710. Random Pick with Blacklist

Given a blacklist B containing unique integers from [0, N), write a function to return a uniform random integer from [0, N) which is NOT in B.

Optimize it such that it minimizes the call to system’s Math.random().

Note:

1. 1 <= N <= 1000000000
2. 0 <= B.length < min(100000, N)
3. [0, N) does NOT include N. See interval notation.

Example 1:

Input: 
["Solution","pick","pick","pick"]
[[1,[]],[],[],[]]
Output: [null,0,0,0]

Example 2:

Input: 
["Solution","pick","pick","pick"]
[[2,[]],[],[],[]]
Output: [null,1,1,1]

Example 3:

Input: 
["Solution","pick","pick","pick"]
[[3,[1]],[],[],[]]
Output: [null,0,0,2]

Example 4:

Input: 
["Solution","pick","pick","pick"]
[[4,[2]],[],[],[]]
Output: [null,1,3,1]

Explanation of Input Syntax:

The input is two lists: the subroutines called and their arguments. Solution's constructor has two arguments, N and the blacklist B. pickhas no arguments. Arguments are always wrapped with a list, even if there aren't any.

 

AC code:

class Solution {
private:
    int N;
    vector<int> blacklist;
    unordered_set<int> blackSet;
    random_device rd;
    mt19937 gen;
    uniform_int_distribution<> dist;

    int findMap(int y) {
        int l = 0, r = N - 1;
        // need to find lower_bound
        // 二分真是一件Tricky的事情
        while (l < r) {
            int mid = (l + r) / 2;
            int smaller = upper_bound(blacklist.begin(), blacklist.end(), mid) - blacklist.begin();
            if (mid - smaller < y)
                l = mid + 1;
            else
                r = mid;
        }

        return l;
    }

public:
    Solution(int N, vector<int> blacklist): gen(rd()), dist(0, N - blacklist.size() - 1) {
        this->N = N;
        this->blacklist = blacklist;
        sort(this->blacklist.begin(), this->blacklist.end());
        for (int b: blacklist)
            blackSet.insert(b);
    }

    int pick() {
        int r = dist(gen);
        int m = findMap(r);
        // cout << r << ' ' << m << endl;
        // 事实证明，保证lower_bound之后，找到的数必然不是黑名单中的数
        /* while (blackSet.find(m) != blackSet.end())
            m++; */
        return m;
    }
};


/**
 * Your Solution object will be instantiated and called as such:
 * Solution obj = new Solution(N, blacklist);
 * int param_1 = obj.pick();
 */

　　

I can't understand this question's intention.