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# Print matrix in zig-zag fashion

Given a matrix of 2D array of n rows and m columns. Print this matrix in ZIG-ZAG fashion as shown in figure.

Example:

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

Approach of C++ code
The approach is simple. Just simply iterate over every diagonal elements one at a time and change the direction according to the previous match.

Approach of Python3 code
This approach is simple. While travelling the matrix in the usual fashion, on basis of parity of the sum of the indices of the element, add that particular element to the list either at the beginning or at the end if sum of i and j is either even or odd respectively. Print the solution list as it is.

Implementation:

## C++

 `/* C++ Program to print matrix in Zig-zag pattern*/` `#include ` `using` `namespace` `std;` `#define C 3`   `// Utility function to print matrix` `// in zig-zag form` `void` `zigZagMatrix(``int` `arr[][C], ``int` `n, ``int` `m)` `{` `    ``int` `row = 0, col = 0;`   `    ``// Boolean variable that will true if we` `    ``// need to increment 'row' value otherwise` `    ``// false- if increment 'col' value` `    ``bool` `row_inc = 0;`   `    ``// Print matrix of lower half zig-zag pattern` `    ``int` `mn = min(m, n);` `    ``for` `(``int` `len = 1; len <= mn; ++len) {` `        ``for` `(``int` `i = 0; i < len; ++i) {` `            ``cout << arr[row][col] << ``" "``;`   `            ``if` `(i + 1 == len)` `                ``break``;` `            ``// If row_increment value is true` `            ``// increment row and decrement col` `            ``// else decrement row and increment` `            ``// col` `            ``if` `(row_inc)` `                ``++row, --col;` `            ``else` `                ``--row, ++col;` `        ``}`   `        ``if` `(len == mn)` `            ``break``;`   `        ``// Update row or col value according` `        ``// to the last increment` `        ``if` `(row_inc)` `            ``++row, row_inc = ``false``;` `        ``else` `            ``++col, row_inc = ``true``;` `    ``}`   `    ``// Update the indexes of row and col variable` `    ``if` `(row == 0) {` `        ``if` `(col == m - 1)` `            ``++row;` `        ``else` `            ``++col;` `        ``row_inc = 1;` `    ``}` `    ``else` `{` `        ``if` `(row == n - 1)` `            ``++col;` `        ``else` `            ``++row;` `        ``row_inc = 0;` `    ``}`   `    ``// Print the next half zig-zag pattern` `    ``int` `MAX = max(m, n) - 1;` `    ``for` `(``int` `len, diag = MAX; diag > 0; --diag) {`   `        ``if` `(diag > mn)` `            ``len = mn;` `        ``else` `            ``len = diag;`   `        ``for` `(``int` `i = 0; i < len; ++i) {` `            ``cout << arr[row][col] << ``" "``;`   `            ``if` `(i + 1 == len)` `                ``break``;`   `            ``// Update row or col value according` `            ``// to the last increment` `            ``if` `(row_inc)` `                ``++row, --col;` `            ``else` `                ``++col, --row;` `        ``}`   `        ``// Update the indexes of row and col variable` `        ``if` `(row == 0 || col == m - 1) {` `            ``if` `(col == m - 1)` `                ``++row;` `            ``else` `                ``++col;`   `            ``row_inc = ``true``;` `        ``}`   `        ``else` `if` `(col == 0 || row == n - 1) {` `            ``if` `(row == n - 1)` `                ``++col;` `            ``else` `                ``++row;`   `            ``row_inc = ``false``;` `        ``}` `    ``}` `}`   `// Driver code` `int` `main()` `{` `    ``int` `matrix[][3] = { { 1, 2, 3 },` `                        ``{ 4, 5, 6 },` `                        ``{ 7, 8, 9 } };` `    ``zigZagMatrix(matrix, 3, 3);`   `    ``return` `0;` `}`

## Java

 `/* Java Program to print matrix in Zig-zag pattern*/` `class` `GFG {` `  ``static` `final` `int` `C = ``3``;`   `  ``// Utility function to print matrix` `  ``// in zig-zag form` `  ``static` `void` `zigZagMatrix(``int` `arr[][], ``int` `n, ``int` `m) {` `    ``int` `row = ``0``, col = ``0``;`   `    ``// Boolean variable that will true if we` `    ``// need to increment 'row' value otherwise` `    ``// false- if increment 'col' value` `    ``boolean` `row_inc = ``false``;`   `    ``// Print matrix of lower half zig-zag pattern` `    ``int` `mn = Math.min(m, n);` `    ``for` `(``int` `len = ``1``; len <= mn; ++len) {` `      ``for` `(``int` `i = ``0``; i < len; ++i) {` `        ``System.out.print(arr[row][col] + ``" "``);`   `        ``if` `(i + ``1` `== len)` `          ``break``;` `        ``// If row_increment value is true` `        ``// increment row and decrement col` `        ``// else decrement row and increment` `        ``// col` `        ``if` `(row_inc) {` `          ``++row;` `          ``--col;` `        ``} ``else` `{` `          ``--row;` `          ``++col;` `        ``}` `      ``}`   `      ``if` `(len == mn)` `        ``break``;`   `      ``// Update row or col value according` `      ``// to the last increment` `      ``if` `(row_inc) {` `        ``++row;` `        ``row_inc = ``false``;` `      ``} ``else` `{` `        ``++col;` `        ``row_inc = ``true``;` `      ``}` `    ``}`   `    ``// Update the indexes of row and col variable` `    ``if` `(row == ``0``) {` `      ``if` `(col == m - ``1``)` `        ``++row;` `      ``else` `        ``++col;` `      ``row_inc = ``true``;` `    ``} ``else` `{` `      ``if` `(row == n - ``1``)` `        ``++col;` `      ``else` `        ``++row;` `      ``row_inc = ``false``;` `    ``}`   `    ``// Print the next half zig-zag pattern` `    ``int` `MAX = Math.max(m, n) - ``1``;` `    ``for` `(``int` `len, diag = MAX; diag > ``0``; --diag) {`   `      ``if` `(diag > mn)` `        ``len = mn;` `      ``else` `        ``len = diag;`   `      ``for` `(``int` `i = ``0``; i < len; ++i) {` `        ``System.out.print(arr[row][col] + ``" "``);`   `        ``if` `(i + ``1` `== len)` `          ``break``;`   `        ``// Update row or col value according` `        ``// to the last increment` `        ``if` `(row_inc) {` `          ``++row;` `          ``--col;` `        ``} ``else` `{` `          ``++col;` `          ``--row;` `        ``}` `      ``}`   `      ``// Update the indexes of row and col variable` `      ``if` `(row == ``0` `|| col == m - ``1``) {` `        ``if` `(col == m - ``1``)` `          ``++row;` `        ``else` `          ``++col;`   `        ``row_inc = ``true``;` `      ``}`   `      ``else` `if` `(col == ``0` `|| row == n - ``1``) {` `        ``if` `(row == n - ``1``)` `          ``++col;` `        ``else` `          ``++row;`   `        ``row_inc = ``false``;` `      ``}` `    ``}` `  ``}` `  ``// Driver code` `  ``public` `static` `void` `main(String[] args) {` `    ``int` `matrix[][] = {{``1``, ``2``, ``3``}, {``4``, ``5``, ``6``}, {``7``, ``8``, ``9``}};` `    ``zigZagMatrix(matrix, ``3``, ``3``);` `  ``}` `}` `// This code is contributed by Anant Agarwal.`

## Python3

 `# Program to print matrix in Zig-zag pattern`   `matrix ``=``[` `            ``[ ``1``, ``2``, ``3``,],` `            ``[ ``4``, ``5``, ``6` `],` `            ``[ ``7``, ``8``, ``9` `],` `        ``]` `rows``=``3` `columns``=``3` `  `  `solution``=``[[] ``for` `i ``in` `range``(rows``+``columns``-``1``)]`   `for` `i ``in` `range``(rows):` `    ``for` `j ``in` `range``(columns):` `        ``sum``=``i``+``j` `        ``if``(``sum``%``2` `=``=``0``):`   `            ``#add at beginning` `            ``solution[``sum``].insert(``0``,matrix[i][j])` `        ``else``:`   `            ``#add at end of the list` `            ``solution[``sum``].append(matrix[i][j])` `        `  `            `  `# print the solution as it as` `for` `i ``in` `solution:` `    ``for` `j ``in` `i:` `        ``print``(j,end``=``" "``)` `        `    `     `

## C#

 `// C# Program to print matrix` `// in Zig-zag pattern` `using` `System;`   `class` `GFG {` `    ``static` `int` `C = 3;`   `    ``// Utility function to print` `    ``// matrix in zig-zag form` `    ``static` `void` `zigZagMatrix(``int``[, ] arr, ``int` `n, ``int` `m)` `    ``{` `        ``int` `row = 0, col = 0;`   `        ``// Boolean variable that will` `        ``// true if we need to increment` `        ``// 'row' valueotherwise false-` `        ``// if increment 'col' value` `        ``bool` `row_inc = ``false``;`   `        ``// Print matrix of lower half` `        ``// zig-zag pattern` `        ``int` `mn = Math.Min(m, n);` `        ``for` `(``int` `len = 1; len <= mn; ++len) {` `                ``for` `(``int` `i = 0; i < len; ++i) {`   `                ``Console.Write(arr[row, col] + ``" "``);`   `                ``if` `(i + 1 == len)` `                    ``break``;`   `                ``// If row_increment value is true` `                ``// increment row and decrement col` `                ``// else decrement row and increment` `                ``// col` `                ``if` `(row_inc) {` `                    ``++row;` `                    ``--col;` `                ``}` `                ``else` `{` `                    ``--row;` `                    ``++col;` `                ``}` `            ``}`   `            ``if` `(len == mn)` `                ``break``;`   `            ``// Update row or col value` `            ``// according to the last` `            ``// increment` `            ``if` `(row_inc) {` `                    ``++row;` `                    ``row_inc = ``false``;` `            ``}` `            ``else` `{` `                ``++col;` `                ``row_inc = ``true``;` `            ``}` `        ``}`   `        ``// Update the indexes of row` `        ``// and col variable` `        ``if` `(row == 0) {` `            ``if` `(col == m - 1)` `                ``++row;` `            ``else` `                ``++col;` `            ``row_inc = ``true``;` `        ``}` `        ``else` `{` `            ``if` `(row == n - 1)` `                ``++col;` `            ``else` `                ``++row;` `            ``row_inc = ``false``;` `        ``}`   `        ``// Print the next half` `        ``// zig-zag pattern` `        ``int` `MAX = Math.Max(m, n) - 1;` `        ``for` `(``int` `len, diag = MAX; diag > 0; --diag) {`   `            ``if` `(diag > mn)` `                    ``len = mn;` `            ``else` `                ``len = diag;`   `            ``for` `(``int` `i = 0; i < len; ++i) {` `                    ``Console.Write(arr[row, col] + ``" "``);`   `                ``if` `(i + 1 == len)` `                    ``break``;`   `                ``// Update row or col value` `                ``// according to the last` `                ``// increment` `                ``if` `(row_inc) {` `                        ``++row;` `                        ``--col;` `                ``}` `                ``else` `{` `                    ``++col;` `                    ``--row;` `                ``}` `            ``}`   `            ``// Update the indexes of` `            ``// row and col variable` `            ``if` `(row == 0 || col == m - 1) {` `                ``if` `(col == m - 1)` `                    ``++row;` `                ``else` `                    ``++col;`   `                ``row_inc = ``true``;` `            ``}`   `            ``else` `if` `(col == 0 || row == n - 1) {` `                ``if` `(row == n - 1)` `                    ``++col;` `                ``else` `                    ``++row;`   `                ``row_inc = ``false``;` `            ``}` `        ``}` `    ``}`   `    ``// Driver code` `    ``public` `static` `void` `Main()` `    ``{` `        ``int``[, ] matrix = { { 1, 2, 3 },` `                        ``{ 4, 5, 6 },` `                        ``{ 7, 8, 9 } };` `        ``zigZagMatrix(matrix, 3, 3);` `    ``}` `}`   `// This code is contributed by vt_m.`

## PHP

 ` 0; --``\$diag``) ` `    ``{` `        ``if` `(``\$diag` `> ``\$mn``)` `            ``\$len` `= ``\$mn``;` `        ``else` `            ``\$len` `= ``\$diag``;`   `        ``for` `(``\$i` `= 0; ` `             ``\$i` `< ``\$len``; ++``\$i``)` `        ``{` `            ``echo``(``\$arr``[``\$row``][``\$col``] . ``" "``);`   `            ``if` `(``\$i` `+ 1 == ``\$len``)` `                ``break``;`   `            ``// Update row or col ` `            ``// value according to` `            ``// the last increment` `            ``if` `(``\$row_inc``)` `            ``{` `                ``++``\$row``; --``\$col``;` `            ``}` `            ``else` `            ``{` `                ``++``\$col``; --``\$row``;` `            ``}` `        ``}`   `        ``// Update the indexes of` `        ``// row and col variable` `        ``if` `(``\$row` `== 0 || ` `            ``\$col` `== ``\$m` `- 1) ` `        ``{` `            ``if` `(``\$col` `== ``\$m` `- 1)` `                ``++``\$row``;` `            ``else` `                ``++``\$col``;`   `            ``\$row_inc` `= true;` `        ``}`   `        ``else` `if` `(``\$col` `== 0 || ` `                 ``\$row` `== ``\$n` `- 1) ` `        ``{` `            ``if` `(``\$row` `== ``\$n` `- 1)` `                ``++``\$col``;` `            ``else` `                ``++``\$row``;`   `            ``\$row_inc` `= false;` `        ``}` `    ``}` `}`   `// Driver code` `\$matrix` `= ``array``(``array``(1, 2, 3),` `                ``array``(4, 5, 6),` `                ``array``(7, 8, 9));` `                `  `zigZagMatrix(``\$matrix``, 3, 3);`   `// This code is contributed by ` `// Manish Shaw(manishshaw1)` `?>`

## Javascript

 `// Javascript Program to print matrix in Zig-zag pattern` `var` `n = 3, m = 3;` `var` `a = [[ 1, 2, 3 ], [ 4, 5, 6 ], [ 7, 8, 9 ]];` `var` `zigZagMatrix=``function``(arr, n, m)` `{` `    ``var` `row = 0;` `    ``var` `col = 0;` ` `  `    ``// Variable that will be 1 if we` `    ``// need to increment 'row' value and 0 otherwise` `    ``// if we need to increment 'col' value` `    ``var` `row_inc = 0;` ` `  `    ``// print matrix of lower half zig-zag pattern` `    ``var` `mn = Math.min(m, n);` `    ``for` `(``var` `len = 1; len <= mn; ++len) {` `        ``for` `(``var` `i = 0; i < len; ++i) {` `            ``console.log(arr[row][col]);` `            ``console.log(``" "``);` ` `  `            ``if` `(i + 1 == len)` `                ``break``;` `            ``// If row_increment value is true` `            ``// increment row and decrement col` `            ``// else decrement row and increment col` `            ``if` `(row_inc)` `                ``++row, --col;` `            ``else` `                ``--row, ++col;` `        ``}` ` `  `        ``if` `(len == mn)` `            ``break``;` ` `  `        ``// Update row or col value according` `        ``// to the last increment` `        ``if` `(row_inc)` `            ``++row, row_inc = ``false``;` `        ``else` `            ``++col, row_inc = ``true``;` `    ``}` ` `  `    ``// Update the indexes of row and col variable` `    ``if` `(row == 0) {` `        ``if` `(col == m - 1)` `            ``++row;` `        ``else` `            ``++col;` `        ``row_inc = 1;` `    ``}` `    ``else` `{` `        ``if` `(row == n - 1)` `            ``++col;` `        ``else` `            ``++row;` `        ``row_inc = 0;` `    ``}` ` `  `    ``// Print the next half zig-zag pattern` `    ``var` `MAX = Math.max(m, n) - 1;` `    ``for` `(``var` `len, diag = MAX; diag > 0; --diag) {` ` `  `        ``if` `(diag > mn)` `            ``len = mn;` `        ``else` `            ``len = diag;` ` `  `        ``for` `(``var` `i = 0; i < len; ++i) {` `            ``console.log(arr[row][col]);` `            ``console.log(``" "``);` `            ``if` `(i + 1 == len)` `                ``break``;` ` `  `            ``// Update row or col value according` `            ``// to the last increment` `            ``if` `(row_inc)` `                ``++row, --col;` `            ``else` `                ``++col, --row;` `        ``}` ` `  `        ``// Update the indexes of row and col variable` `        ``if` `(row == 0 || col == m - 1) {` `            ``if` `(col == m - 1)` `                ``++row;` `            ``else` `                ``++col;` ` `  `            ``row_inc = ``true``;` `        ``}` ` `  `        ``else` `if` `(col == 0 || row == n - 1) {` `            ``if` `(row == n - 1)` `                ``++col;` `            ``else` `                ``++row;` `            ``row_inc = ``false``;` `        ``}` `    ``}` `}` `zigZagMatrix(a, 3, 3);` ` `  `// This code is contributed by Sajal Aggarwal.`

Output

`1 2 4 7 5 3 6 8 9 `

Time complexity: O(n*m)
Auxiliary space: O(1), since no extra space has been taken.

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