Print numbers in matrix diagonal pattern

Given an integer N, the task is to print the given pattern.
Examples:

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

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

Approach:

• Create a matrix of size N X N which will store the pattern before printing.
• Store the elements in the upper triangle of the pattern. As observed the row index increases by 1 and column index decreases by 1 as you move down the diagonal.
• Once the upper triangle is completed then store the elements of the lower triangle in similar way as the upper triangle i.e. row index increases by 1 and column index decreases by 1 as you move down the diagonal.

Below is the implementation of the above approach:

C++

 `// C++ program to print the required pattern` `#include ` `using` `namespace` `std;`   `// Function to print the required pattern` `void` `printPattern(``int` `n)` `{` `    ``// arr[][] will store the pattern matrix` `    ``int` `arr[n][n], k, i, j, p = 1, f;`   `    ``// Store the values for upper triangle` `    ``// of the pattern` `    ``for` `(k = 0; k < n; k++) {` `        ``j = k;` `        ``i = 0;` `        ``while` `(j >= 0) {` `            ``arr[i][j] = p;` `            ``p++;` `            ``i = i + 1;` `            ``j = j - 1;` `        ``}` `    ``}`   `    ``// Store the values for lower triangle` `    ``// of the pattern` `    ``for` `(k = 1; k < n; k++) {` `        ``i = k;` `        ``j = n - 1;` `        ``f = k;` `        ``while` `(j >= f) {` `            ``arr[i][j] = p;` `            ``p++;` `            ``i = i + 1;` `            ``j = j - 1;` `        ``}` `    ``}`   `    ``// Print the pattern` `    ``for` `(i = 0; i < n; i++) {` `        ``for` `(j = 0; j < n; j++) {` `            ``cout << arr[i][j] << ``" "``;` `        ``}` `        ``cout << endl;` `    ``}` `}`   `// Driver code` `int` `main()` `{` `    ``int` `n = 3;`   `    ``printPattern(n);`   `    ``return` `0;` `}`

Java

 `// Java program to print the required pattern `   `public` `class` `GFG{`   `    ``// Function to print the required pattern ` `    ``static` `void` `printPattern(``int` `n) ` `    ``{ ` `        ``// arr[][] will store the pattern matrix ` `        ``int` `arr[][] = ``new` `int``[n][n] ;` `        ``int` `k, i, j, p = ``1``, f ; ` `    `  `        ``// Store the values for upper triangle ` `        ``// of the pattern ` `        ``for` `(k = ``0``; k < n; k++) { ` `            ``j = k; ` `            ``i = ``0``; ` `            ``while` `(j >= ``0``) { ` `                ``arr[i][j] = p; ` `                ``p++; ` `                ``i = i + ``1``; ` `                ``j = j - ``1``; ` `            ``} ` `        ``} ` `    `  `        ``// Store the values for lower triangle ` `        ``// of the pattern ` `        ``for` `(k = ``1``; k < n; k++) { ` `            ``i = k; ` `            ``j = n - ``1``; ` `            ``f = k; ` `            ``while` `(j >= f) { ` `                ``arr[i][j] = p; ` `                ``p++; ` `                ``i = i + ``1``; ` `                ``j = j - ``1``; ` `            ``} ` `        ``} ` `    `  `        ``// Print the pattern ` `        ``for` `(i = ``0``; i < n; i++) { ` `            ``for` `(j = ``0``; j < n; j++) { ` `                ``System.out.print(arr[i][j] + ``" "``) ; ` `            ``} ` `            ``System.out.println() ;` `        ``} ` `    ``} ` `    `  `    ``// Driver code ` `    ``public` `static` `void` `main(String []args) ` `    ``{ ` `        ``int` `n = ``3``; ` `    `  `        ``printPattern(n); ` `    ``} ` `    ``// This code is contributed by Ryuga`   `}`

Python3

 `# Python 3 program to print the` `# required pattern`   `# Function to print the required pattern` `def` `printPattern(n):` `    `  `    ``# arr[][] will store the pattern matrix` `    ``arr ``=` `[[``0` `for` `i ``in` `range``(n)]` `              ``for` `j ``in` `range``(n)]` `    ``p ``=` `1`   `    ``# Store the values for upper ` `    ``# triangle of the pattern` `    ``for` `k ``in` `range``(n):` `        ``j ``=` `k` `        ``i ``=` `0` `        ``while` `(j >``=` `0``):` `            ``arr[i][j] ``=` `p` `            ``p ``+``=` `1` `            ``i ``=` `i ``+` `1` `            ``j ``=` `j ``-` `1` `    `  `    ``# Store the values for lower triangle` `    ``# of the pattern` `    ``for` `k ``in` `range``(``1``, n, ``1``):` `        ``i ``=` `k` `        ``j ``=` `n ``-` `1` `        ``f ``=` `k` `        ``while` `(j >``=` `f):` `            ``arr[i][j] ``=` `p` `            ``p ``+``=` `1` `            ``i ``=` `i ``+` `1` `            ``j ``=` `j ``-` `1` `    `  `    ``# Print the pattern` `    ``for` `i ``in` `range``(``0``, n, ``1``):` `        ``for` `j ``in` `range``(``0``, n, ``1``):` `            ``print``(arr[i][j], end ``=` `" "``)` `        `  `        ``print``(``"\n"``, end ``=` `"")`   `# Driver code` `if` `__name__ ``=``=` `'__main__'``:` `    ``n ``=` `3`   `    ``printPattern(n)`   `# This code is contributed by` `# Sanjit_Prasad`

C#

 `// C# program to print the required pattern ` `using` `System;`   `public` `class` `GFG{`   `    ``// Function to print the required pattern ` `    ``static` `void` `printPattern(``int` `n) ` `    ``{ ` `        ``// arr[][] will store the pattern matrix ` `        ``int` `[,]arr = ``new` `int``[n,n] ;` `        ``int` `k, i, j, p = 1, f ; ` `    `  `        ``// Store the values for upper triangle ` `        ``// of the pattern ` `        ``for` `(k = 0; k < n; k++) { ` `            ``j = k; ` `            ``i = 0; ` `            ``while` `(j >= 0) { ` `                ``arr[i,j] = p; ` `                ``p++; ` `                ``i = i + 1; ` `                ``j = j - 1; ` `            ``} ` `        ``} ` `    `  `        ``// Store the values for lower triangle ` `        ``// of the pattern ` `        ``for` `(k = 1; k < n; k++) { ` `            ``i = k; ` `            ``j = n - 1; ` `            ``f = k; ` `            ``while` `(j >= f) { ` `                ``arr[i,j] = p; ` `                ``p++; ` `                ``i = i + 1; ` `                ``j = j - 1; ` `            ``} ` `        ``} ` `    `  `        ``// Print the pattern ` `        ``for` `(i = 0; i < n; i++) { ` `            ``for` `(j = 0; j < n; j++) { ` `                ``Console.Write(arr[i,j] + ``" "``) ; ` `            ``} ` `            ``Console.WriteLine() ;` `        ``} ` `    ``} ` `    `  `    ``// Driver code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int` `n = 3; ` `    `  `        ``printPattern(n); ` `    ``} ` `    ``// This code is contributed by inder_verma..`   `}`

PHP

 `= 0)` `        ``{ ` `            ``\$arr``[``\$i``][``\$j``] = ``\$p``; ` `            ``\$p``++; ` `            ``\$i` `= ``\$i` `+ 1; ` `            ``\$j` `= ``\$j` `- 1; ` `        ``} ` `    ``} `   `    ``// Store the values for lower ` `    ``// triangle of the pattern ` `    ``for` `(``\$k` `= 1; ``\$k` `< ``\$n``; ``\$k``++) ` `    ``{ ` `        ``\$i` `= ``\$k``; ` `        ``\$j` `= ``\$n` `- 1; ` `        ``\$f` `= ``\$k``; ` `        ``while` `(``\$j` `>= ``\$f``) ` `        ``{ ` `            ``\$arr``[``\$i``][``\$j``] = ``\$p``; ` `            ``\$p``++; ` `            ``\$i` `= ``\$i` `+ 1; ` `            ``\$j` `= ``\$j` `- 1; ` `        ``} ` `    ``} `   `    ``// Print the pattern ` `    ``for` `(``\$i` `= 0; ``\$i` `< ``\$n``; ``\$i``++) ` `    ``{ ` `        ``for` `(``\$j` `= 0; ``\$j` `< ``\$n``; ``\$j``++) ` `        ``{ ` `            ``echo``(``\$arr``[``\$i``][``\$j``] . ``" "``); ` `        ``} ` `        ``echo``(``"\n"``);` `    ``} ` `} `   `// Driver code ` `\$n` `= 3; `   `printPattern(``\$n``); `   `// This code is contributed ` `// by Mukul Singh` `?>`

Javascript

 ``

Output:

```1 2 4
3 5 7
6 8 9```

Time complexity: O(n^2) for given n*n matrix

Auxiliary space: O(n^2) because using space for array arr

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