M - 1.
    • Check either rows[index] is equal to 1 or columns[pos] is equal to 1.
      • Set ARR[index][pos] as 0.
• Return the matrix ARR.

As we have discussed in the previous approach, we have created an array for all rows and an array for all columns to keep information of those rows and columns whose value we need to set to 0 for the entire row and column. In this approach, we will keep the record of all rows and columns in the given matrix. We will use the 0’th row and 0’th column of the matrix to keep to record for all rows and columns. 

To make this approach work, we will maintain a variable isCol, which will store if we need to set all elements value in the 0’th column to 0. 

1. We will iterate the variable row from 0 to N - 1. In each iteration, we will check if ARR[row][0] is equal to 0, then we need to set all elements in the 0’th column to 0. So, we will update isCol with the value true. We will iterate the variable column from 0 to M - 1. We will check if ARR[row][colum] is equal to 0, then we need to set all in the entire row and column of ARR[row][col] to 0 and we will update ARR[0][column] and ARR[row][0] with the value 0.
2. Now, we will update changes in the given matrix. We will iterate the variable row from 0 to N - 1. In each iteration, We will iterate the variable column from 0 to M - 1. We will check either ARR[row][0] or ARR[0][column] is equal to 0, then we will update ARR[row][column] with the value 0.
3. Now, we need to take care of the 0’th row and 0’th column. We will check ARR[0][0] is equal to 0, and then we need to set all elements in the 0’th row to 0. We will iterate the variable column from 0 to M - 1, and we will update ARR[0][column] with the value 0.
4. We will check if isCol is equal to true, then we need to set all elements in the 0’th column to 0. We will iterate the variable row from 0 to N - 1, and we will update ARR[row][0] with the value 0.

In the end, the matrix ARR is converted into the Good matrix. We will return the matrix ARR.
 

Algorithm:
 

• Set the variable isCol as false. The variable isCol stores if we need to set all element’s value in the 0’th column to 0.
• Iterate row from 0 to N - 1.
  • Check if ARR[row][0] is equal to 0.
    • Update the variable isCol with true.
  • Iterate column from 1 to M - 1.
    • Check if ARR[row][column] is equal to 0.
      • Update ARR[0][column] with the value 0.
      • Update ARR[row][0] with the value 0.
• Iterate row from 1 to N - 1.
  • Iterate column from 1 to M - 1.
    • Check either ARR[row][0] is equal to 0 or ARR[0][column] is equal to 0, then update ARR[row][column] with the 0.
• Check if ARR[0][0] is equal to 0.
  • Iterate column from 0 to M - 1, update ARR[0][column] with the 0.
• Check if isCol is equal to true.
  • Iterate row from 0 to N - 1, and update ARR[row][0] with the 0.
• Return the matrix ARR.