Data Modelling & AI Data Structure & Algorithm

Convert given Matrix into sorted Spiral Matrix

23 June 2025

0

Given a matrix, the task is to convert the given Matrix into sorted Spiral Matrix.
Examples:

Input: y[][] = {
          { 2, 5, 12 },
          { 22, 54, 55 },
          { 1, 6, 8 }
        };
Output:
       1 2 5 
       45 55 6
       22 12 8

Input: y[][] = {
          { 2, 5, 12 },
          { 22, 45, 55 },
          { 1, 6, 8 },
          { 13, 56, 10 }
        };
Output:
       1 2 5 
       45 55 6 
       22 56 8 
       13 12 10

Approach:

Convert the given 2D array into a 1D array.
Sort the 1D array
Convert 1D to Spiral matrix
This can be solved by 4 for loops which store all the elements. Every for loop defines a single direction movement along with the matrix. The first for loop represents the movement from left to right, whereas the second crawl represents the movement from top to bottom, the third represents the movement from the right to left, and the fourth represents the movement from bottom to up.

Below is the implementation of the above approach:

C++

// C++ program to Convert given Matrix
// into sorted Spiral Matrix
#include <bits/stdc++.h>
using namespace std;
 
const int MAX = 1000;
 
// Function to convert the array to Spiral
void ToSpiral(int m, int n,
            int Sorted[], int a[MAX][MAX])
{
    // For Array pointer
    int index = 0;
 
    // k - starting row index
    // m - ending row index
    // l - starting column index
    // n - ending column index
    int k = 0, l = 0;
 
    while (k < m && l < n) 
    {
 
        // Print the first row
        // from the remaining rows
        for (int i = l; i < n; ++i)
        {
            a[k][i] = Sorted[index];
            index++;
        }
 
        k++;
 
        // Print the last column
        // from the remaining columns
        for (int i = k; i < m; ++i)
        {
            a[i][n - 1] = Sorted[index];
            index++;
        }
        n--;
 
        // Print the last row
        // from the remaining rows
        if (k < m) 
        {
            for (int i = n - 1; i >= l; --i)
            {
                a[m - 1][i] = Sorted[index];
                index++;
            }
            m--;
        }
 
        // Print the first column
        // from the remaining columns
        if (l < n)
        {
            for (int i = m - 1; i >= k; --i)
            {
                a[i][l] = Sorted[index];
                index++;
            }
            l++;
        }
    }
}
 
// Function to convert 2D array to 1D array
void convert2Dto1D(int y[MAX][MAX], 
                   int m, int n,int x[])
{
 
    int index = 0;
 
    // Store value 2D Matrix To 1D array
    for (int i = 0; i < m; i++) 
    {
        for (int j = 0; j < n; j++) 
        {
            x[index] = y[i][j];
            index++;
        }
    }
}
 
// Function to print the Matrix
void PrintMatrix(int a[MAX][MAX], 
                int m, int n)
{
 
    // Print Spiral Matrix
    for (int i = 0; i < m; i++) 
    {
        for (int j = 0; j < n; j++) 
        {
            cout << a[i][j] << " ";
        }
        cout << endl;
    }
}
 
 
// Function to Convert given Matrix
// into sorted Spiral Matrix
void convertMatrixToSortedSpiral(
    int y[MAX][MAX], int m, int n)
{
    int a[MAX][MAX] = {0};
    int x[m * n];
 
    convert2Dto1D(y, m, n,x);
    sort(x, x + n * m);
    ToSpiral(m, n, x, a);
    PrintMatrix(a, m, n);
}
 
// Driver code
int main()
{
    int m = 4, n = 3;
    int y[MAX][MAX] = {
        { 2, 5, 12 },
        { 22, 45, 55 },
        { 1, 6, 8 },
        { 13, 56, 10 }};
 
    convertMatrixToSortedSpiral(y, m, n);
 
    return 0;
}
 
// This code is contributed by Arnab Kundu

Java

// Java program to Convert given Matrix
// into sorted Spiral Matrix
 
import java.util.*;
 
public class TwistedMatrix {
 
    static int MAX = 1000;
 
    // Function to convert the array to Spiral
    static void ToSpiral(int m, int n,
                         int Sorted[], int a[][])
    {
        // For Array pointer
        int index = 0;
 
        // k - starting row index
        // m - ending row index
        // l - starting column index
        // n - ending column index
        int k = 0, l = 0;
 
        while (k < m && l < n) {
 
            // Print the first row
            // from the remaining rows
            for (int i = l; i < n; ++i) {
                a[k][i] = Sorted[index];
                index++;
            }
 
            k++;
 
            // Print the last column
            // from the remaining columns
            for (int i = k; i < m; ++i) {
                a[i][n - 1] = Sorted[index];
                index++;
            }
            n--;
 
            // Print the last row
            // from the remaining rows
            if (k < m) {
                for (int i = n - 1; i >= l; --i) {
                    a[m - 1][i] = Sorted[index];
                    index++;
                }
                m--;
            }
 
            // Print the first column
            // from the remaining columns
            if (l < n) {
                for (int i = m - 1; i >= k; --i) {
                    a[i][l] = Sorted[index];
                    index++;
                }
                l++;
            }
        }
    }
 
    // Function to convert 2D array to 1D array
    public static int[] convert2Dto1D(
        int y[][], int m, int n)
    {
 
        int index = 0;
        int x[] = new int[m * n];
 
        // Store value 2D Matrix To 1D array
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                x[index] = y[i][j];
                index++;
            }
        }
        return x;
    }
 
    // Function to print the Matrix
    public static void PrintMatrix(
        int a[][], int m, int n)
    {
 
        // Print Spiral Matrix
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                System.out.print(a[i][j] + " ");
            }
            System.out.println();
        }
    }
 
    // Function to sort the array
    public static int[] SortArray(int x[])
    {
 
        // Sort array Using InBuilt Function
        Arrays.sort(x);
 
        return x;
    }
 
    // Function to Convert given Matrix
    // into sorted Spiral Matrix
    public static void convertMatrixToSortedSpiral(
        int y[][], int m, int n)
    {
 
        int a[][] = new int[MAX][MAX];
        int x[] = new int[m * n];
 
        x = convert2Dto1D(y, m, n);
        x = SortArray(x);
        ToSpiral(m, n, x, a);
        PrintMatrix(a, m, n);
    }
 
    // Driver code
    public static void main(String[] args)
    {
        int m = 4, n = 3;
        int y[][] = {
            { 2, 5, 12 },
            { 22, 45, 55 },
            { 1, 6, 8 },
            { 13, 56, 10 }
        };
 
        convertMatrixToSortedSpiral(y, m, n);
    }
}
 
// This article is contributed by VRUND R PATEL

Python 3

# Python3 program to Convert given Matrix
# into sorted Spiral Matrix
MAX = 1000
 
# Function to convert the array to Spiral
def ToSpiral(m, n, Sorted, a):
     
    # For Array pointer
    index = 0
 
    # k - starting row index
    # m - ending row index
    # l - starting column index
    # n - ending column index
    k = 0
    l = 0
 
    while (k < m and l < n):
         
        # Print the first row
        # from the remaining rows
        for i in range(l, n, 1):
            a[k][i] = Sorted[index]
            index += 1
 
        k += 1
 
        # Print the last column
        # from the remaining columns
        for i in range(k, m, 1):
            a[i][n - 1] = Sorted[index]
            index += 1
         
        n -= 1
 
        # Print the last row
        # from the remaining rows
        if (k < m):
            i = n - 1
            while(i >= l):
                a[m - 1][i] = Sorted[index]
                index += 1
                i -= 1
 
            m -= 1
 
        # Print the first column
        # from the remaining columns
        if (l < n):
            i = m - 1
            while(i >= k):
                a[i][l] = Sorted[index]
                index += 1
                i -= 1
             
            l += 1
 
# Function to convert 2D array to 1D array
def convert2Dto1D(y, m, n):
    index = 0
    x = [0 for i in range(m * n)]
 
    # Store value 2D Matrix To 1D array
    for i in range(m):
        for j in range(n):
            x[index] = y[i][j]
            index += 1
         
    return x
 
# Function to print the Matrix
def PrintMatrix(a, m, n):
     
    # Print Spiral Matrix
    for i in range(m):
        for j in range(n):
            print(a[i][j], end =" ")
         
        print('\n', end = "")
 
# Function to sort the array
def SortArray(x):
     
    # Sort array Using InBuilt Function
    x.sort(reverse = False)
 
    return x
 
# Function to Convert given Matrix
# into sorted Spiral Matrix
def convertMatrixToSortedSpiral(y, m, n):
    a = [[0 for i in range(MAX)] 
            for j in range(MAX)]
    x = [0 for i in range(15)]
 
    x = convert2Dto1D(y, m, n)
    x = SortArray(x)
    ToSpiral(m, n, x, a)
    PrintMatrix(a, m, n)
 
# Driver code
if __name__ == '__main__':
    m = 4
    n = 3
    y = [[2, 5, 12], [22, 45, 55],
         [1, 6, 8], [13, 56, 10]]
 
    convertMatrixToSortedSpiral(y, m, n)
 
# This code is contributed by Surendra_Gangwar

C#

// C# program to Convert given Matrix
// into sorted Spiral Matrix
using System;
 
class GFG 
{
    static int MAX = 1000;
 
    // Function to convert the array to Spiral
    static void ToSpiral(int m, int n,
                         int []Sorted, int [,]a)
    {
        // For Array pointer
        int index = 0;
 
        // k - starting row index
        // m - ending row index
        // l - starting column index
        // n - ending column index
        int k = 0, l = 0;
 
        while (k < m && l < n) 
        {
 
            // Print the first row
            // from the remaining rows
            for (int i = l; i < n; ++i) 
            {
                a[k, i] = Sorted[index];
                index++;
            }
 
            k++;
 
            // Print the last column
            // from the remaining columns
            for (int i = k; i < m; ++i)
            {
                a[i, n - 1] = Sorted[index];
                index++;
            }
            n--;
 
            // Print the last row
            // from the remaining rows
            if (k < m) 
            {
                for (int i = n - 1; i >= l; --i) 
                {
                    a[m - 1, i] = Sorted[index];
                    index++;
                }
                m--;
            }
 
            // Print the first column
            // from the remaining columns
            if (l < n) 
            {
                for (int i = m - 1; i >= k; --i) 
                {
                    a[i, l] = Sorted[index];
                    index++;
                }
                l++;
            }
        }
    }
 
    // Function to convert 2D array to 1D array
    public static int[] convert2Dto1D(int [,]y,
                                      int m, int n)
    {
        int index = 0;
        int []x = new int[m * n];
 
        // Store value 2D Matrix To 1D array
        for (int i = 0; i < m; i++)
        {
            for (int j = 0; j < n; j++) 
            {
                x[index] = y[i, j];
                index++;
            }
        }
        return x;
    }
 
    // Function to print the Matrix
    public static void PrintMatrix(int [,]a, 
                                   int m, int n)
    {
 
        // Print Spiral Matrix
        for (int i = 0; i < m; i++) 
        {
            for (int j = 0; j < n; j++)
            {
                Console.Write(a[i, j] + " ");
            }
            Console.WriteLine();
        }
    }
 
    // Function to sort the array
    public static int[] SortArray(int []x)
    {
 
        // Sort array Using InBuilt Function
        Array.Sort(x);
 
        return x;
    }
 
    // Function to Convert given Matrix
    // into sorted Spiral Matrix
    public static void convertMatrixToSortedSpiral(int [,]y, 
                                                   int m, int n)
    {
        int [,]a = new int[MAX, MAX];
        int []x = new int[m * n];
 
        x = convert2Dto1D(y, m, n);
        x = SortArray(x);
        ToSpiral(m, n, x, a);
        PrintMatrix(a, m, n);
    }
 
    // Driver code
    public static void Main(String[] args)
    {
        int m = 4, n = 3;
        int [,]y = {{ 2, 5, 12 },
                    { 22, 45, 55 },
                    { 1, 6, 8 },
                    { 13, 56, 10 }};
 
        convertMatrixToSortedSpiral(y, m, n);
    }
}
 
// This code is contributed by Rajput-Ji

Javascript

<script>
// Javascript program to Convert given Matrix
// into sorted Spiral Matrix
 
let MAX = 1000;
 
// Function to convert the array to Spiral
function ToSpiral(m,n,Sorted,a)
{
     
    // For Array pointer
        let index = 0;
   
        // k - starting row index
        // m - ending row index
        // l - starting column index
        // n - ending column index
        let k = 0, l = 0;
   
        while (k < m && l < n) {
   
            // Print the first row
            // from the remaining rows
            for (let i = l; i < n; ++i) {
                a[k][i] = Sorted[index];
                index++;
            }
   
            k++;
   
            // Print the last column
            // from the remaining columns
            for (let i = k; i < m; ++i) {
                a[i][n - 1] = Sorted[index];
                index++;
            }
            n--;
   
            // Print the last row
            // from the remaining rows
            if (k < m) {
                for (let i = n - 1; i >= l; --i) {
                    a[m - 1][i] = Sorted[index];
                    index++;
                }
                m--;
            }
   
            // Print the first column
            // from the remaining columns
            if (l < n) {
                for (let i = m - 1; i >= k; --i) {
                    a[i][l] = Sorted[index];
                    index++;
                }
                l++;
            }
        }
}
 
// Function to convert 2D array to 1D array
function convert2Dto1D(y,m,n)
{
    let index = 0;
        let x = new Array(m * n);
   
        // Store value 2D Matrix To 1D array
        for (let i = 0; i < m; i++) {
            for (let j = 0; j < n; j++) {
                x[index] = y[i][j];
                index++;
            }
        }
        return x;
}
 
// Function to print the Matrix
function PrintMatrix(a,m,n)
{
    // Print Spiral Matrix
        for (let i = 0; i < m; i++) {
            for (let j = 0; j < n; j++) {
                document.write(a[i][j] + " ");
            }
            document.write("<br>");
        }
}
 
// Function to sort the array
function SortArray(x)
{
    // Sort array Using InBuilt Function
        x.sort(function(a,b){return a-b;});
   
        return x;
}
 
 // Function to Convert given Matrix
    // into sorted Spiral Matrix
function convertMatrixToSortedSpiral(y,m,n)
{
    let a = new Array(MAX);
    for(let i=0;i<MAX;i++)
        a[i]=new Array(MAX);
        let x = new Array(m * n);
   
        x = convert2Dto1D(y, m, n);
        x = SortArray(x);
        ToSpiral(m, n, x, a);
        PrintMatrix(a, m, n);
}
 
 // Driver code
let m = 4, n = 3;
let y = [
[ 2, 5, 12 ],
[ 22, 45, 55 ],
[ 1, 6, 8 ],
[ 13, 56, 10 ]
];
 
convertMatrixToSortedSpiral(y, m, n);
 
// This code is contributed by avanitrachhadiya2155
</script>

Output:

Time Complexity: O(m*n)

Auxiliary Space: O(m*n)

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Convert given Matrix into sorted Spiral Matrix

C++

Java

Python 3

C#

Javascript

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