Print concentric rectangular pattern in a 2d matrix

Given a positive integer n, print the matrix filled with rectangle pattern as shown below:
a a a a a
a b b b a
a b c b a
a b b b a
a a a a a

where a = n, b = n – 1,c = n – 2 and so on.

Examples:

Input : n = 4
Output :
4 4 4 4 4 4 4 
4 3 3 3 3 3 4 
4 3 2 2 2 3 4 
4 3 2 1 2 3 4 
4 3 2 2 2 3 4 
4 3 3 3 3 3 4 
4 4 4 4 4 4 4 

Input : n = 3
Output :
3 3 3 3 3 
3 2 2 2 3 
3 2 1 2 3 
3 2 2 2 3 
3 3 3 3 3 

For the given n, the number of rows or columns to be printed will be 2*n – 1. We will print the matrix in two parts. We will first print upper half from rows from 0 to floor((2*n – 1)/2) and then second half from floor((2*n – 1)/2) + 1 to 2*n – 2.
Now for each row, we will print it in three parts. First part is decreasing sequence which will start from n and decrease by 1 in each iteration. The number of iteration will be equal to row number, the second part is a constant sequence where constant is n – i and it will be print 2*n – 1 – 2 * row number, and the third part is increasing sequence which is nothing but opposite of the first sequence.
For lower half, observe, it is a mirror image of upper half (excluding middle row). So, simply run a loop of the upper half from (2*n – 1)/2 to 0.



Below is the basic implementation of this approach:

C++

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// C++ program for printing
// the rectangular pattern
#include <bits/stdc++.h>
using namespace std;
  
// Function to print the pattern
void printPattern(int n)
{
    // number of rows and columns to be printed
    int s = 2 * n - 1;
  
    // Upper Half
    for (int i = 0; i < (s / 2) + 1; i++) {
         
        int m = n;
  
        // Decreasing part
        for (int j = 0; j < i; j++) {
            cout << m << " ";
            m--;
        }
  
        // Conatsant Part
        for (int k = 0; k < s - 2 * i; k++) {
            cout << n - i << " ";
        }
  
        // Increasing part.
        m = n - i + 1;
        for (int l = 0; l < i; l++) {
            cout << m << " ";
            m++;
        }
  
        cout << endl;
    }
  
    // Lower Half
    for (int i = s / 2 - 1; i >= 0; i--) {
  
        // Decreasing Part
        int m = n;
        for (int j = 0; j < i; j++) {
            cout << m << " ";
            m--;
        }
  
        // Constant Part.
        for (int k = 0; k < s - 2 * i; k++) {
            cout << n - i << " ";
        }
  
        // Decreasing Part
        m = n - i + 1;
        for (int l = 0; l < i; l++) {
            cout << m << " ";
            m++;
        }
        cout << endl;
    }
}
// Driven Program
int main()
{
    int n = 3;
  
    printPattern(n);
    return 0;
}

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Java

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// Java program for printing
// the rectangular pattern
import java.io.*;
  
class GFG 
{
  
// Function to 
// print the pattern
static void printPattern(int n)
{
    // number of rows and 
    // columns to be printed
    int s = 2 * n - 1;
  
    // Upper Half
    for (int i = 0;
             i < (s / 2) + 1; i++) 
    {
        int m = n;
  
        // Decreasing part
        for (int j = 0; j < i; j++) 
        {
            System.out.print(m + " ");
            m--;
        }
  
        // Constant Part
        for (int k = 0
                 k < s - 2 * i; k++) 
        {
            System.out.print(n - i + " ");
        }
  
        // Increasing part.
        m = n - i + 1;
        for (int l = 0; l < i; l++) 
        {
            System.out.print(m + " ");
            m++;
        }
  
        System.out.println();
    }
  
    // Lower Half
    for (int i = s / 2 - 1;
             i >= 0; i--) 
    {
  
        // Decreasing Part
        int m = n;
        for (int j = 0; j < i; j++)
        {
            System.out.print(m + " ");
            m--;
        }
  
        // Constant Part.
        for (int k = 0
                 k < s - 2 * i; k++)
        {
            System.out.print(n - i + " ");
        }
  
        // Decreasing Part
        m = n - i + 1;
        for (int l = 0; l < i; l++) 
        {
            System.out.print(m + " ");
            m++;
        }
        System.out.println();
    }
}
// Driver Code
public static void main (String[] args) 
{
    int n = 3;
  
    printPattern(n);
}
}
  
// This code is contributed 
// by anuj_67.

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Python3

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# Python3 program for printing 
# the rectangular pattern 
  
# Function to print the pattern 
def printPattern(n) :
  
    # number of rows and columns to be printed 
    s = 2 * n - 1
  
    # Upper Half 
    for i in range(0, int(s / 2) + 1): 
          
        m =
  
        # Decreasing part 
        for j in range(0, i): 
            print(m ,end= " " )
            m-=1
          
        # Conatsant Part 
        for k in range(0, s - 2 * i):
            print(n-i ,end= " " )
          
        # Increasing part. 
        m = n - i + 1
        for l in range(0, i): 
            print(m ,end= " "
            m+=1
          
        print("") 
      
    # Lower Half 
    for i in range(int(s / 2),-1,-1): 
  
        # Decreasing Part 
        m =
        for j in range(0, i):
            print(m ,end= " " )
            m-=1
          
  
        # Constant Part. 
        for k in range(0, s - 2 * i):
            print(n-i ,end= " " )
          
  
        # Decreasing Part 
        m = n - i + 1
        for l in range(0, i): 
            print(m ,end= " "
            m+=1
          
        print("") 
      
# Driven Program 
if __name__=='__main__':
    n = 3
    printPattern(n) 
  
# this code is contributed by Smitha Dinesh 
# Semwal

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C#

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// C# program for printing
// the rectangular pattern
using System;
  
class GFG 
{
  
// Function to 
// print the pattern
static void printPattern(int n)
{
    // number of rows and 
    // columns to be printed
    int s = 2 * n - 1;
  
    // Upper Half
    for (int i = 0;
             i < (s / 2) + 1; i++) 
    {
        int m = n;
  
        // Decreasing part
        for (int j = 0; j < i; j++) 
        {
            Console.Write(m + " ");
            m--;
        }
  
        // Constant Part
        for (int k = 0; 
                 k < s - 2 * i; k++) 
        {
            Console.Write(n - i + " ");
        }
  
        // Increasing part.
        m = n - i + 1;
        for (int l = 0; l < i; l++) 
        {
            Console.Write(m + " ");
            m++;
        }
  
        Console.WriteLine();
    }
  
    // Lower Half
    for (int i = s / 2 - 1;
             i >= 0; i--) 
    {
  
        // Decreasing Part
        int m = n;
        for (int j = 0; j < i; j++)
        {
            Console.Write(m + " ");
            m--;
        }
  
        // Constant Part.
        for (int k = 0; 
                 k < s - 2 * i; k++)
        {
            Console.Write(n - i + " ");
        }
  
        // Decreasing Part
        m = n - i + 1;
        for (int l = 0; l < i; l++) 
        {
            Console.Write(m + " ");
            m++;
        }
        Console.WriteLine();
    }
}
// Driver Code
public static void Main () 
{
    int n = 3;
  
    printPattern(n);
}
}
  
// This code is contributed 
// by anuj_67.

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PHP

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<?php
// PHP program for printing 
// the rectangular pattern 
  
// Function to print the pattern 
function printPattern($n
    // number of rows and columns 
    // to be printed 
    $s = 2 * $n - 1; 
  
    // Upper Half 
    for ($i = 0; 
         $i < (int)($s / 2) + 1; $i++)
    
          
        $m = $n
  
        // Decreasing part 
        for ($j = 0; $j < $i; $j++)
        
            echo $m , " "
            $m--; 
        
  
        // Conatsant Part 
        for ($k = 0; $k < $s - 2 * $i; $k++) 
        
            echo ($n - $i) , " "
        
  
        // Increasing part. 
        $m = $n - $i + 1; 
        for ($l = 0; $l < $i; $l++) 
        
            echo $m , " "
            $m++; 
        
  
        echo "\n"
    
  
    // Lower Half 
    for ($i = (int)($s / 2 - 1); 
         $i >= 0; $i--) 
    
  
        // Decreasing Part 
        $m = $n
        for ($j = 0; $j < $i; $j++)
        
            echo $m, " "
            $m--; 
        
  
        // Constant Part. 
        for ($k = 0; $k < $s - 2 * $i; $k++) 
        
            echo $n - $i , " "
        
  
        // Decreasing Part 
        $m = $n - $i + 1; 
        for ($l = 0; $l < $i; $l++)
        
            echo $m , " "
            $m++; 
        
        echo "\n"
    
  
// Driver Code
$n = 3; 
printPattern($n); 
  
// This code is contributed 
// by Sach_Code    
?>

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Output

3 3 3 3 3 
3 2 2 2 3 
3 2 1 2 3 
3 2 2 2 3 
3 3 3 3 3  

Another Approach:

C++

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// C++ program for printing
// the rectangular pattern
#include<bits/stdc++.h>
using namespace std;
  
// Function to print the pattern
void printPattern(int n)
{
    int arraySize = n * 2 - 1;
    int result[arraySize][arraySize];
          
    // Fill the values
    for(int i = 0; i < arraySize; i++)
    {
        for(int j = 0; j < arraySize; j++)
        {
            if(abs(i - arraySize / 2) > abs(j - arraySize / 2))
                result[i][j] = abs(i - arraySize / 2) + 1;
            else
                result[i][j] = (abs(j-arraySize / 2) + 1);
              
        }
    }
          
    // Print the array
    for(int i = 0; i < arraySize; i++)
    {
        for(int j = 0; j < arraySize; j++)
        {
            cout << result[i][j] << " ";
        }
        cout << endl;
    }
}
  
// Driver Code
int main()
{
    int n = 3;
  
    printPattern(n);
    return 0;
}
  
// This code is contributed 
// by Rajput-Ji.

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Java

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// Java program for printing
// the rectangular pattern
import java.io.*;
  
class GFG 
{
  
// Function to print the pattern
static void printPattern(int n)
{
        int arraySize = n * 2 - 1;
        int[][] result = new int[arraySize][arraySize];
          
        //Fill the values
        for(int i = 0; i < arraySize; i++)
        {
            for(int j = 0; j < arraySize; j++)
            {
                result[i][j] = Math.max(Math.abs(i-arraySize/2),
                                    Math.abs(j-arraySize/2))+1;
            }
        }
          
        //Print the array
        for(int i = 0; i < arraySize; i++)
        {
            for(int j = 0; j < arraySize; j++)
            {
            System.out.print(result[i][j]);
            }
            System.out.println();
        }
}
// Driver Code
public static void main (String[] args) 
{
    int n = 3;
  
    printPattern(n);
}
}
  
// This code is contributed 
// by MohitSharma23.

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Python3

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# Python3 program for printing
# the rectangular pattern
  
# Function to print the pattern
def printPattern(n):
  
    arraySize = n * 2 - 1;
    result = [[0 for x in range(arraySize)] 
                 for y in range(arraySize)];
          
    # Fill the values
    for i in range(arraySize):
        for j in range(arraySize):
            if(abs(i - (arraySize // 2)) > 
               abs(j - (arraySize // 2))):
                result[i][j] = abs(i - (arraySize // 2)) + 1;
            else:
                result[i][j] = abs(j - (arraySize // 2)) + 1;
              
    # Print the array
    for i in range(arraySize):
        for j in range(arraySize):
            print(result[i][j], end = " ");
        print("");
  
# Driver Code
n = 3;
  
printPattern(n);
  
# This code is contributed by mits

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C#

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// C# program for printing 
// the rectangular pattern 
using System; 
  
class GFG 
  
// Function to print the pattern 
static void printPattern(int n) 
        int arraySize = n * 2 - 1; 
        int[,] result = new int[arraySize,arraySize]; 
          
        // Fill the values 
        for(int i = 0; i < arraySize; i++) 
        
            for(int j = 0; j < arraySize; j++) 
            
                result[i,j] = Math.Max(Math.Abs(i-arraySize/2), 
                                    Math.Abs(j-arraySize/2))+1; 
            
        
          
        // Print the array 
        for(int i = 0; i < arraySize; i++) 
        
            for(int j = 0; j < arraySize; j++) 
            
                Console.Write(result[i,j]+" "); 
            
            Console.WriteLine(); 
        
  
// Driver Code 
public static void Main (String[] args) 
    int n = 3; 
  
    printPattern(n); 
  
// This code has been contributed by 29AjayKumar

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PHP

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<?php
// PHP program for printing
// the rectangular pattern
  
// Function to print the pattern
function printPattern($n)
{
    $arraySize = $n * 2 - 1;
    $result=array_fill(0,$arraySize,array_fill(0,$arraySize,0));
          
    // Fill the values
    for($i = 0; $i < $arraySize; $i++)
    {
        for($j = 0; $j < $arraySize; $j++)
        {
            if(abs($i - (int)($arraySize / 2)) > 
                    abs($j - (int)($arraySize / 2)))
                $result[$i][$j] = abs($i
                        (int)($arraySize / 2)) + 1;
            else
                $result[$i][$j] = (abs($j-(int)
                                ($arraySize / 2)) + 1);
              
        }
    }
          
    // Print the array
    for($i = 0; $i < $arraySize; $i++)
    {
        for($j = 0; $j < $arraySize; $j++)
        {
            echo $result[$i][$j]." ";
        }
        echo "\n";
    }
}
  
// Driver Code
  
    $n = 3;
  
    printPattern($n);
  
// This code is contributed by mits
?>

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Output

3 3 3 3 3 
3 2 2 2 3 
3 2 1 2 3 
3 2 2 2 3 
3 3 3 3 3  


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