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花花酱 LeetCode 880. Random Pick with Weight

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]

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 wpickIndex has no arguments. Arguments are always wrapped with a list, even if there aren’t any.

Solution: Binary Search

  1. Convert PDF to CDF
  2. Uniformly sample a value s in [1, sum(weights)].
  3. Use binary search to find first index such that PDF[index] >= s.

Time complexity: Init O(n), query O(logn)

Space complexity: O(n)

C++

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