Traversing 2D Arrays in PHP With Conditional Moves

Introduction

Hello, and welcome back to our coding lesson series. In this unit, we have a fascinating problem at hand that uses the concept of 2D arrays or grids in PHP . What's interesting about this problem is that it involves not only the simple traversal of the grid but also making this traversal in a unique manner. Initially, the concept might seem a bit tricky, but as we dissect the task and take it step by step, you're sure to enjoy how it unfolds. Are you ready to embark on this adventure? Let's dive right in!

Task Statement

3 \times 3

Solution Building: Step 1

The first thing we need to do is determine the dimensions of our grid, which is relatively easy in PHP with the count() function. We can also establish the directions that our traversal can take. In the context of matrices, when we say we are moving "up," we are moving one step towards the first row (decreasing the row index). Similarly, moving "down" corresponds to moving one step towards the last row (increasing the row index), and moving left or right relates to decrementing or incrementing the column index, respectively. PHP <?php function pathTraverse($grid, $startRow, $startCol) {$rows = count($grid); $cols = count($grid[0]); $directions = [[-1, 0], // Up [1, 0], // Down [0, -1], // Left [0, 1] // Right]; In the $directions array, each pair represents a direction in terms of a pair (rowOffset, colOffset) . So, if we are at a cell (r, c), moving up corresponds to going to the cell (r-1, c), moving down corresponds to (r+1, c), moving left corresponds to (r, c-1), and moving right corresponds to (r, c+1) .

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Solution Building: Step 3

Let's initiate the grid traversal process in our function. We first set up an infinite loop that will only stop when we break it based on a condition. Inside the infinite loop, for each iteration, we'll have the function try to select the next cell with the maximum value among the adjacent cells. If we find such a cell, we'll capture its value, and it will be our next cell.

PHP

<?php

function pathTraverse($grid, $startRow, $startCol) {
    $rows = count($grid);
    $cols = count($grid[0]);

    // Check the validity of the input
    if ($startRow < 0 || $startRow >= $rows || $startCol < 0 || $startCol >= $cols) {
        echo "Invalid input\n";
        return [];
    }
    
    // Define all four possible directions of movement
    $directions = [
        [1, 0], [-1, 0], [0, -1], [0, 1]
    ];

    // Start with the value at the starting cell
    $visited = [];
    $visited[] = $grid[$startRow][$startCol];

    while (true) {
        // Initialize the current maximum as negative one 
        $currMax = -1;
        $nextRow = -1;
        $nextCol = -1;

        // Loop over each adjacent cell in all the directions
        foreach ($directions as $dir) {
            // Calculate the new cell's row and column indices
            $newRow = $startRow + $dir[0];
            $newCol = $startCol + $dir[1];

            // If the new cell is out of the grid boundary, ignore it
            if ($newRow < 0 || $newRow >= $rows || $newCol < 0 || $newCol >= $cols) {
                continue;
            }

            // If the new cell's value is greater than the current maximum
            if ($grid[$newRow][$newCol] > $currMax) {
                // Save it as the next cell to visit
                $nextRow = $newRow;
                $nextCol = $newCol;
                $currMax = $grid[$newRow][$newCol];
            }
        }

        // If we don't have any valid cell to visit, break from the loop  
        if ($currMax <= $grid[$startRow][$startCol]) {
            break;
        }

        // Otherwise, go to the next cell
        $startRow = $nextRow;
        $startCol = $nextCol;

        // Append the cell's value to the result list
        $visited[] = $currMax;
    }

    // Return the list of visited cells' values    
    return $visited;
}

// Example usage
$grid = [
    [1, 2, 3],
    [4, 5, 6],
    [7, 8, 9]
];
$res = pathTraverse($grid, 1, 1);
foreach ($res as $val) {
    echo $val . ' ';
}
echo PHP_EOL;

Introduction

Task Statement

Solution Building: Step 1

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Solution Building: Step 2

Solution Building: Step 3

Lesson Summary