Minesweeper Game I

Minesweeper is a classic single-player game where players must determine which unknown tiles in a grid are mines based on given information and mark the mines' positions.

In this game challenge, the problem provides you with three parameters: width, height, and mineCount. You are required to implement an algorithm that generates the initial map of a Minesweeper game, which is a two-dimensional array with width rows and height columns, randomly distributed with mineCount mines.

Requirement: Your algorithm must be uniformly random, meaning each tile must have an equal probability of being a mine ($P(x) = \frac{mineCount}{width \times height}$).

Try to implement this algorithm, and after clicking the "Submit" button, you can generate a Minesweeper game map with your algorithm and enjoy playing!

Advanced

First question: What is the time complexity and space complexity of your random algorithm? Can you manage to keep the space complexity of the algorithm at $O(mineCount)$?

Second question: How can you prove that your random algorithm is uniformly random? How can you prove that each tile has an equal probability of being selected?

Explanation