Print a given matrix in spiral form

Given a 2D array, print it in spiral form. See the following examples.

Examples:

```Input:  1    2   3   4
5    6   7   8
9   10  11  12
13  14  15  16
Output: 1 2 3 4 8 12 16 15 14 13 9 5 6 7 11 10
Explanation: The output is matrix in spiral format.

Input:  1   2   3   4  5   6
7   8   9  10  11  12
13  14  15 16  17  18
Output: 1 2 3 4 5 6 12 18 17 16 15 14 13 7 8 9 10 11
Explanation :The output is matrix in spiral format.
```

Method 1: This is a simple method to solve the following problem.

Approach: The problem can be solved by dividing the matrix into loops or squares or boundaries. It can be seen that the elements of the outer loop are printed first in a clockwise manner then the elements of the inner loop is printed. So printing the elements of a loop can be solved using four loops which prints all the elements. Every ‘for’ loop defines a single direction movement along with the matrix. The first for loop represents the movement from left to right, whereas the second crawl represents the movement from top to bottom, the third represents the movement from the right to left, and the fourth represents the movement from bottom to up.

• Algorithm:
1. Create and initialize variables k – starting row index, m – ending row index, l – starting column index, n – ending column index
2. Run a loop until all the squares of loops are printed.
3. In each outer loop traversal print the elements of a square in a clockwise manner.
4. Print the top row, i.e. Print the elements of the kth row from column index l to n, and increase the count of k.
5. Print the right column, i.e. Print the last column or n-1th column from row index k to m and decrease the count of n.
6. Print the bottom row, i.e. if k < m, then print the elements of m-1th row from column n-1 to l and decrease the count of m
7. Print the left column, i.e. if l < n, then print the elements of lth column from m-1th row to k and increase the count of l.

Below is the implementation of the above algorithm:

 `// C++ Program to print a matrix spirally`   `#include ` `using` `namespace` `std;` `#define R 3` `#define C 6`   `void` `spiralPrint(``int` `m, ``int` `n, ``int` `a[R][C])` `{` `    ``int` `i, k = 0, l = 0;`   `    ``/* k - starting row index` `        ``m - ending row index` `        ``l - starting column index` `        ``n - ending column index` `        ``i - iterator` `    ``*/`   `    ``while` `(k < m && l < n) {` `        ``/* Print the first row from` `               ``the remaining rows */` `        ``for` `(i = l; i < n; ++i) {` `            ``cout << a[k][i] << ``" "``;` `        ``}` `        ``k++;`   `        ``/* Print the last column` `         ``from the remaining columns */` `        ``for` `(i = k; i < m; ++i) {` `            ``cout << a[i][n - 1] << ``" "``;` `        ``}` `        ``n--;`   `        ``/* Print the last row from` `                ``the remaining rows */` `        ``if` `(k < m) {` `            ``for` `(i = n - 1; i >= l; --i) {` `                ``cout << a[m - 1][i] << ``" "``;` `            ``}` `            ``m--;` `        ``}`   `        ``/* Print the first column from` `                   ``the remaining columns */` `        ``if` `(l < n) {` `            ``for` `(i = m - 1; i >= k; --i) {` `                ``cout << a[i][l] << ``" "``;` `            ``}` `            ``l++;` `        ``}` `    ``}` `}`   `/* Driver Code */` `int` `main()` `{` `    ``int` `a[R][C] = { { 1, 2, 3, 4, 5, 6 },` `                    ``{ 7, 8, 9, 10, 11, 12 },` `                    ``{ 13, 14, 15, 16, 17, 18 } };` `    `  `      ``// Function Call` `    ``spiralPrint(R, C, a);` `    ``return` `0;` `}`   `// This is code is contributed by rathbhupendra`

 `// C program to print the array in a` `// spiral form`   `#include ` `#define R 3` `#define C 6`   `void` `spiralPrint(``int` `m, ``int` `n, ``int` `a[R][C])` `{` `    ``int` `i, k = 0, l = 0;`   `    ``/*  k - starting row index` `        ``m - ending row index` `        ``l - starting column index` `        ``n - ending column index` `        ``i - iterator` `    ``*/`   `    ``while` `(k < m && l < n) {` `        ``/* Print the first row from the remaining rows */` `        ``for` `(i = l; i < n; ++i) {` `            ``printf``(``"%d "``, a[k][i]);` `        ``}` `        ``k++;`   `        ``/* Print the last column from the remaining columns` `         ``*/` `        ``for` `(i = k; i < m; ++i) {` `            ``printf``(``"%d "``, a[i][n - 1]);` `        ``}` `        ``n--;`   `        ``/* Print the last row from the remaining rows */` `        ``if` `(k < m) {` `            ``for` `(i = n - 1; i >= l; --i) {` `                ``printf``(``"%d "``, a[m - 1][i]);` `            ``}` `            ``m--;` `        ``}`   `        ``/* Print the first column from the remaining columns` `         ``*/` `        ``if` `(l < n) {` `            ``for` `(i = m - 1; i >= k; --i) {` `                ``printf``(``"%d "``, a[i][l]);` `            ``}` `            ``l++;` `        ``}` `    ``}` `}`   `/* Driver Code */` `int` `main()` `{` `    ``int` `a[R][C] = { { 1, 2, 3, 4, 5, 6 },` `                    ``{ 7, 8, 9, 10, 11, 12 },` `                    ``{ 13, 14, 15, 16, 17, 18 } };` `    `  `    ``// Function Call` `    ``spiralPrint(R, C, a);` `    ``return` `0;` `}`

 `// Java program to print a given matrix in spiral form` `import` `java.io.*;`   `class` `GFG {`   `    ``// Function print matrix in spiral form` `    ``static` `void` `spiralPrint(``int` `m, ``int` `n, ``int` `a[][])` `    ``{` `        ``int` `i, k = ``0``, l = ``0``;`   `        ``/*  k - starting row index` `        ``m - ending row index` `        ``l - starting column index` `        ``n - ending column index` `        ``i - iterator` `        ``*/`   `        ``while` `(k < m && l < n) {` `            ``// Print the first row from the remaining rows` `            ``for` `(i = l; i < n; ++i) {` `                ``System.out.print(a[k][i] + ``" "``);` `            ``}` `            ``k++;`   `            ``// Print the last column from the remaining` `            ``// columns` `            ``for` `(i = k; i < m; ++i) {` `                ``System.out.print(a[i][n - ``1``] + ``" "``);` `            ``}` `            ``n--;`   `            ``// Print the last row from the remaining rows */` `            ``if` `(k < m) {` `                ``for` `(i = n - ``1``; i >= l; --i) {` `                    ``System.out.print(a[m - ``1``][i] + ``" "``);` `                ``}` `                ``m--;` `            ``}`   `            ``// Print the first column from the remaining` `            ``// columns */` `            ``if` `(l < n) {` `                ``for` `(i = m - ``1``; i >= k; --i) {` `                    ``System.out.print(a[i][l] + ``" "``);` `                ``}` `                ``l++;` `            ``}` `        ``}` `    ``}`   `    ``// Driver Code` `    ``public` `static` `void` `main(String[] args)` `    ``{` `        ``int` `R = ``3``;` `        ``int` `C = ``6``;` `        ``int` `a[][] = { { ``1``, ``2``, ``3``, ``4``, ``5``, ``6` `},` `                      ``{ ``7``, ``8``, ``9``, ``10``, ``11``, ``12` `},` `                      ``{ ``13``, ``14``, ``15``, ``16``, ``17``, ``18` `} };` `       `  `        ``// Function Call` `          ``spiralPrint(R, C, a);` `    ``}` `}`   `// Contributed by Pramod Kumar`

 `# Python3 program to print` `# given matrix in spiral form`     `def` `spiralPrint(m, n, a):` `    ``k ``=` `0` `    ``l ``=` `0`   `    ``''' k - starting row index` `        ``m - ending row index` `        ``l - starting column index` `        ``n - ending column index` `        ``i - iterator '''`   `    ``while` `(k < m ``and` `l < n):`   `        ``# Print the first row from` `        ``# the remaining rows` `        ``for` `i ``in` `range``(l, n):` `            ``print``(a[k][i], end``=``" "``)`   `        ``k ``+``=` `1`   `        ``# Print the last column from` `        ``# the remaining columns` `        ``for` `i ``in` `range``(k, m):` `            ``print``(a[i][n ``-` `1``], end``=``" "``)`   `        ``n ``-``=` `1`   `        ``# Print the last row from` `        ``# the remaining rows` `        ``if` `(k < m):`   `            ``for` `i ``in` `range``(n ``-` `1``, (l ``-` `1``), ``-``1``):` `                ``print``(a[m ``-` `1``][i], end``=``" "``)`   `            ``m ``-``=` `1`   `        ``# Print the first column from` `        ``# the remaining columns` `        ``if` `(l < n):` `            ``for` `i ``in` `range``(m ``-` `1``, k ``-` `1``, ``-``1``):` `                ``print``(a[i][l], end``=``" "``)`   `            ``l ``+``=` `1`     `# Driver Code` `a ``=` `[[``1``, ``2``, ``3``, ``4``, ``5``, ``6``],` `     ``[``7``, ``8``, ``9``, ``10``, ``11``, ``12``],` `     ``[``13``, ``14``, ``15``, ``16``, ``17``, ``18``]]`   `R ``=` `3` `C ``=` `6`   `# Function Call` `spiralPrint(R, C, a)`   `# This code is contributed by Nikita Tiwari.`

 `// C# program to print a given` `// matrix in spiral form` `using` `System;`   `class` `GFG {` `    ``// Function print matrix in spiral form` `    ``static` `void` `spiralPrint(``int` `m, ``int` `n, ``int``[, ] a)` `    ``{` `        ``int` `i, k = 0, l = 0;` `        ``/* k - starting row index` `        ``m - ending row index` `        ``l - starting column index` `        ``n - ending column index` `        ``i - iterator` `        ``*/`   `        ``while` `(k < m && l < n) {` `            ``// Print the first row` `            ``// from the remaining rows` `            ``for` `(i = l; i < n; ++i) {` `                ``Console.Write(a[k, i] + ``" "``);` `            ``}` `            ``k++;`   `            ``// Print the last column from the` `            ``// remaining columns` `            ``for` `(i = k; i < m; ++i) {` `                ``Console.Write(a[i, n - 1] + ``" "``);` `            ``}` `            ``n--;`   `            ``// Print the last row from` `            ``// the remaining rows` `            ``if` `(k < m) {` `                ``for` `(i = n - 1; i >= l; --i) {` `                    ``Console.Write(a[m - 1, i] + ``" "``);` `                ``}` `                ``m--;` `            ``}`   `            ``// Print the first column from` `            ``// the remaining columns` `            ``if` `(l < n) {` `                ``for` `(i = m - 1; i >= k; --i) {` `                    ``Console.Write(a[i, l] + ``" "``);` `                ``}` `                ``l++;` `            ``}` `        ``}` `    ``}`   `    ``// Driver Code` `    ``public` `static` `void` `Main()` `    ``{` `        ``int` `R = 3;` `        ``int` `C = 6;` `        ``int``[, ] a = { { 1, 2, 3, 4, 5, 6 },` `                      ``{ 7, 8, 9, 10, 11, 12 },` `                      ``{ 13, 14, 15, 16, 17, 18 } };` `        `  `          ``// Function Call` `          ``spiralPrint(R, C, a);` `    ``}` `}`   `// This code is contributed by Sam007`

 `= ``\$l``; --``\$i``)` `            ``{` `                ``echo` `\$a``[``\$m` `- 1][``\$i``] . ``" "``;` `            ``}` `            ``\$m``--;` `        ``}`   `        ``/* Print the first column from` `           ``the remaining columns */` `        ``if` `(``\$l` `< ``\$n``)` `        ``{` `            ``for` `(``\$i` `= ``\$m` `- 1; ``\$i` `>= ``\$k``; --``\$i``)` `            ``{` `                ``echo` `\$a``[``\$i``][``\$l``] . ``" "``;` `            ``}` `            ``\$l``++; ` `        ``}     ` `    ``}` `}`   `// Driver code` `\$a` `= ``array``(``array``(1, 2, 3, 4, 5, 6),` `           ``array``(7, 8, 9, 10, 11, 12),` `           ``array``(13, 14, 15, 16, 17, 18));`   `// Function Call` `spiralPrint(``\$R``, ``\$C``, ``\$a``);`   `// This code is contributed` `// by ChitraNayal` `?>`

Output
`1 2 3 4 5 6 12 18 17 16 15 14 13 7 8 9 10 11 `

Complexity Analysis:

• Time Complexity: O(m*n).
To traverse the matrix O(m*n) time is required.
• Space Complexity: O(1).
No extra space is required.

Method 2: (Recursive Approach)

Approach: The above problem can be solved by printing the boundary of the Matrix recursively. In each recursive call, we decrease the dimensions of the matrix. The idea of printing the boundary or loops is the same.

• Algorithm:
1. create a recursive function that takes a matrix and some variables (k – starting row index, m – ending row index, l – starting column index, n – ending column index) as parameters
2. Check the base cases (stating index is less than or equal to ending index) and print the boundary elements in clockwise manner
3. Print the top row, i.e. Print the elements of kth row from column index l to n, and increase the count of k.
4. Print the right column, i.e. Print the last column or n-1th column from row index k to m and decrease the count of n.
5. Print the bottom row, i.e. if k > m, then print the elements of m-1th row from column n-1 to l and decrease the count of m
6. Print the left column, i.e. if l < n, then print the elements of lth column from m-1th row to k and increase the count of l.
7. Call the function recursively with the values of starting and ending indices of rows and columns.

Below is the implementation of the above algorithm:

 `// C++. program for the above approach` `#include ` `using` `namespace` `std;`   `#define R 4` `#define C 4`   `// Function for printing matrix in spiral` `// form i, j: Start index of matrix, row` `// and column respectively m, n: End index` `// of matrix row and column respectively` `void` `print(``int` `arr[R][C], ``int` `i, ``int` `j, ``int` `m, ``int` `n)` `{` `    ``// If i or j lies outside the matrix` `    ``if` `(i >= m or j >= n)` `        ``return``;`   `    ``// Print First Row` `    ``for` `(``int` `p = i; p < n; p++)` `        ``cout << arr[i][p] << ``" "``;`   `    ``// Print Last Column` `    ``for` `(``int` `p = i + 1; p < m; p++)` `        ``cout << arr[p][n - 1] << ``" "``;`   `    ``// Print Last Row, if Last and` `    ``// First Row are not same` `    ``if` `((m - 1) != i)` `        ``for` `(``int` `p = n - 2; p >= j; p--)` `            ``cout << arr[m - 1][p] << ``" "``;`   `    ``// Print First Column,  if Last and` `    ``// First Column are not same` `    ``if` `((n - 1) != j)` `        ``for` `(``int` `p = m - 2; p > i; p--)` `            ``cout << arr[p][j] << ``" "``;`   `    ``print(arr, i + 1, j + 1, m - 1, n - 1);` `}`   `// Driver Code` `int` `main()` `{`   `    ``int` `a[R][C] = { { 1, 2, 3, 4 },` `                    ``{ 5, 6, 7, 8 },` `                    ``{ 9, 10, 11, 12 },` `                    ``{ 13, 14, 15, 16 } };`   `    ``// Function Call` `    ``print(a, 0, 0, R, C);` `    ``return` `0;` `}` `// This Code is contributed by Ankur Goel`

 `// Java program for the above approach` `import` `java.util.*;`   `class` `GFG {` `    ``static` `int` `R = ``4``;` `    ``static` `int` `C = ``4``;`   `    ``// Function for printing matrix in spiral` `    ``// form i, j: Start index of matrix, row` `    ``// and column respectively m, n: End index` `    ``// of matrix row and column respectively` `    ``static` `void` `print(``int` `arr[][], ``int` `i, ``int` `j, ``int` `m,` `                      ``int` `n)` `    ``{` `        ``// If i or j lies outside the matrix` `        ``if` `(i >= m || j >= n) {` `            ``return``;` `        ``}`   `        ``// Print First Row` `        ``for` `(``int` `p = i; p < n; p++) {` `            ``System.out.print(arr[i][p] + ``" "``);` `        ``}`   `        ``// Print Last Column` `        ``for` `(``int` `p = i + ``1``; p < m; p++) {` `            ``System.out.print(arr[p][n - ``1``] + ``" "``);` `        ``}`   `        ``// Print Last Row, if Last and` `        ``// First Row are not same` `        ``if` `((m - ``1``) != i) {` `            ``for` `(``int` `p = n - ``2``; p >= j; p--) {` `                ``System.out.print(arr[m - ``1``][p] + ``" "``);` `            ``}` `        ``}`   `        ``// Print First Column, if Last and` `        ``// First Column are not same` `        ``if` `((n - ``1``) != j) {` `            ``for` `(``int` `p = m - ``2``; p > i; p--) {` `                ``System.out.print(arr[p][j] + ``" "``);` `            ``}` `        ``}` `        ``print(arr, i + ``1``, j + ``1``, m - ``1``, n - ``1``);` `    ``}`   `    ``// Driver Code` `    ``public` `static` `void` `main(String[] args)` `    ``{` `        ``int` `a[][] = { { ``1``, ``2``, ``3``, ``4` `},` `                      ``{ ``5``, ``6``, ``7``, ``8` `},` `                      ``{ ``9``, ``10``, ``11``, ``12` `},` `                      ``{ ``13``, ``14``, ``15``, ``16` `} };`   `        ``// Function Call` `        ``print(a, ``0``, ``0``, R, C);` `    ``}` `}`   `// This code is contributed by 29AjayKumar`

 `# Python3 program for the above approach`   `# Function for printing matrix in spiral` `# form i, j: Start index of matrix, row` `# and column respectively m, n: End index` `# of matrix row and column respectively`     `def` `printdata(arr, i, j, m, n):`   `    ``# If i or j lies outside the matrix` `    ``if` `(i >``=` `m ``or` `j >``=` `n):` `        ``return`   `    ``# Print First Row` `    ``for` `p ``in` `range``(i, n):` `        ``print``(arr[i][p], end``=``" "``)`   `    ``# Print Last Column` `    ``for` `p ``in` `range``(i ``+` `1``, m):` `        ``print``(arr[p][n ``-` `1``], end``=``" "``)`   `    ``# Print Last Row, if Last and` `    ``# First Row are not same` `    ``if` `((m ``-` `1``) !``=` `i):` `        ``for` `p ``in` `range``(n ``-` `2``, j ``-` `1``, ``-``1``):` `            ``print``(arr[m ``-` `1``][p], end``=``" "``)`   `    ``# Print First Column, if Last and` `    ``# First Column are not same` `    ``if` `((n ``-` `1``) !``=` `j):` `        ``for` `p ``in` `range``(m ``-` `2``, i, ``-``1``):` `            ``print``(arr[p][j], end``=``" "``)`   `    ``printdata(arr, i ``+` `1``, j ``+` `1``, m ``-` `1``, n ``-` `1``)`     `# Driver code` `R ``=` `4` `C ``=` `4` `arr ``=` `[[``1``, ``2``, ``3``, ``4``],` `       ``[``5``, ``6``, ``7``, ``8``],` `       ``[``9``, ``10``, ``11``, ``12``],` `       ``[``13``, ``14``, ``15``, ``16``]]`   `# Function Call` `printdata(arr, ``0``, ``0``, R, C)`   `# This code is contributed by avsadityavardhan`

 `// C# program for the above approach` `using` `System;`   `class` `GFG {` `    ``static` `int` `R = 4;` `    ``static` `int` `C = 4;`   `    ``// Function for printing matrix in spiral` `    ``// form i, j: Start index of matrix, row` `    ``// and column respectively m, n: End index` `    ``// of matrix row and column respectively` `    ``static` `void` `print(``int``[, ] arr, ``int` `i, ``int` `j, ``int` `m,` `                      ``int` `n)` `    ``{` `        ``// If i or j lies outside the matrix` `        ``if` `(i >= m || j >= n) {` `            ``return``;` `        ``}`   `        ``// Print First Row` `        ``for` `(``int` `p = i; p < n; p++) {` `            ``Console.Write(arr[i, p] + ``" "``);` `        ``}`   `        ``// Print Last Column` `        ``for` `(``int` `p = i + 1; p < m; p++) {` `            ``Console.Write(arr[p, n - 1] + ``" "``);` `        ``}`   `        ``// Print Last Row, if Last and` `        ``// First Row are not same` `        ``if` `((m - 1) != i) {` `            ``for` `(``int` `p = n - 2; p >= j; p--) {` `                ``Console.Write(arr[m - 1, p] + ``" "``);` `            ``}` `        ``}`   `        ``// Print First Column, if Last and` `        ``// First Column are not same` `        ``if` `((n - 1) != j) {` `            ``for` `(``int` `p = m - 2; p > i; p--) {` `                ``Console.Write(arr[p, j] + ``" "``);` `            ``}` `        ``}` `        ``print(arr, i + 1, j + 1, m - 1, n - 1);` `    ``}`   `    ``// Driver Code` `    ``public` `static` `void` `Main(String[] args)` `    ``{` `        ``int``[, ] a = { { 1, 2, 3, 4 },` `                      ``{ 5, 6, 7, 8 },` `                      ``{ 9, 10, 11, 12 },` `                      ``{ 13, 14, 15, 16 } };` `        ``// Function Call` `        ``print(a, 0, 0, R, C);` `    ``}` `}`   `// This code is contributed by Princi Singh`

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

```

Complexity Analysis:

• Time Complexity: O(m*n).
To traverse the matrix O(m*n) time is required.
• Space Complexity: O(1).
No extra space is required.