Rotating the Box

Problem Description

You are given an m x n matrix of characters boxGrid representing a side-view of a box. Each cell of the box is one of the following:

• A stone '#'
• A stationary obstacle '*'
• Empty '.'

The box is rotated 90 degrees clockwise, causing some of the stones to fall due to gravity. Each stone falls down until it lands on an obstacle, another stone, or the bottom of the box. Gravity does not affect the obstacles' positions, and the inertia from the box's rotation does not affect the stones' horizontal positions.

It is guaranteed that each stone in boxGrid rests on an obstacle, another stone, or the bottom of the box.

Return an n x m matrix representing the box after the rotation described above.

Key Insights

• Stones (#) will fall to the lowest available position in their column after rotation.
• Obstacles (*) block the falling stones and maintain their position.
• The rotation transforms the matrix, switching rows with columns, which requires careful manipulation of indices.

Space and Time Complexity

Time Complexity: O(m * n)
Space Complexity: O(n)

Solution

To solve this problem, we can follow these steps:

1. Create a new matrix of dimensions n x m for the rotated box.
2. Iterate through each column of the original matrix and determine where each stone should fall within that column in the new matrix.
3. For each stone, check how far down it can fall until it hits an obstacle or the bottom of the new column.
4. Fill in the new matrix with stones and obstacles accordingly.

The algorithm primarily uses a nested loop to traverse the original matrix and build the new one, ensuring we account for the positions of stones and obstacles correctly.

Code Solutions