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This approach involves creating a cumulative sum array based on the provided weights. The idea is to convert the weight array into a cumulative distribution, where each element represents the summed result of all previous weights including the current one. When we generate a random number, we search for its position in this cumulative array to determine which index to return.
Time Complexity: O(N) for initialization, O(N) for the pickIndex.
Space Complexity: O(N) due to the cumulative sum storage.
1import random
2
3class Solution:
4
5 def __init__(self, w):
6 self.prefixSum = []
7 current_sum = 0
8 for weight in w:
9 current_sum += weight
10 self.prefixSum.append(current_sum)
11
12 def pickIndex(self):
13 target = random.randint(0, self.prefixSum[-1] - 1)
14 for i, total in enumerate(self.prefixSum):
15 if target < total:
16 return iPython's 'random' module is utilized to generate a random number. The cumulative weight distribution is maintained in a list, and we go through it linearly to find the appropriate index.
This optimized approach also uses a cumulative sum array, but instead of performing a linear search to find the appropriate index, we use a binary search. This greatly improves the efficiency when determining which index corresponds to a given cumulative value, especially beneficial for larger arrays.
Time Complexity: O(N) for initialization, O(log N) for pickIndex.
Space Complexity: O(N) for the cumulative sum array.
1In JavaScript, a custom binary search locates the target index in the prefix sum array, which boosts the search efficiency compared to linear checking.