# Spiral form of matrix

The Spiral Form of a matrix is a way of arranging the elements of a matrix in a spiral order, starting from the top-left corner and moving in a clockwise direction towards the center. This arrangement is useful in various applications such as image processing, pattern recognition, and data visualization. ## Problem Statement

Given a matrix, the task is to print its elements in a spiral order, starting from the top-left corner and moving towards the center in a clockwise manner.

## Example

Consider the following 6x6 matrix:

``````1  2  3  4  5  6
22 23 24 25 26 7
21 36 37 38 27 8
20 35 42 39 28 9
19 34 41 40 29 10
18 33 32 31 30 11
17 16 15 14 13 12``````

The spiral order of the matrix is:

``1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42``

## Idea to Solve the Problem

To solve this problem, we can iterate through the matrix in a spiral order by following these steps:

1. Traverse the top row from left to right.
2. Traverse the right column from top to bottom.
3. Traverse the bottom row from right to left.
4. Traverse the left column from bottom to top.

After completing one cycle, we repeat these steps for the inner submatrix until all elements have been visited.

## Pseudocode

``````function spiral(matrix, startRow, startCol, endRow, endCol, element):
Traverse top row from startCol to endCol
Traverse right column from startRow + 1 to endRow
Traverse bottom row from endCol - 1 to startCol if startRow < endRow
Traverse left column from endRow - 1 to startRow + 1 if startCol < endCol
If startRow + 1 <= endRow - 1 and startCol < endCol - 1:
Recursive call with inner submatrix``````

## Algorithm Explanation

1. The algorithm takes a matrix and boundaries (`startRow`, `startCol`, `endRow`, `endCol`) as inputs.

2. It traverses the top row from `startCol` to `endCol` and prints each element.

3. It traverses the right column from `startRow + 1` to `endRow` and prints each element.

4. It traverses the bottom row from `endCol - 1` to `startCol` if `startRow` is less than `endRow`, and prints each element.

5. It traverses the left column from `endRow - 1` to `startRow + 1` if `startCol` is less than `endCol`, and prints each element.

6. If there is an inner submatrix (when `startRow + 1 <= endRow - 1` and `startCol < endCol - 1`), the algorithm makes a recursive call to the same function with the inner submatrix as arguments.

## Time Complexity

The time complexity of the spiral matrix traversal algorithm is O(m * n), where m is the number of rows and n is the number of columns in the matrix. This is because each element of the matrix is visited exactly once.

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