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# Spiral view of diamond element in square matrix

The Spiral view of diamond elements in a square matrix is a problem where you need to traverse and print certain elements of a square matrix in a spiral pattern. The matrix is divided into four quadrants, and the diagonal elements from each quadrant are traversed in a spiral order.

## Problem Statement

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

## Example

Consider the following 7x7 square matrix:

``````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
43  44  45  46  47  48  49``````

The diagonal elements in the spiral view are:

``4  12  20  28  34  40  46  38  30  22  16  10  11  19  27  33  39  31  23  17  18  26  32  24  25``

## Idea to Solve the Problem

To solve this problem, we need to divide the matrix into four quadrants: P1, P2, P3, and P4. The diagonal elements of these quadrants are traversed in a spiral order, and the elements are printed accordingly.

## Pseudocode

``````function spiralDiamondView(matrix, x, y, m, n, k):
midCol = y + (n - y) / 2
midRow = midCol

Traverse diagonal elements in quadrant P1 and print them

Traverse diagonal elements in quadrant P2 and print them

Traverse diagonal elements in quadrant P3 and print them

Traverse diagonal elements in quadrant P4 and print them

if x + 1 <= m - 1 and k > 0:
Recursive call with inner submatrix

function diamondSpiral(matrix):
row = number of rows in matrix
col = number of columns in matrix

if row != col or col is even:
Print "Not perfect odd square matrix"
return

Call spiralDiamondView with initial parameters``````

## Algorithm Explanation

1. The `spiralDiamondView` function takes a matrix and boundaries (`x`, `y`, `m`, `n`) as inputs.

2. It calculates the middle column and row indices.

3. It traverses the diagonal elements in quadrant P1 and prints them.

4. It traverses the diagonal elements in quadrant P2 and prints them.

5. It traverses the diagonal elements in quadrant P3 and prints them.

6. It traverses the diagonal elements in quadrant P4 and prints them.

7. If there is an inner submatrix (when `x + 1 <= m - 1`), the algorithm makes a recursive call to the same function with the inner submatrix as arguments.

8. The `diamondSpiral` function checks if the matrix is a perfect odd square matrix and then calls `spiralDiamondView` with initial parameters.

## Time Complexity

The time complexity of the diagonal spiral traversal algorithm is O(n), where n is the number of elements in the matrix. This is because each element is visited exactly once.

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