random-pick-with-weight.py

# Time:  ctor: O(n)
#        pickIndex: O(logn)
# Space: O(n)

# 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.
    
import random
import bisect


class Solution(object):

    def __init__(self, w):
        """
        :type w: List[int]
        """
        self.__prefix_sum = list(w)
        for i in xrange(1, len(w)):
            self.__prefix_sum[i] += self.__prefix_sum[i-1]

    def pickIndex(self):
        """
        :rtype: int
        """
        target = random.randint(0, self.__prefix_sum[-1]-1)
        return bisect.bisect_right(self.__prefix_sum, target)


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