Fill an empty 2D Matrix with integers from 1 to N*N filled diagonally

Namachila November 19, 2025

0 0 5 minutes read

Given an integer N, the task is to fill a matrix M of size NxN, starting from the main diagonal and then alternating between the lower and upper triangular diagonals, in an increasing fashion such that each number from 1 to N² appears only once.

Examples:

Input: N = 4
Output: 
1 8 13 16
5 2 9 14
11 6 3 10
15 12 7 4
Explanation:
First filling the main diagonal:
 1   
    2  
       3 
          4
Next, fill the lower diagonal below the main diagonal
 1 
 5  2  
    6  3 
      7  4
Next, fill the upper diagonal above the main diagonal
 1  8 
 5  2  9 
    6  3 10
       7  4
Following the same pattern and altering between 
upper and lower triangular matrix, 
we get the final matrix as
 1  8 13 16
 5  2  9 14
11  6  3 10
15 12  7  4

Input: N = 3
Output:
1 6 9
4 2 7
8 5 3

Approach: Follow the below steps to solve the problem:

Initialize a variable cur to 1. This will keep track of the current number
Initialize a variable d to 1. This keeps track of the diagonals.
Iterate from 1 to (N+N-1) using d. This is the number of diagonals.
- If d is even, initialize two variables r and c to d/2 and 0 respectively.
- Otherwise, initialize the two variables r and c to 0 and d/2 respectively.
- Iterate till r and c both are less than N
  - Update the matrix M as M[r]=cur.
  - Increment cur, r, and c.
- After exiting the inner loop, increment d.
Finally, display the matrix M.

Below is the implementation of the above approach:

C++

// C++ implementation of the above approach
#include <bits/stdc++.h>
using namespace std;
// Function to fill the matrix diagonally alternating
// between upper and lower diagonals
void fillMatrix(int N)
{
    // variables to keep track of
    // diagonals and current number
    int d = 1, cur = 1;
    // Matrix
    int M[N][N];
    // Iterating over all diagonals
    while (d <= 2 * N - 1) {
        int r, c;
        // For lower triangle
        if (d % 2 == 0)
            r = d / 2, c = 0;
        // For upper triangle
        else
            r = 0, c = d / 2;
        // Placing the current number
        // in appropriate position
        while (r < N && c < N) {
            M[r] = cur;
            cur++;
            r++;
            c++;
        }
        d++;
    }
 
    // Displaying the matrix
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++) {
            cout << M[i][j] << " ";
        }
        cout << endl;
    }
}
// Driver code
int main()
{
    // Input
    int N = 4;
 
    // Function calling
    fillMatrix(N);
    return 0;
}

Java

// Java implementation of the above approach
 
import java.io.*;
 
class GFG {
    static void fillmatrix(int m[][], int n)
    {
 
        int r, c;
        int num = 1, d = 1;
        // 2*n-1 is no of diagonals
        while (d <= 2 * n - 1) {
            // If d%2==0 switch to
            // lower triangular diagonal
            if (d % 2 == 0) {
                r = d / 2;
                c = 0;
                while (r < n && c < n) {
                    m[r] = num++;
                    r++;
                    c++;
                }
            }
            // If d%2==1 switch to
            // upper triangular diagonal
            else {
                r = 0;
                c = d / 2;
                while (c < n && r < n) {
                    m[r] = num++;
                    r++;
                    c++;
                }
            }
            d++;
        }
    }
    // Utility function to display the matrix
    static void display(int m[][], int n)
    {
        int i, j;
        for (i = 0; i < n; i++) {
            for (j = 0; j < n; j++) {
                System.out.printf(m[i][j] + " ");
            }
            System.out.println();
        }
    }
 
    public static void main(String[] args)
    {
        int n = 4;
        int[][] m = new int[4][4];
        fillmatrix(m, n);
        display(m, n);
    }
}

Python3

# Python3 implementation of the above approach
 
# Function to fill the matrix diagonally 
# alternating between upper and lower diagonals
def fillMatrix(N):
     
    # Variables to keep track of
    # diagonals and current number
    d = 1
    cur = 1
     
    # Matrix
    M = [[0 for i in range(N)] 
            for i in range(N)]
             
    # Iterating over all diagonals
    while (d <= 2 * N - 1):
        r, c = 0, 0
         
        # For lower triangle
        if (d % 2 == 0):
            r = d // 2
            c = 0
             
        # For upper triangle
        else:
            r = 0
            c = d // 2
             
        # Placing the current number
        # in appropriate position
        while (r < N and c < N):
            M[r] = cur
            cur += 1
            r += 1
            c += 1
 
        d += 1
 
    # Displaying the matrix
    for i in M:
        print(*i)
 
# Driver code
if __name__ == '__main__':
     
    # Input
    N = 4
 
    # Function calling
    fillMatrix(N)
 
# This code is contributed by mohit kumar 29

C#

// C# implementation of the above approach
using System.IO;
using System;
 
class GFG{
     
static void fillmatrix(int[, ] m, int n)
{
    int r, c;
    int num = 1, d = 1;
     
    // 2*n-1 is no of diagonals
    while (d <= 2 * n - 1)
    {
         
        // If d%2==0 switch to
        // lower triangular diagonal
        if (d % 2 == 0) 
        {
            r = d / 2;
            c = 0;
            while (r < n && c < n) 
            {
                m[r, c] = num++;
                r++;
                c++;
            }
        }
         
        // If d%2==1 switch to
        // upper triangular diagonal
        else
        {
            r = 0;
            c = d / 2;
             
            while (c < n && r < n) 
            {
                m[r, c] = num++;
                r++;
                c++;
            }
        }
        d++;
    }
}
 
// Utility function to display the matrix
static void display(int[,] m, int n)
{
    int i, j;
    for(i = 0; i < n; i++) 
    {
        for(j = 0; j < n; j++) 
        {
            Console.Write(m[i, j] + " ");
        }
        Console.WriteLine();
    }
}
 
// Driver code
static void Main()
{
    int n = 4;
    int[,] m = new int[4, 4];
     
    fillmatrix(m, n);
    display(m, n);
}
}
 
// This code is contributed by abhinavjain194

Javascript

<script>
    // Javascript implementation of the above approach
    function fillmatrix(m, n)
    {
  
        let r, c;
        let num = 1, d = 1;
         
        // 2*n-1 is no of diagonals
        while (d <= 2 * n - 1)
        {
         
            // If d%2==0 switch to
            // lower triangular diagonal
            if (d % 2 == 0) 
            {
                r = parseInt(d / 2, 10);
                c = 0;
                while (r < n && c < n) 
                {
                    m[r] = num++;
                    r++;
                    c++;
                }
            }
             
            // If d%2==1 switch to
            // upper triangular diagonal
            else {
                r = 0;
                c = parseInt(d / 2, 10);
                while (c < n && r < n) {
                    m[r] = num++;
                    r++;
                    c++;
                }
            }
            d++;
        }
    }
     
    // Utility function to display the matrix
    function display(m, n)
    {
        let i, j;
        for (i = 0; i < n; i++) {
            for (j = 0; j < n; j++) {
                document.write(m[i][j] + " ");
            }
            document.write("</br>");
        }
    }
     
    let n = 4;
    let m = new Array(4);
    for(let i = 0; i < m.length; i++)
    {
        m[i] = new Array(m.length);
        for(let j = 0; j < m.length; j++)
        {
            m[i][j] = 0;
        }
    }
    fillmatrix(m, n);
    display(m, n);
     
    // This code is contributed by divyeshrabadiya07.
</script>

Output

Time Complexity: O(N²)
Auxiliary Space: O(1)

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