LeetCode 528. Random Pick with Weight
Description:
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:
input:
[“Solution”,”pickIndex”] [[[1]],[]]
output:
[null,0,1,1,1,0]
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.
Solution:
class Solution:
pickLst = None
def __init__(self, w):
"""
:type w: List[int]
"""
self.pickLst = [0.0]
sum = 0
for ele in w:
sum += ele
for ele in w:
self.pickLst.append(self.pickLst[1] + ele / sum)
def pickIndex(self):
"""
:rtype: int
"""
rnd = random.random()
left = 0
right = len(self.pickLst)  1
result = 1
while(right > left):
mid = math.ceil((left + right) / 2)
if self.pickLst[mid  1] <= rnd < self.pickLst[mid]:
result = mid  1
break
if rnd < self.pickLst[mid  1]:
right = mid
elif rnd > self.pickLst[mid]:
left = mid
if result == 1:
raise RuntimeError('cannot find')
return result
# Your Solution object will be instantiated and called as such:
# obj = Solution(w)
# param_1 = obj.pickIndex()
This is simulation of multinomial distribution. We can use bins and random floating point numbers to achieve simulation.