LeetCode #528 - Random Pick with Weight

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本文介绍了一种基于权重比例的随机抽取算法实现。通过累计前缀和的方式，将权重转换为概率分布，再利用二分搜索快速定位到指定权重的元素。此方法适用于长度不超过10000的数组，每个元素的权重范围在1到10^5之间，且能高效处理最多10000次的随机抽取请求。

题目描述：

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]

Example 2:

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.

对w数组累积前缀和，然后随机生成一个数，利用二分搜索确定下标。

class Solution {
public:
    Solution(vector<int> w) {
        sum=vector<int>(w.size(),0);
        sum[0]=w[0];
        for(int i=0;i<w.size();i++) sum[i]=sum[i-1]+w[i];
    }
    
    int pickIndex() {
        int x=rand()%sum.back();
        int pos=upper_bound(sum.begin(),sum.end(),x)-sum.begin();
        return pos;
    }

private:
    vector<int> sum;
};

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