885 Spiral Matrix III

[mah-shamim]

Topics: Array, Matrix, Simulation

You start at the cell (rStart, cStart) of an rows x cols grid facing east. The northwest corner is at the first row and column in the grid, and the southeast corner is at the last row and column.

You will walk in a clockwise spiral shape to visit every position in this grid. Whenever you move outside the grid's boundary, we continue our walk outside the grid (but may return to the grid boundary later.). Eventually, we reach all rows * cols spaces of the grid.

Return an array of coordinates representing the positions of the grid in the order you visited them.

Example 1:

• Input: rows = 1, cols = 4, rStart = 0, cStart = 0
• Output: [[0,0],[0,1],[0,2],[0,3]]

Example 2:

• Input: rows = 5, cols = 6, rStart = 1, cStart = 4
• Output: [[1,4],[1,5],[2,5],[2,4],[2,3],[1,3],[0,3],[0,4],[0,5],[3,5],[3,4],[3,3],[3,2],[2,2],[1,2],[0,2],[4,5],[4,4],[4,3],[4,2],[4,1],[3,1],[2,1],[1,1],[0,1],[4,0],[3,0],[2,0],[1,0],[0,0]]

Constraints:

• 1 <= rows, cols <= 100
• 0 <= rStart < rows
• 0 <= cStart < cols

[mah-shamim]

To solve this problem, we can follow these steps:

1. Direction Array: Use a direction array to facilitate movement in the right order (east → south → west → north). Each direction will have a corresponding change in the row and column indices.
2. Steps Management: You need to control how many steps to take in each direction. Initially, you move 1 step east, then 1 step south, 2 steps west, 2 steps north, and so on.
3. Boundary Check: Ensure that after every move, you check whether the new position is within the grid boundaries. If it is, add it to the result array.
4. Stopping Condition: Stop the loop once you have visited all rows * cols positions.

Let's implement this solution in PHP: 885. Spiral Matrix III

<?php
function spiralMatrixIII($rows, $cols, $rStart, $cStart) {
    // Initialize directions: right, down, left, up
    $directions = [[0,1], [1,0], [0,-1], [-1,0]];
    $result = [];
    
    // Initial position
    $r = $rStart;
    $c = $cStart;
    
    // Initial steps for each direction
    $stepCount = 1;
    $totalSteps = 0;

    // The number of positions to cover
    $totalPositions = $rows * $cols;
    
    // Add the starting position
    $result[] = [$r, $c];
    $totalSteps++;

    while ($totalSteps < $totalPositions) {
        for ($i = 0; $i < 4; $i++) {
            // Moving direction: east -> south -> west -> north
            for ($j = 0; $j < $stepCount; $j++) {
                $r += $directions[$i][0];
                $c += $directions[$i][1];
                
                // Check if within the bounds of the grid
                if ($r >= 0 && $r < $rows && $c >= 0 && $c < $cols) {
                    $result[] = [$r, $c];
                    $totalSteps++;
                    if ($totalSteps == $totalPositions) {
                        return $result;
                    }
                }
            }

            // Increase steps after every two directions (right and down; left and up)
            if ($i == 1 || $i == 3) {
                $stepCount++;
            }
        }
    }
    
    return $result;
}

// Example Usage:
print_r(spiralMatrixIII(1, 4, 0, 0)); // [[0,0],[0,1],[0,2],[0,3]]
print_r(spiralMatrixIII(5, 6, 1, 4)); // [[1,4],[1,5],[2,5],[2,4], ...]

?>

Explanation:

1. Directions: The directions array holds the change in row and column for moving east, south, west, and north.
2. Movement: We start at (rStart, cStart) and move according to the directions in the spiral pattern.
3. Boundary Checking: Only add the position to result if it is within the grid.
4. Steps Control: stepCount manages how many steps are taken in the current direction before turning. It increases after two turns.
5. Termination: The loop continues until all positions in the grid have been visited.

This approach ensures that we visit every cell in the grid in the required spiral order.

[basharul-siddike]

Thanks for solving the problem of "Spiral Matrix III"

[mah-shamim]

Thanks