710. Random Pick with Blacklist
Hard
767
103

You are given an integer `n` and an array of unique integers `blacklist`. Design an algorithm to pick a random integer in the range `[0, n - 1]` that is not in `blacklist`. Any integer that is in the mentioned range and not in `blacklist` should be equally likely to be returned.

Optimize your algorithm such that it minimizes the number of calls to the built-in random function of your language.

Implement the `Solution` class:

• `Solution(int n, int[] blacklist)` Initializes the object with the integer `n` and the blacklisted integers `blacklist`.
• `int pick()` Returns a random integer in the range `[0, n - 1]` and not in `blacklist`.

Example 1:

```Input
["Solution", "pick", "pick", "pick", "pick", "pick", "pick", "pick"]
[[7, [2, 3, 5]], [], [], [], [], [], [], []]
Output
[null, 0, 4, 1, 6, 1, 0, 4]

Explanation
Solution solution = new Solution(7, [2, 3, 5]);
solution.pick(); // return 0, any integer from [0,1,4,6] should be ok. Note that for every call of pick,
// 0, 1, 4, and 6 must be equally likely to be returned (i.e., with probability 1/4).
solution.pick(); // return 4
solution.pick(); // return 1
solution.pick(); // return 6
solution.pick(); // return 1
solution.pick(); // return 0
solution.pick(); // return 4
```

Constraints:

• `1 <= n <= 109`
• `0 <= blacklist.length <= min(105, n - 1)`
• `0 <= blacklist[i] < n`
• All the values of `blacklist` are unique.
• At most `2 * 104` calls will be made to `pick`.
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