## Algorithm

Problem Name: 519. Random Flip Matrix

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 <= 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`.

## Code Examples

### #1 Code Example with Javascript Programming

```Code - Javascript Programming```

``````
const Solution = function(n_rows, n_cols) {
this.r = n_rows
this.c = n_cols
this.total = n_rows * n_cols
this.m = new Map()
}

Solution.prototype.flip = function() {
const r = (Math.random() * this.total--) >> 0
const i = this.m.get(r) || r
this.m.set(r, this.m.get(this.total) || this.total)
return [(i / this.c) >> 0, i % this.c]
}

Solution.prototype.reset = function() {
this.m.clear()
this.total = this.c * this.r
}
``````
Copy The Code &

Input

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

Output

cmd
[null, [1, 0], [2, 0], [0, 0], null, [2, 0]]

### #2 Code Example with Python Programming

```Code - Python Programming```

``````
class Solution:

def __init__(self, n_rows, n_cols):
self.rows, self.cols, self.used = n_rows, n_cols, set()

def flip(self):
while True:
r, c = random.randint(1, self.rows), random.randint(1, self.cols)
if (r, c) not in self.used:
return [r - 1, c - 1]

def reset(self):
self.used = set()
``````
Copy The Code &

Input

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

Output

cmd
[null, [1, 0], [2, 0], [0, 0], null, [2, 0]]