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.

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++

#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; 
} 

Python3

# 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 

PHP

<?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 
?> 

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

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:

#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; 
} 

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

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:

#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; 
} 

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

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:

#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; 
} 

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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C++

Python3

PHP

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