# 519. Random Flip Matrix

## 1. Question

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.

## 2. Examples

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.


## 3. Constraints

• 1 <= m, n <= 104
• There will be at least one free cell for each call to flip.
• At most 1000 calls will be made to flip and reset.

## 5. Solutions

class Solution {
int m;
int n;
int total;
Set<Integer> set = new HashSet<>();
Random random = new Random();

public Solution(int m, int n) {
this.m = m;
this.n = n;
this.total = m * n;
reset();
}

public int[] flip() {
int a = random.nextInt(total);
while(set.contains(a)) {
a = random.nextInt(total);
}
return new int[]{a / n, a % n};
}

public void reset() {
set.clear();
}
}

/**
* Your Solution object will be instantiated and called as such:
* Solution obj = new Solution(m, n);
* int[] param_1 = obj.flip();
* obj.reset();
*/