leetcode_528

Given an array w of positive integers, where w[i] describes the weight of index i(0-indexed), write a function pickIndex which randomly picks an index in proportion to its weight.

For example, given an input list of values w = [2, 8], when we pick up a number out of it, the chance is that 8 times out of 10 we should pick the number 1 as the answer since it's the second element of the array (w[1] = 8).

Example 1:

Input ["Solution","pickIndex"] [[[1]],[]] Output [null,0]

Explanation Solution solution = new Solution([1]); solution.pickIndex(); // return 0. Since there is only one single element on the array the only option is to return the first element. Example 2:

Input ["Solution","pickIndex","pickIndex","pickIndex","pickIndex","pickIndex"] [[[1,3]],[],[],[],[],[]] Output [null,1,1,1,1,0]

Explanation Solution solution = new Solution([1, 3]); solution.pickIndex(); // return 1. It's returning the second element (index = 1) that has probability of 3/4. solution.pickIndex(); // return 1 solution.pickIndex(); // return 1 solution.pickIndex(); // return 1 solution.pickIndex(); // return 0. It's returning the first element (index = 0) that has probability of 1/4.

Since this is a randomization problem, multiple answers are allowed so the following outputs can be considered correct : [null,1,1,1,1,0] [null,1,1,1,1,1] [null,1,1,1,0,0] [null,1,1,1,0,1] [null,1,0,1,0,0] ...... and so on.

Constraints:

1 <= w.length <= 10000 1 <= w[i] <= 10^5 pickIndex will be called at most 10000 times.

Solutions

1. prefix weight sum

class Solution {
public:
    vector<int> psum;
    mt19937 gen{random_device{}()};
    uniform_int_distribution<int> uni;

    Solution(vector<int>& w) {
        int sum = 0;
        for (auto n : w)
            psum.push_back(sum += n);
        uni = uniform_int_distribution<>(0, sum - 1);
    }

    int pickIndex() {
        int rn = uni(gen);
        return upper_bound(psum.begin(), psum.end(), rn) - psum.begin();
    }
};

/**
 * Your Solution object will be instantiated and called as such:
 * Solution* obj = new Solution(w);
 * int param_1 = obj->pickIndex();
 */