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# Arrange numbers 1 to N^2 in a Zig-Zag Matrix in ascending order

Given a positive integer N, the task is to print an N × N zig-zag matrix consisting of numbers from 1 to N2, such that the ZigZag traversal of the matrix yields the number in ascending order.
Examples:

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

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

Approach:
The required matrix can be broken down into two right-angled triangles.

• An upside-down right-angled triangle(considered as an upper triangle).
• A normal right-angled triangle(considered as a lower triangle).

The idea is to iterate two nested loops to fill the upper triangle with respective values. Then iterate two nested loop again to fill the lower triangle with respective values. After the above two operations print the desired matrix.
Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach``#include ``using` `namespace` `std;` `// Function to print the pattern``void` `printPattern(``int` `n)``{``    ``// N * N matrix to store the``    ``// values``    ``int` `arr[n][n];` `    ``arr[0][0] = 1;` `    ``// Fill the values of``    ``// upper triangle``    ``for` `(``int` `i = 0; i < n; i++) {` `        ``if` `(i > 0) {``            ``arr[i][0] = arr[i - 1][0] + i + 1;``        ``}``        ``for` `(``int` `j = 1;``             ``j < n - i; j++) {` `            ``arr[i][j] = arr[i][j - 1] + i + j;``        ``}``    ``}` `    ``// Fill the values of``    ``// lower triangle``    ``arr[1][n - 1] = arr[n - 1][0] + 1;``    ``int` `div` `= 0;` `    ``for` `(``int` `i = 2; i < n; i++) {` `        ``div` `= n - 2;``        ``for` `(``int` `j = n - i;``             ``j < n; j++) {` `            ``if` `(j == n - i) {``                ``arr[i][j] = arr[i - 1][j + 1]``                            ``+ 1;``            ``}``            ``else` `{``                ``arr[i][j] = arr[i][j - 1]``                            ``+ ``div``;``                ``div``--;``            ``}``        ``}``    ``}` `    ``// Print the array``    ``for` `(``int` `i = 0; i < n; i++) {` `        ``for` `(``int` `j = 0; j < n; j++) {` `            ``cout << arr[i][j] << ``" "``;``        ``}``        ``cout << ``"\n"``;``    ``}``}` `// Driver Code``int` `main()``{``    ``// Given size of matrix``    ``int` `N = 4;` `    ``// Function Call``    ``printPattern(N);``    ``return` `0;``}`

## Java

 `// Java program for``// the above approach``import` `java.util.*;``class` `GFG{` `// Function to print the pattern``static` `void` `printPattern(``int` `n)``{``  ``// N * N matrix to store the``  ``// values``  ``int` `[][]arr = ``new` `int``[n][n];` `  ``arr[``0``][``0``] = ``1``;` `  ``// Fill the values of``  ``// upper triangle``  ``for` `(``int` `i = ``0``; i < n; i++)``  ``{``    ``if` `(i > ``0``)``    ``{``      ``arr[i][``0``] = arr[i - ``1``][``0``] +``                      ``i + ``1``;``    ``}``    ``for` `(``int` `j = ``1``; j < n - i; j++)``    ``{``      ``arr[i][j] = arr[i][j - ``1``] +``                      ``i + j;``    ``}``  ``}` `  ``// Fill the values of``  ``// lower triangle``  ``arr[``1``][n - ``1``] = arr[n - ``1``][``0``] + ``1``;``  ``int` `div = ``0``;` `  ``for` `(``int` `i = ``2``; i < n; i++)``  ``{``    ``div = n - ``2``;``    ``for` `(``int` `j = n - i; j < n; j++)``    ``{``      ``if` `(j == n - i)``      ``{``        ``arr[i][j] = arr[i - ``1``][j + ``1``] + ``1``;``      ``}``      ``else``      ``{``        ``arr[i][j] = arr[i][j - ``1``] + div;``        ``div--;``      ``}``    ``}``  ``}` `  ``// Print the array``  ``for` `(``int` `i = ``0``; i < n; i++)``  ``{``    ``for` `(``int` `j = ``0``; j < n; j++)``    ``{``      ``System.out.print(arr[i][j] + ``" "``);``    ``}``    ``System.out.print(``"\n"``);``  ``}``}` `// Driver Code``public` `static` `void` `main(String[] args)``{``  ``// Given size of matrix``  ``int` `N = ``4``;` `  ``// Function Call``  ``printPattern(N);``}``}` `// This code is contributed by Princi Singh`

## Python3

 `# Python3 program for the above approach` `# Function to print the pattern``def` `printPattern(n):``        ` `        ``# N * N matrix to store the values``    ``arr ``=` `[[``0` `for` `i ``in` `range``(n)]``        ``for` `j ``in` `range``(n)]` `    ``# Fill the values of upper triangle``    ``arr[``0``][``0``] ``=` `1``    ``for` `i ``in` `range``(n):``        ``if` `i > ``0``:``            ``arr[i][``0``] ``=` `arr[i ``-` `1``][``0``] ``+` `i ``+` `1``        ``for` `j ``in` `range``(``1``, n``-``i):``            ``arr[i][j] ``=` `arr[i][j ``-` `1``] ``+` `i ``+` `j` `    ``# Fill the values of lower triangle``    ``if` `n > ``1``:``        ``arr[``1``][n ``-` `1``] ``=` `arr[n ``-` `1``][``0``] ``+` `1``    ``div ``=` `0``    ``for` `i ``in` `range``(``2``, n):``        ``div ``=` `n``-``2``        ``for` `j ``in` `range``(n``-``i, n):``            ``if` `j ``=``=` `n``-``i:``                ``arr[i][j] ``=` `arr[i ``-` `1``][j ``+` `1``] ``+` `1``            ``else``:``                ``arr[i][j] ``=` `arr[i][j ``-` `1``] ``+` `div``                ``div ``-``=` `1` `    ``# Print the array``    ``for` `i ``in` `range``(n):``        ``for` `j ``in` `range``(n):``            ``print``(arr[i][j], end``=``' '``)``        ``print``("")`  `# Driver code``# Given size of matrix``N ``=` `4` `# Function Call``printPattern(N)`

## C#

 `// C# program for``// the above approach``using` `System;``class` `GFG{` `// Function to print the pattern``static` `void` `printPattern(``int` `n)``{``  ``// N * N matrix to store the``  ``// values``  ``int` `[,]arr = ``new` `int``[n, n];` `  ``arr[0,0] = 1;` `  ``// Fill the values of``  ``// upper triangle``  ``for` `(``int` `i = 0; i < n; i++)``  ``{``    ``if` `(i > 0)``    ``{``      ``arr[i, 0] = arr[i - 1, 0] +``                      ``i + 1;``    ``}``    ``for` `(``int` `j = 1; j < n - i; j++)``    ``{``      ``arr[i, j] = arr[i, j - 1] +``                      ``i + j;``    ``}``  ``}` `  ``// Fill the values of``  ``// lower triangle``  ``arr[1, n - 1] = arr[n - 1, 0] + 1;``  ``int` `div = 0;` `  ``for` `(``int` `i = 2; i < n; i++)``  ``{``    ``div = n - 2;``    ``for` `(``int` `j = n - i; j < n; j++)``    ``{``      ``if` `(j == n - i)``      ``{``        ``arr[i, j] = arr[i - 1, j + 1] + 1;``      ``}``      ``else``      ``{``        ``arr[i, j] = arr[i, j - 1] + div;``        ``div--;``      ``}``    ``}``  ``}` `  ``// Print the array``  ``for` `(``int` `i = 0; i < n; i++)``  ``{``    ``for` `(``int` `j = 0; j < n; j++)``    ``{``      ``Console.Write(arr[i, j] + ``" "``);``    ``}``    ``Console.Write(``"\n"``);``  ``}``}` `// Driver Code``public` `static` `void` `Main(String[] args)``{``  ``// Given size of matrix``  ``int` `N = 4;` `  ``// Function Call``  ``printPattern(N);``}``}` `// This code is contributed by shikhasingrajput`

## Javascript

 ``

Output

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

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

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