Modify a given matrix by placing sorted boundary elements in clockwise manner

Given a square matrix A[][] of  N * N, the task is to sort the boundary elements of a matrix starting from the outermost to the innermost boundary and place them in a clockwise manner.

Examples:

Input: A[][] = {{9, 7, 4, 5}, {1, 6, 2, -6}, {12, 20, 2, 0}, {-5, -6, 7, -2}}
Output: {{-6, -6, -5, -2}, {12, 2, 2, 0}, {9, 20, 6, 1}, {7, 7, 5, 4}}            
Explanation: 
The outermost boundary elements are {9, 7, 4, 5, -6, 0, -2, 7, -6, -5, 12, 1}. 
Sorted order of the boundary elements are {-6, -6, -5, -2, 0, 1, 4, 5, 7, 7, 9, 12}. 
Placing these sorted sequence of elements back into the matrix in clockwise manner, starting from the top-left corner modifies A[][] to {{-6, -6, -5, -2}, {12, 6, 2, 0}, {9, 20, 2, 1}, {7, 7, 5, 4}}
The next level of boundary elements are {6, 2, 2, 20}. 
Sorted order of these elements are {2, 2, 6, 20}.
Placing these sorted sequence of elements back into the matrix in clockwise manner, starting from the top-left corner modifies A[][] to {{-6, -6, -5, -2}, {12, 2, 2, 0}, {9, 20, 6, 1}, {7, 7, 5, 4}}

Input: A[][] = {{4, 3,}, {1, 2}}
Output: {{1, 2,}, {4, 3}}

Approach: The idea is to use boundary variables to get the current boundary elements and store them in an array. Then, sort the array in ascending order and place the sorted elements back into the matrix in clockwise direction. 
Follow the steps below to solve the problem:

• Initialize variables, say k, m, l, and n, representing the starting row index, ending row index, starting column index, and ending column index.
• Iterate until all the squares of loops are visited.
  • In each outer loop traversal, store the elements of the square in an array, say V, in a clockwise manner.
  • Push the top row in V, i.e. push the elements of the k^th row from column indices l to n. Increase count of k.
  • Push the right column in V, i.e. push the elements of the n – 1^th column from row indices k to m. Decrease count of n.
  • Push the bottom row, i.e. if k < m, then push the elements of the m-1^th row from column indices n – 1 to l. Decrease count of m.
  • Push the left column, i.e. if l < n, then push the elements of the l^th column from row indices m – 1 to k. Increase count of l.
  • Sort the array V in ascending order.
  • Repeat the above steps and update elements of the matrix with the sorted elements from V.
• After complete traversal of the matrix, print the modified matrix A.

Below is the implementation of the above approach:

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to print the elements
// of the matrix in row-wise manner
void printMatrix(vector<vector<int> > a)
{
    for (auto x : a) {
        for (auto y : x) {
            cout << y << " ";
        }
        cout << "\n";
    }
}

// Function to sort boundary elements
// of a matrix starting from the outermost
// to the innermost boundary and place them
// in a clockwise manner
void sortBoundaryWise(vector<vector<int> > a)
{
    /*  k - starting row index
        m - ending row index
        l - starting column index
        n - ending column index
        i - iterator
      */
    int i, k = 0, l = 0;
    int m = a.size(), n = a[0].size();
    int n_i, n_k = 0, n_l = 0, n_m = m, n_n = n;

    while (k < m && l < n) {

        // Stores the current
        // boundary elements
        vector<int> boundary;

        // Push the first row
        for (i = l; i < n; ++i) {
            boundary.push_back(a[k][i]);
        }
        k++;

        // Push the last column
        for (i = k; i < m; ++i) {
            boundary.push_back(a[i][n - 1]);
        }
        n--;

        // Push the last row
        if (k < m) {
            for (i = n - 1; i >= l; --i) {
                boundary.push_back(a[m - 1][i]);
            }
            m--;
        }

        // Push the first column
        if (l < n) {
            for (i = m - 1; i >= k; --i) {
                boundary.push_back(a[i][l]);
            }
            l++;
        }

        // Sort the boundary elements
        sort(boundary.begin(), boundary.end());
        int ind = 0;

        // Update the current boundary
        // with sorted elements

        // Update the first row
        for (i = n_l; i < n_n; ++i) {
            a[n_k][i] = boundary[ind++];
        }
        n_k++;

        // Update the last column
        for (i = n_k; i < n_m; ++i) {
            a[i][n_n - 1] = boundary[ind++];
        }
        n_n--;

        // Update the last row
        if (n_k < n_m) {
            for (i = n_n - 1; i >= n_l; --i) {
                a[n_m - 1][i] = boundary[ind++];
            }
            n_m--;
        }

        // Update the first column
        if (n_l < n_n) {
            for (i = n_m - 1; i >= n_k; --i) {
                a[i][n_l] = boundary[ind++];
            }
            n_l++;
        }
    }

    // Print the resultant matrix
    printMatrix(a);
}

// Driver Code
int main()
{
    // Given matrix
    vector<vector<int> > matrix = { { 9, 7, 4, 5 },
                                    { 1, 6, 2, -6 },
                                    { 12, 20, 2, 0 },
                                    { -5, -6, 7, -2 } };

    sortBoundaryWise(matrix);

    return 0;
}

Java

// Java program for the above approach
import java.util.*;

class GFG{

// Function to print the elements
// of the matrix in row-wise manner
static void printMatrix(ArrayList<ArrayList<Integer>> a)
{
    for(int i = 0; i < a.size(); i++)
    {
        for(int j = 0; j < a.get(i).size(); j++)
        {
            System.out.print(a.get(i).get(j) + " ");
        }
        System.out.println();
    }
}

// Function to sort boundary elements
// of a matrix starting from the outermost
// to the innermost boundary and place them
// in a clockwise manner
static void sortBoundaryWise(ArrayList<ArrayList<Integer>> a)
{
    /*  k - starting row index
        m - ending row index
        l - starting column index
        n - ending column index
        i - iterator
      */
    int i, k = 0, l = 0;
    int m = a.size(), n = a.get(0).size();
    int n_i, n_k = 0, n_l = 0, n_m = m, n_n = n;

    while (k < m && l < n)
    {

        // Stores the current
        // boundary elements
        ArrayList<Integer> boundary = new ArrayList<Integer>();

        // Push the first row
        for(i = l; i < n; ++i)
        {
            boundary.add(a.get(k).get(i));
        }
        k++;

        // Push the last column
        for(i = k; i < m; ++i)
        {
            boundary.add(a.get(i).get(n - 1));
        }
        n--;

        // Push the last row
        if (k < m)
        {
            for(i = n - 1; i >= l; --i)
            {
                boundary.add(a.get(m - 1).get(i));
            }
            m--;
        }

        // Push the first column
        if (l < n)
        {
            for(i = m - 1; i >= k; --i)
            {
                boundary.add(a.get(i).get(l));
            }
            l++;
        }

        // Sort the boundary elements
        Collections.sort(boundary);
        int ind = 0;

        // Update the current boundary
        // with sorted elements

        // Update the first row
        for(i = n_l; i < n_n; ++i)
        {
            a.get(n_k).set(i, boundary.get(ind));
            ind++;
        }
        n_k += 1;

        // Update the last column
        for(i = n_k; i < n_m; ++i)
        {
            a.get(i).set(n_n - 1, boundary.get(ind));
             ind++;
        }
        n_n--;

        // Update the last row
        if (n_k < n_m)
        {
            for(i = n_n - 1; i >= n_l; --i)
            {
                a.get(n_m - 1).set(i, boundary.get(ind));
                ind++;
            }
            n_m--;
        }

        // Update the first column
        if (n_l < n_n)
        {
            for(i = n_m - 1; i >= n_k; --i)
            {
                a.get(i).set(n_l, boundary.get(ind));
                ind++;
            }
            n_l++;
        }
    }

    // Print the resultant matrix
    printMatrix(a);
}

// Driver Code
public static void main(String args[])
{

    // Given matrix
    ArrayList<
    ArrayList<Integer>> matrix = new ArrayList<
                                     ArrayList<Integer>>();
    ArrayList<Integer> list1 = new ArrayList<Integer>(
        Arrays.asList(9, 7, 4, 5));
    ArrayList<Integer> list2 = new ArrayList<Integer>(
        Arrays.asList(1, 6, 2, -6));
    ArrayList<Integer> list3 = new ArrayList<Integer>(
        Arrays.asList(12, 20, 2, 0));
    ArrayList<Integer> list4 = new ArrayList<Integer>(
        Arrays.asList(-5, -6, 7, -2));

    matrix.add(list1);
    matrix.add(list2);
    matrix.add(list3);
    matrix.add(list4);

    sortBoundaryWise(matrix);
}
}

// This code is contributed by ipg2016107

Python3

# Python3 program for the above approach

# Function to print the elements
# of the matrix in row-wise manner
def printMatrix(a):
    for x in a:
        for y in x:
            print(y, end = " ")

        print()

# Function to sort boundary elements
# of a matrix starting from the outermost
# to the innermost boundary and place them
# in a clockwise manner
def sortBoundaryWise(a):

    '''  k - starting row index
        m - ending row index
        l - starting column index
        n - ending column index
        i - iterator
      '''
    k = 0
    l = 0
    m = len(a)
    n = len(a[0])
    n_k = 0
    n_l = 0
    n_m = m
    n_n = n

    while (k < m and l < n):

        # Stores the current
        # boundary elements
        boundary = []

        # Push the first row
        for i in range(l, n):
            boundary.append(a[k][i])
        k += 1

        # Push the last column
        for i in range(k, m):
            boundary.append(a[i][n - 1])
        n -= 1

        # Push the last row
        if (k < m):
            for i in range(n - 1,  l - 1, -1):
                boundary.append(a[m - 1][i])
            m -= 1

        # Push the first column
        if (l < n):
            for i in range(m - 1, k - 1, -1):
                boundary.append(a[i][l])
            l += 1

        # Sort the boundary elements
        boundary.sort()
        ind = 0

        # Update the current boundary
        # with sorted elements

        # Update the first row
        for i in range(n_l, n_n):
            a[n_k][i] = boundary[ind]
            ind += 1

        n_k += 1

        # Update the last column
        for i in range(n_k, n_m):
            a[i][n_n - 1] = boundary[ind]
            ind += 1
        n_n -= 1

        # Update the last row
        if (n_k < n_m):
            for i in range(n_n - 1, n_l - 1, -1):
                a[n_m - 1][i] = boundary[ind]
                ind += 1

            n_m -= 1

        # Update the first column
        if (n_l < n_n):
            for i in range(n_m - 1, n_k - 1, -1):
                a[i][n_l] = boundary[ind]
                ind += 1
            n_l += 1

    # Print the resultant matrix
    printMatrix(a)

# Driver Code
if __name__ == "__main__":

    # Given matrix
    matrix = [[9, 7, 4, 5],
              [1, 6, 2, -6],
              [12, 20, 2, 0],
              [-5, -6, 7, -2]]

    sortBoundaryWise(matrix)

    # This code is contributed by ukasp.

C#

// C# program for the above approach
using System;
using System.Collections.Generic;


class GFG
{

  // Function to print the elements
  // of the matrix in row-wise manner
  static void printMatrix(List<List<int>> a)
  {
    foreach(List<int> x in a) {
      foreach(int y in x) {
        Console.Write(y + " ");
      }
      Console.WriteLine();
    }
  }

  // Function to sort boundary elements
  // of a matrix starting from the outermost
  // to the innermost boundary and place them
  // in a clockwise manner
  static void sortBoundaryWise(List<List<int>> a)
  {
    /*  k - starting row index
            m - ending row index
            l - starting column index
            n - ending column index
            i - iterator
          */
    int i, k = 0, l = 0;
    int m = a.Count, n = a[0].Count;
    int n_k = 0, n_l = 0, n_m = m, n_n = n;

    while (k < m && l < n) {

      // Stores the current
      // boundary elements
      List<int> boundary = new List<int>();

      // Push the first row
      for (i = l; i < n; ++i) {
        boundary.Add(a[k][i]);
      }
      k++;

      // Push the last column
      for (i = k; i < m; ++i) {
        boundary.Add(a[i][n - 1]);
      }
      n--;

      // Push the last row
      if (k < m) {
        for (i = n - 1; i >= l; --i) {
          boundary.Add(a[m - 1][i]);
        }
        m--;
      }

      // Push the first column
      if (l < n) {
        for (i = m - 1; i >= k; --i) {
          boundary.Add(a[i][l]);
        }
        l++;
      }

      // Sort the boundary elements
      boundary.Sort();
      int ind = 0;

      // Update the current boundary
      // with sorted elements

      // Update the first row
      for (i = n_l; i < n_n; ++i) {
        a[n_k][i] = boundary[ind++];
      }
      n_k++;

      // Update the last column
      for (i = n_k; i < n_m; ++i) {
        a[i][n_n - 1] = boundary[ind++];
      }
      n_n--;

      // Update the last row
      if (n_k < n_m) {
        for (i = n_n - 1; i >= n_l; --i) {
          a[n_m - 1][i] = boundary[ind++];
        }
        n_m--;
      }

      // Update the first column
      if (n_l < n_n) {
        for (i = n_m - 1; i >= n_k; --i) {
          a[i][n_l] = boundary[ind++];
        }
        n_l++;
      }
    }

    // Print the resultant matrix
    printMatrix(a);
  }

  // Driver code
  static void Main()
  {
    // Given matrix
    List<List<int>> matrix = new List<List<int>>();
    matrix.Add(new List<int>(new int[]{9, 7, 4, 5}));
    matrix.Add(new List<int>(new int[]{1, 6, 2, -6}));
    matrix.Add(new List<int>(new int[]{12, 20, 2, 0}));
    matrix.Add(new List<int>(new int[]{-5, -6, 7, -2}));

    sortBoundaryWise(matrix);
  }
}

// This code is contributed by divyeshrabadiya07.

Javascript

<script>

// JavaScript program for the above approach

// Function to print the elements
// of the matrix in row-wise manner
function printMatrix(a)
{
    for(let i = 0; i < a.length; i++)
    {
        for(let j = 0; j < a[i].length; j++)
        {
            document.write(a[i][j] + " ");
        }
        document.write("<br>");
    }
}

// Function to sort boundary elements
// of a matrix starting from the outermost
// to the innermost boundary and place them
// in a clockwise manner
function sortBoundaryWise(a)
{
    /*  k - starting row index
        m - ending row index
        l - starting column index
        n - ending column index
        i - iterator
      */
    let i, k = 0, l = 0;
    let m = a.length, n = a[0].length;
    let n_i, n_k = 0, n_l = 0, n_m = m, n_n = n;

    while (k < m && l < n)
    {

        // Stores the current
        // boundary elements
        let boundary = [];

        // Push the first row
        for(i = l; i < n; ++i)
        {
            boundary.push(a[k][i]);
        }
        k++;

        // Push the last column
        for(i = k; i < m; ++i)
        {
            boundary.push(a[i][n - 1]);
        }
        n--;

        // Push the last row
        if (k < m)
        {
            for(i = n - 1; i >= l; --i)
            {
                boundary.push(a[m - 1][i]);
            }
            m--;
        }

        // Push the first column
        if (l < n)
        {
            for(i = m - 1; i >= k; --i)
            {
                boundary.push(a[i][l]);
            }
            l++;
        }

        // Sort the boundary elements
        boundary.sort(function(a,b){return a-b;});
        let ind = 0;

        // Update the current boundary
        // with sorted elements

        // Update the first row
        for(i = n_l; i < n_n; ++i)
        {
            a[n_k][i] = boundary[ind];
            ind++;
        }
        n_k += 1;

        // Update the last column
        for(i = n_k; i < n_m; ++i)
        {
            a[i][n_n - 1] = boundary[ind];
             ind++;
        }
        n_n--;

        // Update the last row
        if (n_k < n_m)
        {
            for(i = n_n - 1; i >= n_l; --i)
            {
                a[n_m - 1][i] = boundary[ind];
                ind++;
            }
            n_m--;
        }

        // Update the first column
        if (n_l < n_n)
        {
            for(i = n_m - 1; i >= n_k; --i)
            {
                a[i][n_l] = boundary[ind];
                ind++;
            }
            n_l++;
        }
    }

    // Print the resultant matrix
    printMatrix(a);
}

// Driver Code
 // Given matrix
let matrix = [];
let list1 = [9, 7, 4, 5];
let list2=[1, 6, 2, -6];

let list3=[12, 20, 2, 0];
let list4=[-5, -6, 7, -2];

matrix.push(list1);
matrix.push(list2);
matrix.push(list3);
matrix.push(list4);

sortBoundaryWise(matrix);


// This code is contributed by avanitrachhadiya2155

</script>

Output

-6 -6 -5 -2 
12 2 2 0 
9 20 6 1 
7 7 5 4 

Time Complexity: O(N³*log(N))
Auxiliary Space: O(N²)