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528.random-pick-with-weight.cpp
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83 lines (78 loc) · 2.36 KB
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// Tag: Array, Math, Binary Search, Prefix Sum, Randomized
// Time: O(NlogN)
// Space: O(N)
// Ref: -
// Note: -
// 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.
//
//
class Solution {
public:
vector<int> prefix;
Solution(vector<int>& w) {
int cur = 0;
for (auto x: w) {
cur += x;
prefix.push_back(cur);
}
}
int pickIndex() {
int range = prefix.back();
int t = rand() % range + 1;
return lower_bound(prefix.begin(), prefix.end(), t) - prefix.begin();
}
};
/**
* Your Solution object will be instantiated and called as such:
* Solution* obj = new Solution(w);
* int param_1 = obj->pickIndex();
*/