Diagonal Matrix Traversal and Perfect Square Identification in C#

Introduction

Hello, budding programmer! Are you ready to embark on a journey into the land of matrices? In this unit, we're in for a thrilling ride into the world of unique matrix traversal . We'll be navigating through the realm of 2D arrays following an intriguing and distinctive order. Stay seated, and let's dive right in!

Task Statement

Suppose we have a matrix where each cell represents a distinct symbol or integer. Our task is to decode this matrix by reading the cells in a particular order. The decoding begins from the top-left cell of the matrix. We move in a bottom-left downward diagonal direction until we hit the left boundary. Upon hitting the left boundary, we move one cell down (unless we're at the bottom-left corner already, in which case we move one cell to the right) and start moving in an upward diagonal direction toward the upper-right. While moving diagonally up-right, if we hit the top boundary, we move one cell to the right and start moving in a downward diagonal direction toward the bottom-left. However, if we hit the right boundary while moving diagonally upward, we move one cell down and start moving in a bottom-left direction. In other words, we keep zigzagging diagonally across the matrix until every cell in the matrix is visited. Upon completing this zigzag traversal, we will have a list of traversed cell values. Next, we process this list to uncover the indices of the perfect square numbers. The function should implement this traversal and return a list containing the positions of perfect square numbers in the traversed sequence. Take a 3x4 matrix, for instance: C# {{1, 2, 3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12}} Upon completing the diagonal traversal, we'll get the list: {1, 5, 2, 3, 6, 9, 10, 7, 4, 8, 11, 12} . From this list, we see that 1, 9, and 4 are perfect squares and are located at the 1st, 6th, and 9th positions in the list. Thus, our function returns: {0, 5, 8} .

Step Overview

To tackle this problem, we will take the following steps: Traverse the Matrix Diagonally : Begin from the top-left cell and zigzag through the matrix in a specific diagonal pattern. Record Traversed Values : As you traverse, collect the cell values in a list. Identify Perfect Squares : Inspect the collected values to determine which are perfect squares. Return Positions : Gather the positions of the perfect squares in the list and return them.

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Traversing the Matrix Diagonally

To traverse the matrix diagonally in a zigzag pattern, we need to adhere to a specific movement strategy that alternates between two directions: down-left and up-right. Here's a clearer breakdown of the traversal logic.

Initialize Variables: We start by initializing row and col to zero, representing the top-left position of the matrix. We also set dir to 1 for the initial down-left direction.
Traverse the Matrix: We loop through each cell in the matrix using a loop that runs rows * cols times, which is the total number of elements in the matrix.
Add Current Value: In each iteration, add the current matrix element located at (row, col) to the traversal list.
Determine Move Direction:
- Direction = 1 (down-left):
  - If row == rows - 1 (bottom boundary), move one step right (col += 1) and change direction to up-right (dir = -1).
  - If col == 0 (left boundary), move one step down (row += 1) and change direction to up-right (dir = -1).
  - Otherwise, move diagonally down-left (row += 1; col -= 1).
- Direction = -1 (up-right):
  - If col == cols - 1 (right boundary), move one step down (row += 1) and change direction to down-left (dir = 1).
  - If row == 0 (top boundary), move one step right (col += 1) and change direction to down-left (dir = 1).
  - Otherwise, move diagonally up-right (row -= 1; col += 1).

This approach ensures that the traversal covers all cells in a zigzag manner while respecting the matrix boundaries.

int row = 0, col = 0, dir = 1;
for (int i = 0; i < rows * cols; i++)
{
    traversal.Add(matrix[row, col]);  // Append current cell value to traversal list

    // Determine next position based on current direction
    if (dir == 1)  // Moving down-left
    {
        if (row == rows - 1)  // Hit bottom boundary
        {
            col += 1;
            dir = -1;  // Switch direction to up-right
        }
        else if (col == 0)  // Hit left boundary
        {
            row += 1;
            dir = -1;  // Switch direction to up-right
        }
        else
        {
            row += 1;
            col -= 1;  // Continue down-left
        }
    }
    else  // Moving up-right
    {
        if (col == cols - 1)  // Hit right boundary
        {
            row += 1;
            dir = 1;  // Switch direction to down-left
        }
        else if (row == 0)  // Hit top boundary
        {
            col += 1;
            dir = 1;  // Switch direction to down-left
        }
        else
        {
            row -= 1;
            col += 1;  // Continue up-right
        }
    }
}

int row = 0, col = 0, dir = 1;
for (int i = 0; i < rows * cols; i++)
{
    traversal.Add(matrix[row, col]);  // Append current cell value to traversal list

    // Determine next position based on current direction
    if (dir == 1)  // Moving down-left
    {
        if (row == rows - 1)  // Hit bottom boundary
        {
            col += 1;
            dir = -1;  // Switch direction to up-right
        }
        else if (col == 0)  // Hit left boundary
        {
            row += 1;
            dir = -1;  // Switch direction to up-right
        }
        else
        {
            row += 1;
            col -= 1;  // Continue down-left
        }
    }
    else  // Moving up-right
    {
        if (col == cols - 1)  // Hit right boundary
        {
            row += 1;
            dir = 1;  // Switch direction to down-left
        }
        else if (row == 0)  // Hit top boundary
        {
            col += 1;
            dir = 1;  // Switch direction to down-left
        }
        else
        {
            row -= 1;
            col += 1;  // Continue up-right
        }
    }
}

This detailed explanation should help in understanding how each movement decision contributes to the zigzag traversal pattern across the matrix.

Introduction

Task Statement

Step Overview

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Understanding Matrix Dimensions

Traversing the Matrix Diagonally

Identifying Perfect Squares

Example Usage

Conclusion