Leetcode 528. Random Pick with Weight LowerBound

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本文介绍了一种基于数组权重的随机采样算法实现，通过累积权重和二分查找的方法，实现了在权重比例下随机选取数组索引的功能。讨论了算法的设计思路及边界条件的处理，提供了Python代码示例。

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 <= w.length <= 10000
1 <= w[i] <= 10^5
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.

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两个问题：

1. 很容易想到二分，但是不知道有没有O(1)的解法，去Discussion看了别人都二分，才确定

2. 二分时候想了半天，才明确边界是lower_bound，第一个插入位置，思路得加速啊

import random

class Solution:

    def __init__(self, w):
        self.wl = len(w)
        cur = 0
        self.accu = [0 for i in range(self.wl)]
        for idx, v in enumerate(w):
            cur += v
            self.accu[idx] = cur
        
    def pickIndex(self):
        l,r = 0, self.wl-1
        rdint = random.randint(1, self.accu[-1])
        while (l <= r):
            mid = l + ((r-l)>>1)
            if (rdint > self.accu[mid]):
                l = mid+1
            else:
                r = mid-1
        return l