Random Pick with Weight

Problem Statement

You are given a 0-indexed array of positive integers w where w[i] describes the weight of the i_th index.

You need to implement the function pickIndex(), which randomly picks an index in the range [0, w.length - 1] (inclusive) and returns it. The probability of picking an index i is w[i] / sum(w).

For example, if w = [1, 3], the probability of picking index 0 is 1 / (1 + 3) = 0.25 (i.e., 25%), and the probability of picking index 1 is 3 / (1 + 3) = 0.75 (i.e., 75%).

Leetcode Link

Example 1:

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

Explanation
Solution solution = new Solution([1]);
solution.pickIndex(); // return 0. The only option is to return 0 since there is only one element in w.

Example 2:

Input
["Solution","pickIndex","pickIndex","pickIndex","pickIndex","pickIndex"]
[[[1,3]],[],[],[],[],[]]
Output
[null,1,1,1,1,0]

Explanation
Solution solution = new Solution([1, 3]);
solution.pickIndex(); // return 1. It is returning the second element (index = 1) that has a probability of 3/4.
solution.pickIndex(); // return 1
solution.pickIndex(); // return 1
solution.pickIndex(); // return 1
solution.pickIndex(); // return 0. It is returning the first element (index = 0) that has a probability of 1/4.

Since this is a randomization problem, multiple answers are allowed.
All of the following outputs can be considered correct:
[null,1,1,1,1,0]
[null,1,1,1,1,1]
[null,1,1,1,0,0]
[null,1,1,1,0,1]
[null,1,0,1,0,0]
......
and so on.

Constraints:

• 1 <= w.length <= 10⁴
• 1 <= w[i] <= 10⁵
• pickIndex will be called at most 10⁴ times.

Code

Python Code

import random
class Solution:

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

    def pickIndex(self):
        """
        :rtype: int
        """
        seed = random.randint(1,self.s)
        l,r = 0, self.n-1
        while l<r:
            mid = (l+r)//2
            if seed <= self.w[mid]:
                r = mid
            else:
                l = mid+1
        return l