Day-5_Random_pick_with_weight.py

'''
	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.




'''
class Solution:
    def __init__(self, w: List[int]):
        self.prefix_sum = []
        prefix_sum = 0
        for weight in w:
            prefix_sum += weight
            self.prefix_sum.append(prefix_sum)
        self.total_sum = prefix_sum

    def pickIndex(self) -> int:
        random_num = self.total_sum * random.random()
        low, high = 0, len(self.prefix_sum)
        while low < high:
            mid = low + (high - low) // 2
            if random_num > self.prefix_sum[mid]:
                low = mid + 1
            else:
                high = mid
        return low


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