new_contents: # Time:  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
  
  
  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()
  
subject: Create random-pick-with-weight.py