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.
Solution
class Solution {
Random random = new Random();
int[] prefix;
int sum = 0;
public Solution(int[] w) {
this.prefix = new int[w.length];
for (int i = 0; i < prefix.length; i++) {
sum += w[i];
prefix[i] = sum;
}
}
public int pickIndex() {
double val = Math.random() * prefix[prefix.length - 1];
int lo = 0;
int hi = prefix.length;
while (lo < hi) {
int mid = lo + (hi - lo) / 2;
if (val > prefix[mid]) {
lo = mid + 1;
} else {
hi = mid;
}
}
return lo;
}
}
/**
* Your Solution object will be instantiated and called as such:
* Solution obj = new Solution(w);
* int param_1 = obj.pickIndex();
*/
Solution 2021-11-18 Double Array
class Solution {
double[] prob;
public Solution(int[] w) {
int sum = 0;
for (int i = 0; i < w.length; i++) {
sum += w[i];
}
int preSum = 0;
prob = new double[w.length];
for (int i = 0; i < w.length; i++) {
preSum += w[i];
prob[i] += (double) preSum / sum;
}
}
public int pickIndex() {
double val = Math.random();
int index = Arrays.binarySearch(prob, val);
if (index < 0) {
index = -(index + 1);
}
return index;
}
}
/**
* Your Solution object will be instantiated and called as such:
* Solution obj = new Solution(w);
* int param_1 = obj.pickIndex();
*/
Solution 2022-01-24, Integer Array
class Solution {
Random RANDOM = new Random();
int[] p;
public Solution(int[] w) {
p = new int[w.length];
int sum = 0;
for (int i = 0; i < w.length; i++) {
sum += w[i];
p[i] = sum;
}
System.out.println(Arrays.toString(p));
}
public int pickIndex() {
int value = RANDOM.nextInt(p[p.length - 1]) + 1;
int index = Arrays.binarySearch(p, value);
return index >= 0 ? index : -(index + 1);
}
}
/**
* Your Solution object will be instantiated and called as such:
* Solution obj = new Solution(w);
* int param_1 = obj.pickIndex();
*/