Remove any corner X rows and columns from a matrix

Given a NxN matrix and an integer X. The task is to remove X rows and X columns from the NxN matrix.

1. Remove first X rows and columns from the matrix.

   Examples:

   Input: n = 4, 
          arr[][] = {{20, 2, 10, 16},
                     {20, 17, 11, 6},
                     {14, 16, 1, 3},
                     {10, 2, 17, 4}}, 
          x = 2
   Output:
   1 3
   17 4
   
   Explanation:
   Here the value of X is 2.
   So remove the first 2 rows 
   and the first 2 columns from the matrix. 
   Hence the output is
   1 3 
   17 4
   

   Simple Approach:

   • Skip the first x rows and columns and print the remaining elements in the matrix.
   • Start from the xth row and print till the n-1th row.
   • Start from the xth column and print till the n-1th column.

   Implementation:
   

   C++

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   #include <iostream> using namespace std;    // Function to remove first x // rows and columns from an array void remove_X_Rows_and_Columns(int* a, int n, int x) {        cout << "\nRemoving First " << x          << " rows and columns:\n";        // Start from the xth row     // and print till n-1th row     for (int i = x; i < n; i++) {            // Start from the xth column         // and print till the n-1th column         for (int j = x; j < n; j++) {                // Accessing the array using pointers             cout << *((a + i * n) + j) << " ";         }         cout << endl;     } }    // Print the matrix void printMatrix(int* a, int n) {        for (int i = 0; i < n; i++) {         for (int j = 0; j < n; j++) {             cout << *((a + i * n) + j) << " ";         }         cout << endl;     } }    int main() {     int n = 4;        // get the array inputs     int a[n][n];     for (int i = 0; i < n; i++) {         for (int j = 0; j < n; j++) {             a[i][j] = (i * 10 + j);         }     }        // Print the matrix     cout << "Original Matrix:\n";     printMatrix((int*)a, n);        int x = 2;        // passing the two dimensional     // array using a single pointer     remove_X_Rows_and_Columns((int*)a, n, x);        return 0; }

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   Python3

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   # Python3 implementation of the above approach     # Function to remove first x # rows and columns from an array def remove_X_Rows_and_Columns(a, n, x):        print("Removing First ", x,            " rows and columns:")        # Start from the xth row     # and pr till n-1th row     for i in range(x, n):            # Start from the xth column         # and pr till the n-1th column         for j in range(x, n):                # Accessing the array using poers             print(a[i][j], end = " ")            print()        # Print the matrix def prMatrix(a, n):        for i in range(n):         for j in range(n):             print(a[i][j], end = " ")            print()        # Driver Code if __name__ == '__main__':         n = 4        # get the array inputs     a = [[0 for i in range(n)]              for i in range(n)]     for i in range(n):         for j in range(n):             a[i][j] = (i * 10 + j)                # Print the matrix     print("Original Matrix:")     prMatrix(a, n)        x = 2        # passing the two dimensional     # array using a single poer     remove_X_Rows_and_Columns(a, n, x)    # This code is contributed by # Mohit kumar 29

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   PHP

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   <?php // PHP implementation of the above approach    // Function to remove first x  // rows and columns from an array  function remove_X_Rows_and_Columns($a, $n, $x)  {      echo "\nRemoving First ", $x,           " rows and columns:\n";         // Start from the xth row      // and print till n-1th row      for ($i = $x; $i < $n; $i++)      {             // Start from the xth column          // and print till the n-1th column          for ($j = $x; $j < $n; $j++)          {                 // Accessing the array using pointers              echo $a[$i][$j], " ";          }          echo "\n";      }  }     // Print the matrix  function printMatrix($a, $n)  {         for ($i = 0; $i < $n; $i++)     {          for ($j = 0; $j < $n; $j++)          {              echo $a[$i][$j], " ";          }          echo "\n";      }  }     $n = 4;     // get the array inputs  $a = array(array());    for ($i = 0; $i < $n; $i++)  {      for ($j = 0; $j < $n; $j++)     {          $a[$i][$j] = $i * 10 + $j;      }  }     // Print the matrix  echo "Original Matrix:\n";  printMatrix($a, $n);     $x = 2;     // passing the two dimensional  // array using a single pointer  remove_X_Rows_and_Columns($a, $n, $x);     // This code is contributed by Ryuga ?>

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   Output:

   
   

   
   

   Original Matrix:
   0 1 2 3 
   10 11 12 13 
   20 21 22 23 
   30 31 32 33 
   
   Removing First 2 rows and columns:
   22 23 
   32 33
   

2. Remove last X rows and columns from the matrix.

   Examples:

   Input: n = 4, 
          arr[][] = {{20, 2, 10, 16},
                     {20, 17, 11, 6},
                     {14, 16, 1, 3},
                     {10, 2, 17, 4}}, 
          x = 2
   Output:
   20 2
   20 17
   
   Explanation:
   Here the value of X is 2.
   So remove the last 2 rows and 
   the last 2 columns from the matrix. 
   Hence the output is
   20 2
   20 17
   

   Simple Approach

   • Skip the last x rows and columns and print the remaining elements in the matrix.
   • Start from the 0th row and print till the n-xth row.
   • Start from the 0th column and print till the n-xth column.

   Implementation:

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   #include <iostream> using namespace std;    // Function to remove last x rows // and columns from an array void remove_X_Rows_and_Columns(int* a, int n, int x) {        cout << "\nRemoving Last " << x          << " rows and columns:\n";        // Start from the 0th row     // and print till n-xth row     for (int i = 0; i < n - x; i++) {            // Start from the 0th column         // and print till the n-xth column         for (int j = 0; j < n - x; j++) {                // Accessing the array using pointers             cout << *((a + i * n) + j) << " ";         }         cout << endl;     } }    // Print the matrix void printMatrix(int* a, int n) {        for (int i = 0; i < n; i++) {         for (int j = 0; j < n; j++) {             cout << *((a + i * n) + j) << " ";         }         cout << endl;     } }    int main() {     int n = 4;        // get the array inputs     int a[n][n];     for (int i = 0; i < n; i++) {         for (int j = 0; j < n; j++) {             a[i][j] = (i * 10 + j);         }     }        // Print the matrix     cout << "Original Matrix:\n";     printMatrix((int*)a, n);        int x = 2;        // passing the two dimensional     // array using a single pointer     remove_X_Rows_and_Columns((int*)a, n, x);        return 0; }

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   Output:

   Original Matrix:
   0 1 2 3 
   10 11 12 13 
   20 21 22 23 
   30 31 32 33 
   
   Removing Last 2 rows and columns:
   0 1 
   10 11
   

3. Remove first X rows and last X columns from the matrix.

   Examples:

   Input: n = 4, 
          arr[][] = {{20, 2, 10, 16},
                     {20, 17, 11, 6},
                     {14, 16, 1, 3},
                     {10, 2, 17, 4}}, 
          x = 2
   Output:
   14 16
   10 2
   
   Explanation:
   Here the value of X is 2.
   So remove the first 2 rows 
   and the last 2 columns from the matrix. 
   Hence the output is
   14 16
   10 2
   

   Simple Approach

   • Skip the first x rows and last x columns and print the remaining elements in the matrix.
   • Start from the xth row and print till the n-1th row.
   • Start from the 0th column and print till the n-xth column.

   Implementation:

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   #include <iostream> using namespace std;    // Function to remove first x rows // and last x columns from an array void remove_X_Rows_and_Columns(int* a, int n, int x) {        cout << "\nRemoving First " << x          << " rows and Last " << x          << " columns:\n";        // Start from the xth row     // and print till n-1th row     for (int i = x; i < n; i++) {            // Start from the 0th column         // and print till the n-xth column         for (int j = 0; j < n - x; j++) {                // Accessing the array using pointers             cout << *((a + i * n) + j) << " ";         }         cout << endl;     } }    // Print the matrix void printMatrix(int* a, int n) {        for (int i = 0; i < n; i++) {         for (int j = 0; j < n; j++) {             cout << *((a + i * n) + j) << " ";         }         cout << endl;     } }    int main() {     int n = 4;        // get the array inputs     int a[n][n];     for (int i = 0; i < n; i++) {         for (int j = 0; j < n; j++) {             a[i][j] = (i * 10 + j);         }     }        // Print the matrix     cout << "Original Matrix:\n";     printMatrix((int*)a, n);        int x = 2;        // passing the two dimensional     // array using a single pointer     remove_X_Rows_and_Columns((int*)a, n, x);        return 0; }

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   Output:

   Original Matrix:
   0 1 2 3 
   10 11 12 13 
   20 21 22 23 
   30 31 32 33 
   
   Removing First 2 rows and Last 2 columns:
   20 21 
   30 31
   

4. Remove last X rows and first x columns from the matrix.

   Examples:

   Input: n = 4, 
          arr[][] = {{20, 2, 10, 16},
                     {20, 17, 11, 6},
                     {14, 16, 1, 3},
                     {10, 2, 17, 4}}, 
          x = 2
   Output:
   10 16
   11 6
   
   Explanation:
   Here the value of X is 2.
   So remove the last 2 rows and
   the first 2 columns from the matrix. 
   Hence the output is
   10 16
   11 6
   

   Simple Approach

   • Skip the last x rows and first x columns and print the remaining elements in the matrix.
   • Start from the 0th row and print till the n-xth row.
   • Start from the xth column and print till the n-1th column.

   Implementation:

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   #include <iostream> using namespace std;    // Function to remove last x rows // and first x columns from an array void remove_X_Rows_and_Columns(int* a, int n, int x) {        cout << "\nRemoving Last " << x          << " rows and First " << x          << " columns:\n";        // Start from the 0th row     // and print till n-xth row     for (int i = 0; i < n - x; i++) {            // Start from the xth column and         // print till the n-1th column         for (int j = x; j < n; j++) {                // Accessing the array using pointers             cout << *((a + i * n) + j) << " ";         }         cout << endl;     } }    // Print the matrix void printMatrix(int* a, int n) {        for (int i = 0; i < n; i++) {         for (int j = 0; j < n; j++) {             cout << *((a + i * n) + j) << " ";         }         cout << endl;     } }    int main() {     int n = 4;        // get the array inputs     int a[n][n];     for (int i = 0; i < n; i++) {         for (int j = 0; j < n; j++) {             a[i][j] = (i * 10 + j);         }     }        // Print the matrix     cout << "Original Matrix:\n";     printMatrix((int*)a, n);        int x = 2;        // passing the two dimensional     // array using a single pointer     remove_X_Rows_and_Columns((int*)a, n, x);        return 0; }

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   Output:

   Original Matrix:
   0 1 2 3 
   10 11 12 13 
   20 21 22 23 
   30 31 32 33 
   
   Removing Last 2 rows and First 2 columns:
   2 3 
   12 13
   

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