【LeetCode】528. Random Pick with Weight 解题报告（Python）

标签（空格分隔）： LeetCode

作者：负雪明烛
id： fuxuemingzhu
个人博客： http://fuxuemingzhu.me/

题目地址：https://leetcode.com/problems/random-pick-with-weight/description/

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 <= 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.

题目大意

这个题目不太好理解，是要求按照权重挑选索引。比如[1,99]中，有1%的概率挑选到索引0，有99%的概率挑选到索引1.

解题方法

这个题很巧妙，我是想不出来的。做法是把概率分布函数转化为累计概率分布函数。然后通过随机数，进行二分查找。

比如，输入是[1,2,3,4]，那么概率分布是[1/10, 2/10, 3/10, 4/10, 5/10]，累积概率分布是[1/10, 3/10, 6/10, 10/10].总和是10。如果我们产生一个随机数，在0~9之中，然后判断这个数字在哪个区间中就能得到对应的索引。

各区间的含义是：

[0], [1, 2], [3, 4, 5], [6, 7, 8, 9]

如果随机的数字在哪个区间当中，那么就返回这个区间的索引即可。

这个二分查找也可以好好学习一下。

代码如下：

class Solution:

    def __init__(self, w):
        """
        :type w: List[int]
        """
        self.preSum = [0] * len(w)
        self.preSum[0] = w[0]
        for i in range(1, len(w)):
            self.preSum[i] = self.preSum[i - 1] + w[i]

    def pickIndex(self):
        """
        :rtype: int
        """
        total = self.preSum[-1]
        rand = random.randint(0, total - 1)
        left, right = 0, len(self.preSum) - 1
        while left + 1 < right:
            mid = (left + right) // 2
            if rand >= self.preSum[mid]:
                left = mid
            else:
                right = mid
        if rand < self.preSum[left]:
            return left
        return right


# Your Solution object will be instantiated and called as such:
# obj = Solution(w)
# param_1 = obj.pickIndex()

日期

2018 年 8 月 18 日 ———— 天在下雨