519 - Random Flip Matrix.

Medium

There is an m x n binary grid matrix with all the values set 0 initially. Design an algorithm to randomly pick an index (i, j) where matrix[i][j] == 0 and flips it to 1. All the indices (i, j) where matrix[i][j] == 0 should be equally likely to be returned.

Optimize your algorithm to minimize the number of calls made to the built-in random function of your language and optimize the time and space complexity.

Implement the Solution class:

• Solution(int m, int n) Initializes the object with the size of the binary matrix m and n.

• int[] flip() Returns a random index [i, j] of the matrix where matrix[i][j] == 0 and flips it to 1.

• void reset() Resets all the values of the matrix to be 0.

Example 1:

Input "Solution", "flip", "flip", "flip", "reset", "flip" [3, 1, [], [], [], [], []]

Output: [null, 1, 0, 2, 0, 0, 0, null, 2, 0]

Explanation:

Solution solution = new Solution(3, 1);
solution.flip(); // return [1, 0], [0,0], [1,0], and [2,0] should be equally likely to be returned.
solution.flip(); // return [2, 0], Since [1,0] was returned, [2,0] and [0,0]
solution.flip(); // return [0, 0], Based on the previously returned indices, only [0,0] can be returned.
solution.reset(); // All the values are reset to 0 and can be returned.
solution.flip(); // return [2, 0], [0,0], [1,0], and [2,0] should be equally likely to be returned.

Constraints:

• <code>1 <= m, n <= 10⁴</code>

• There will be at least one free cell for each call to flip.

• At most 1000 calls will be made to flip and reset.