Print matrix in diagonal pattern

Given a matrix of n*n size, the task is to print its elements in diagonal pattern.

matrix-diagonal-traversal

Input : mat[3][3] = {{1, 2, 3},
                     {4, 5, 6},
                     {7, 8, 9}}
Output : 1 2 4 7 5 3 6 8 9.
Explanation: We start from 1 
Then from upward to downward diagonally i.e. 2 and 4
Then from downward to upward diagonally i.e 7, 5, 3 
Then from up to down diagonally i.e  6, 8 
Then down to up i.e. end at 9.

Input : mat[4][4] =  {{1,  2,  3,  10},
                      {4,  5,  6,  11},
                      {7,  8,  9,  12},
                      {13, 14, 15, 16}}
Output:  1 2 4 7 5 3 10 6 8 13 14 9 11 12 15 16 .



  1. We use a flag isUp to decide whether we need to go upward direction or downward direction. We set isUp = true initially that first we are going upward.
  2. If isUp = 1 then start printing elements by incrementing column index and decrementing the row index.
  3. Similarly if isUp = 0, then decrement the column index and increment the row index.
  4. Do this till all the elements get traversed.

Below is the implementation of above steps.

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ program to print matrix in diagonal order
#include <bits/stdc++.h>
using namespace std;
const int MAX = 100;
  
void printMatrixDiagonal(int mat[MAX][MAX], int n)
{
    // Initialize indexes of element to be printed next
    int i = 0, j = 0;
  
    // Direction is initially from down to up
    bool isUp = true;
  
    // Traverse the matrix till all elements get traversed
    for (int k = 0; k < n * n;) {
        // If isUp = true then traverse from downward
        // to upward
        if (isUp) {
            for (; i >= 0 && j < n; j++, i--) {
                cout << mat[i][j] << " ";
                k++;
            }
  
            // Set i and j according to direction
            if (i < 0 && j <= n - 1)
                i = 0;
            if (j == n)
                i = i + 2, j--;
        }
  
        // If isUp = 0 then traverse up to down
        else {
            for (; j >= 0 && i < n; i++, j--) {
                cout << mat[i][j] << " ";
                k++;
            }
  
            // Set i and j according to direction
            if (j < 0 && i <= n - 1)
                j = 0;
            if (i == n)
                j = j + 2, i--;
        }
  
        // Revert the isUp to change the direction
        isUp = !isUp;
    }
}
  
int main()
{
    int mat[MAX][MAX] = { { 1, 2, 3 },
                          { 4, 5, 6 },
                          { 7, 8, 9 } };
  
    int n = 3;
    printMatrixDiagonal(mat, n);
    return 0;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java program to print matrix in diagonal order
class GFG {
    static final int MAX = 100;
  
    static void printMatrixDiagonal(int mat[][], int n)
    {
        // Initialize indexes of element to be printed next
        int i = 0, j = 0;
  
        // Direction is initially from down to up
        boolean isUp = true;
  
        // Traverse the matrix till all elements get traversed
        for (int k = 0; k < n * n;) {
            // If isUp = true then traverse from downward
            // to upward
            if (isUp) {
                for (; i >= 0 && j < n; j++, i--) {
                    System.out.print(mat[i][j] + " ");
                    k++;
                }
  
                // Set i and j according to direction
                if (i < 0 && j <= n - 1)
                    i = 0;
                if (j == n) {
                    i = i + 2;
                    j--;
                }
            }
  
            // If isUp = 0 then traverse up to down
            else {
                for (; j >= 0 && i < n; i++, j--) {
                    System.out.print(mat[i][j] + " ");
                    k++;
                }
  
                // Set i and j according to direction
                if (j < 0 && i <= n - 1)
                    j = 0;
                if (i == n) {
                    j = j + 2;
                    i--;
                }
            }
  
            // Revert the isUp to change the direction
            isUp = !isUp;
        }
    }
  
    // Driver code
    public static void main(String[] args)
    {
        int mat[][] = { { 1, 2, 3 },
                        { 4, 5, 6 },
                        { 7, 8, 9 } };
  
        int n = 3;
        printMatrixDiagonal(mat, n);
    }
}
// This code is contributed by Anant Agarwal.

chevron_right


Python 3

filter_none

edit
close

play_arrow

link
brightness_4
code

# Pthon 3 program to print matrix in diagonal order
MAX = 100
  
def printMatrixDiagonal(mat, n):
    # Initialize indexes of element to be printed next
    i = 0
    j = 0
    k = 0
    # Direction is initially from down to up
    isUp = True
  
     # Traverse the matrix till all elements get traversed
    while k<n * n:
         # If isUp = True then traverse from downward
         # to upward
        if isUp:
            while i >= 0 and j<n :
                print(str(mat[i][j]), end = " ")
                k += 1
                j += 1
                i -= 1
  
              # Set i and j according to direction
            if i < 0 and j <= n - 1:
                i = 0
            if j == n:
                i = i + 2
                j -= 1
  
         # If isUp = 0 then traverse up to down
        else:
            while j >= 0 and i<n :
                print(mat[i][j], end = " ")
                k += 1
                i += 1
                j -= 1
  
              # Set i and j according to direction
            if j < 0 and i <= n - 1:
                j = 0
            if i == n:
                j = j + 2
                i -= 1
  
         # Revert the isUp to change the direction
        isUp = not isUp
  
# Driver program
if __name__ == "__main__":
    mat = [[1, 2, 3],
        [4, 5, 6],
        [7, 8, 9] ]
  
   n = 3
   printMatrixDiagonal(mat, n)
  
# This code is contributed by Chitra Nayal

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# program to print matrix in diagonal order
using System;
class GFG {
    static int MAX = 100;
  
    static void printMatrixDiagonal(int[, ] mat, int n)
    {
        // Initialize indexes of element to be printed next
        int i = 0, j = 0;
  
        // Direction is initially from down to up
        bool isUp = true;
  
        // Traverse the matrix till all elements get traversed
        for (int k = 0; k < n * n;) {
            // If isUp = true then traverse from downward
            // to upward
            if (isUp) {
                for (; i >= 0 && j < n; j++, i--) {
                    Console.Write(mat[i, j] + " ");
                    k++;
                }
  
                // Set i and j according to direction
                if (i < 0 && j <= n - 1)
                    i = 0;
                if (j == n) {
                    i = i + 2;
                    j--;
                }
            }
  
            // If isUp = 0 then traverse up to down
            else {
                for (; j >= 0 && i < n; i++, j--) {
                    Console.Write(mat[i, j] + " ");
                    k++;
                }
  
                // Set i and j according to direction
                if (j < 0 && i <= n - 1)
                    j = 0;
                if (i == n) {
                    j = j + 2;
                    i--;
                }
            }
  
            // Revert the isUp to change the direction
            isUp = !isUp;
        }
    }
  
    // Driver code
    public static void Main()
    {
        int[, ] mat = { { 1, 2, 3 },
                        { 4, 5, 6 },
                        { 7, 8, 9 } };
  
        int n = 3;
        printMatrixDiagonal(mat, n);
    }
}
// This code is contributed by vt_m.

chevron_right


PHP

filter_none

edit
close

play_arrow

link
brightness_4
code

<?php
// php program to print matrix
// in diagonal order
  
$MAX = 100;
  
function printMatrixDiagonal($mat, $n)
{
      
    // Initialize indexes of element
    // to be printed next
    $i = 0;
    $j = 0 ;
  
    // Direction is initially
    // from down to up
    $isUp = true;
  
    // Traverse the matrix till
    // all elements get traversed
    for ($k = 0;$k < $n * $n😉
    {
        // If isUp = true then traverse 
        // from downward to upward
        if ($isUp)
        {
            for ( ;$i >= 0 && $j < $n;$j++, $i--)
            {
                echo $mat[$i][$j]." ";
                $k++;
            }
  
            // Set i and j according 
            // to direction
            if ($i < 0 && $j <= $n - 1)
                $i = 0;
            if ($j == $n)
            {
                $i = $i + 2;
                $j--;
            }
        }
  
        // If isUp = 0 then 
        // traverse up to down
        else
        {
            for ( ; $j >= 0 && 
                 $i<$n ; $i++, $j--)
            {
                echo $mat[$i][$j]." ";
                $k++;
            }
  
            // Set i and j according
            // to direction
            if ($j < 0 && $i <= $n - 1)
                $j = 0;
            if ($i == $n)
            {
                $j = $j + 2;
                $i--;
            }
        }
  
        // Revert the isUp to
        // change the direction
        $isUp = !$isUp;
    }
}
  
    // Driver code
    $mat= array(array(1, 2, 3),
          array(4, 5, 6),
          array(7, 8, 9));
  
    $n = 3;
    printMatrixDiagonal($mat, $n);
  
// This code is contributed by mits 
?>

chevron_right


Output:

1 2 4 7 5 3 6 8 9

Another approach to print the elements of a given matrix of n*n size in diagonal pattern is given below.

Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java program to print matrix in diagonal order
public class MatrixDiag {
  
    public static void main(String[] args)
    {
        // Initialize matrix
        int[][] mat = { { 1, 2, 3, 4 }, 
                        { 5, 6, 7, 8 }, 
                        { 9, 10, 11, 12 }, 
                        { 13, 14, 15, 16 } };
        // n - size
        // mode - switch to derive up/down traversal
        // it - iterator count - increases until it 
        // reaches n and then decreases
        int n = 4, mode = 0, it = 0, lower = 0;
  
        // 2n will be the number of iterations
        for (int t = 0; t < (2 * n - 1); t++) {
            int t1 = t;
            if (t1 >= n) {
                mode++;
                t1 = n - 1;
                it--;
                lower++;
            }
            else {
                lower = 0;
                it++;
            }
            for (int i = t1; i >= lower; i--) {
                if ((t1 + mode) % 2 == 0) {
                    System.out.println(mat[i][t1 + lower - i]);
                }
                else {
                    System.out.println(mat[t1 + lower - i][i]);
                }
            }
        }
    }
}

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# program to print matrix in diagonal order
using System;
  
public class MatrixDiag 
{
    // Driver code
    public static void Main(String[] args)
    {
        // Initialize matrix
        int[,] mat = { { 1, 2, 3, 4 }, 
                        { 5, 6, 7, 8 }, 
                        { 9, 10, 11, 12 }, 
                        { 13, 14, 15, 16 } };
        // n - size
        // mode - switch to derive up/down traversal
        // it - iterator count - increases until it 
        // reaches n and then decreases
        int n = 4, mode = 0, it = 0, lower = 0;
  
        // 2n will be the number of iterations
        for (int t = 0; t < (2 * n - 1); t++) 
        {
            int t1 = t;
            if (t1 >= n) 
            {
                mode++;
                t1 = n - 1;
                it--;
                lower++;
            }
            else
            {
                lower = 0;
                it++;
            }
            for (int i = t1; i >= lower; i--)
            {
                if ((t1 + mode) % 2 == 0) 
                {
                    Console.WriteLine(mat[i,t1 + lower - i]);
                }
                else
                {
                    Console.WriteLine(mat[t1 + lower - i,i]);
                }
            }
        }
    }
}
  
// This code contributed by Rajput-Ji

chevron_right


Output:

1
2
5
9
6
3
4
7
10
13
14
11
8
12
15
16

This article is contributed by Sahil Chhabra. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.



My Personal Notes arrow_drop_up