<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.b = sorted(blacklist)
        self.n = n
        self.m = n - len(self.b)
        self.exist = defaultdict(bool)
        mappingKey = [x for x in self.b if x < self.m]
        for i in mappingKey:
            self.exist[i] = True
        mappingValue = [i for i in range(self.m, n) if not self.isT(i)]
        self.mapping = dict(zip(mappingKey, mappingValue))
        

    def isT(self, target):
        left, right = 0, len(self.b) - 1

        while left <= right:
            mid = left + (right - left) // 2

            if self.b[mid] == target:
                return True
            elif self.b[mid] < target:
                left = mid + 1
            else:
                right = mid - 1
        return False

        

    def pick(self) -> int:
        a = random.randint(0, self.m - 1)
        if self.exist[a]:
            return self.mapping[a]
        return a


# Your Solution object will be instantiated and called as such:
# obj = Solution(n, blacklist)
# param_1 = obj.pick()
28700