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.

Program List

1) Spiral view of diamond elements in square matrix in java 2) Spiral view of diamond elements in square matrix in c++ 3) Spiral view of diamond elements in square matrix in c 4) Spiral view of diamond elements in square matrix in c# 5) Spiral view of diamond elements in square matrix in vb.net 6) Spiral view of diamond elements in square matrix in php 7) Spiral view of diamond elements in square matrix in node js 8) Spiral view of diamond elements in square matrix in typescript 9) Spiral view of diamond elements in square matrix in python 10) Spiral view of diamond elements in square matrix in ruby 11) Spiral view of diamond elements in square matrix in scala 12) Spiral view of diamond elements in square matrix in swift 13) Spiral view of diamond elements in square matrix in kotlin 14) Spiral view of diamond elements in square matrix in golang

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.