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 most10000
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.
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兩個問題:
1. 很容易想到二分,但是不知道有沒有O(1)的解法,去Discussion看了別人都二分,才確定
2. 二分時候想了半天,才明確邊界是lower_bound,第一個插入位置,思路得加速啊
import random
class Solution:
def __init__(self, w):
self.wl = len(w)
cur = 0
self.accu = [0 for i in range(self.wl)]
for idx, v in enumerate(w):
cur += v
self.accu[idx] = cur
def pickIndex(self):
l,r = 0, self.wl-1
rdint = random.randint(1, self.accu[-1])
while (l <= r):
mid = l + ((r-l)>>1)
if (rdint > self.accu[mid]):
l = mid+1
else:
r = mid-1
return l