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## Problem

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:

• 1 <= m, n <= 10^4
• There will be at least one free cell for each call to flip.
• At most 1000 calls will be made to flip and reset.

## Code

384

class Solution {
Map<Integer, Integer> map;
int rows;
int cols;
int total;
Random random;

public Solution(int n_rows, int n_cols) {
map = new HashMap<>();
random = new Random();
rows = n_rows;
cols = n_cols;
total = rows * cols;
}

public int[] flip() {
int rand = random.nextInt(total--);

int index = rand;
if(map.containsKey(rand)) {
index = map.get(rand);
}

map.put(rand, total);
if(map.containsKey(total)) {
map.put(rand, map.get(total));
}

return new int[]{index / cols, index % cols};
}

public void reset() {
map.clear();
total = rows * cols;
}
}