528. Random Pick with Weight

Medium (Trung bình) Python 🔗 Xem trên LeetCode

📋 Đề Bài

You are given a 0-indexed array of positive integers w where w[i] describes the weight of the ith index.

You need to implement the function pickIndex(), which randomly picks an index in the range [0, w.length - 1] (inclusive) and returns it. The probability of picking an index i is w[i] / sum(w).

  • For example, if w = [1, 3], the probability of picking index 0 is 1 / (1 + 3) = 0.25 (i.e., 25%), and the probability of picking index 1 is 3 / (1 + 3) = 0.75 (i.e., 75%).

 

Example 1:

Input
["Solution","pickIndex"]
[[[1]],[]]
Output
[null,0]

Explanation
Solution solution = new Solution([1]);
solution.pickIndex(); // return 0. The only option is to return 0 since there is only one element in w.

Example 2:

Input
["Solution","pickIndex","pickIndex","pickIndex","pickIndex","pickIndex"]
[[[1,3]],[],[],[],[],[]]
Output
[null,1,1,1,1,0]

Explanation
Solution solution = new Solution([1, 3]);
solution.pickIndex(); // return 1. It is returning the second element (index = 1) that has a probability of 3/4.
solution.pickIndex(); // return 1
solution.pickIndex(); // return 1
solution.pickIndex(); // return 1
solution.pickIndex(); // return 0. It is returning the first element (index = 0) that has a probability of 1/4.

Since this is a randomization problem, multiple answers are allowed.
All of the following outputs can be considered correct:
[null,1,1,1,1,0]
[null,1,1,1,1,1]
[null,1,1,1,0,0]
[null,1,1,1,0,1]
[null,1,0,1,0,0]
......
and so on.

 

Constraints:

  • 1 <= w.length <= 104
  • 1 <= w[i] <= 105
  • pickIndex will be called at most 104 times.

🧠 Thuật Toán & Kỹ Thuật

Binary Search (Tìm kiếm nhị phân)
⏱️ Thời gian O(log n)
💾 Không gian O(n)

💻 Lời Giải

Python 0528-random-pick-with-weight.py 
class Solution:

    def __init__(self, w: List[int]):
        t = sum(w)
        w = list(map(lambda x: x/t, w))
        n = len(w)
        for i in range(1, n):
            w[i] += w[i - 1]
        self.w = w

    def pickIndex(self) -> int:
        rd = random.random()
        return bisect_left(self.w, rd)


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