# 528. Random Pick with Weight 按权重随机选择

## # 题目描述：

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. 1 <= w.length <= 10000
2. 1 <= w[i] <= 10^5
3. 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.

## # 解题方法

preSum:  	1,	3,	6,	10

class Solution:

def __init__(self, w):
"""
:type w: List[int]
"""
self.preSum = [0] * len(w)
self.preSum[0] = w[0]
for i in range(1, len(w)):
self.preSum[i] = self.preSum[i - 1] + w[i]

def pickIndex(self):
"""
:rtype: int
"""
total = self.preSum[-1]
rand = random.randint(0, total - 1)
left, right = 0, len(self.preSum) - 1
while left + 1 < right:
mid = (left + right) // 2
if rand >= self.preSum[mid]:
left = mid
else:
right = mid
if rand < self.preSum[left]:
return left
return right

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

## # 日期

2018 年 8 月 18 日 —— 天在下雨