# Random Flip Matrix Problem

## Description

LeetCode Problem 519.

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:

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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.

## Sample C++ Code

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class Solution {
public:
int mx = 0;
int row = 0;
int col = 0;
unordered_set<int> v;
Solution(int n_rows, int n_cols) {
mx = n_rows * n_cols;
row = n_rows;
col = n_cols;
}
vector<int> flip() {
if(v.size() == mx) return {};
int r = rand() % mx;
while(v.count(r)) {
r = (++r) %mx;
}
v.insert(r);
return {r / col, r % col };
}
void reset() {
v = {};
}
};
/**
* Your Solution object will be instantiated and called as such:
* Solution* obj = new Solution(m, n);
* vector<int> param_1 = obj->flip();
* obj->reset();
*/