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

<p>Optimize your algorithm such that it minimizes the number of calls to the <strong>built-in</strong> random function of your language.</p>

<p>Implement the <code>Solution</code> class:</p>

<ul>
	<li><code>Solution(int n, int[] blacklist)</code> Initializes the object with the integer <code>n</code> and the blacklisted integers <code>blacklist</code>.</li>
	<li><code>int pick()</code> Returns a random integer in the range <code>[0, n - 1]</code> and not in <code>blacklist</code>.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input</strong>
[&quot;Solution&quot;, &quot;pick&quot;, &quot;pick&quot;, &quot;pick&quot;, &quot;pick&quot;, &quot;pick&quot;, &quot;pick&quot;, &quot;pick&quot;]
[[7, [2, 3, 5]], [], [], [], [], [], [], []]
<strong>Output</strong>
[null, 0, 4, 1, 6, 1, 0, 4]

<strong>Explanation</strong>
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
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 10<sup>9</sup></code></li>
	<li><code>0 &lt;= blacklist.length &lt;= min(10<sup>5</sup>, n - 1)</code></li>
	<li><code>0 &lt;= blacklist[i] &lt; n</code></li>
	<li>All the values of <code>blacklist</code> are <strong>unique</strong>.</li>
	<li>At most <code>2 * 10<sup>4</sup></code> calls will be made to <code>pick</code>.</li>
</ul>

class Solution:

    def __init__(self, N: int, blacklist: List[int]):
        self.N = N
        self.blacklist = blacklist
        self.whitelist = {}

        tempWL = set()
        for n in range(N-len(blacklist), N):
            tempWL.add(n)

        for n in blacklist:
            if n in tempWL:
                tempWL.remove(n)

        setIterator = iter(tempWL)

        for n in blacklist:
            if n<N-len(blacklist):
                self.whitelist[n] = next(setIterator)

        

    def pick(self) -> int:
        rand = random.randint(0, self.N-len(self.blacklist)-1)

        return self.whitelist[rand] if rand in self.whitelist else rand
        


# Your Solution object will be instantiated and called as such:
# obj = Solution(n, blacklist)
# param_1 = obj.pick()
29100