912. Random Pick with Weight

• Difficulty: Medium

• Topics: Binary Search, Random

• Similar Questions:

  • Random Pick Index

  • Random Pick with Blacklist

  • Random Point in Non-overlapping Rectangles

Problem:

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

Note:

1. 1 <= w.length <= 10000
2. 1 <= w[i] <= 10^5
3. pickIndex will be called at most 10000 times.

Example 1:

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

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

Explanation of Input Syntax:

The input is two lists: the subroutines called and their arguments. Solution's constructor has one argument, the array w. pickIndex has no arguments. Arguments are always wrapped with a list, even if there aren't any.

Solutions:

class Solution {
public:
    Solution(vector<int>& w) {
        sum = 0;
        for (int i = 0; i < w.size(); ++i) {
            sum += w[i];
            prefixSums[sum] = i;
        }
    }

    int pickIndex() {
        int r = (rand() % sum) + 1;
        return prefixSums.lower_bound(r)->second;
    }
private:
    map<int, int> prefixSums;
    int sum;

};

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