LeetCode 528. Random Pick with Weight

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Words count in article: 238 | Reading time ≈ 1

题目

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:

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

Example 2:

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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.

思路

Binary search.
Randomly pick an index proportional to its weight.

代码

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class Solution(object):

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

    def pickIndex(self):
        """
        :rtype: int
        """
        l, r, seed = 0, len(self.nums), random.randrange(0, self.nums[-1])
        while l < r:
            m = (l+r)/2
            if self.nums[m] <= seed:
                l = m+1
            else:
                r = m
        return l


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