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.
'''

# used for random number generation
import random

class Solution:
    def __init__(self, w: List[int]):
        self.w = w
		# 1. calculate relative frequency
        denom = sum(self.w)
        for i in range(len(self.w)):
            self.w[i] = self.w[i] / denom
        # 2. put relative frequencies on the number line between 0 and 1
		# Note self.w[-1] = 1
        for i in range(1,len(self.w)):
            self.w[i] += self.w[i-1]
        
    def pickIndex(self) -> int:

	# this is where we pick the index
        N = random.uniform(0,1)
      
        flag = 1
        index = -1
        
	# test each region of the numberline to see if N falls in it, if it 
	# does not then go to the next index and check if N falls in it
	# this is gaurenteed to break because of previous normalization
        while flag:
            index +=1 
            if N <= self.w[index]:
                flag = 0

        return index