Leetcode #528: Random Pick with Weight
In this guide, we solve Leetcode #528 Random Pick with Weight in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
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.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Array, Math, Binary Search, Prefix Sum, Randomized
Intuition
The problem structure suggests a monotonic decision, which makes binary search a natural fit.
By halving the search space each step, we reach the answer efficiently.
Approach
Search either directly on a sorted array or on the answer space using a check function.
Each check is fast, and the logarithmic search keeps the overall runtime low.
Steps:
- Define the search bounds.
- Check the mid point condition.
- Narrow the bounds until convergence.
Example
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.
Python Solution
class Solution:
def __init__(self, w: List[int]):
self.s = [0]
for c in w:
self.s.append(self.s[-1] + c)
def pickIndex(self) -> int:
x = random.randint(1, self.s[-1])
left, right = 1, len(self.s) - 1
while left < right:
mid = (left + right) >> 1
if self.s[mid] >= x:
right = mid
else:
left = mid + 1
return left - 1
# Your Solution object will be instantiated and called as such:
# obj = Solution(w)
# param_1 = obj.pickIndex()
Complexity
The time complexity is O(log n) or O(n log n). The space complexity is O(1).
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.