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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.
1#include <cstdlib>
#include <algorithm>
using namespace std;
class Solution {
vector<int> prefixSum;
public:
Solution(vector<int>& w) {
int sum = 0;
for (int weight : w) {
sum += weight;
prefixSum.push_back(sum);
}
}
int pickIndex() {
int totalWeight = prefixSum.back();
int target = rand() % totalWeight;
return lower_bound(prefixSum.begin(), prefixSum.end(), target + 1) - prefixSum.begin();
}
};This C++ solution employs the standard library's 'lower_bound' function, which performs a binary search to identify the first element not less than the target, giving the desired index efficiently.