0528. Random Pick with Weight
https://leetcode.com/problems/random-pick-with-weight
Description
You are given an array of positive integers w
where w[i]
describes the weight of i``th
index (0-indexed).
We need to call the function pickIndex()
which randomly returns an integer in the range [0, w.length - 1]
. pickIndex()
should return the integer proportional to its weight in the w
array. For example, for w = [1, 3]
, the probability of picking the index 0
is 1 / (1 + 3) = 0.25
(i.e 25%) while the probability of picking the index 1
is 3 / (1 + 3) = 0.75
(i.e 75%).
More formally, the probability of picking index i
is w[i] / sum(w)
.
Example 1:
**Input**
["Solution","pickIndex"]
[[[1]],[]]
**Output**
[null,0]
**Explanation**
Solution solution = new Solution([1]);
solution.pickIndex(); // return 0. Since there is only one single element on the array the only option is to return the first element.
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's returning the second element (index = 1) that has probability of 3/4.
solution.pickIndex(); // return 1
solution.pickIndex(); // return 1
solution.pickIndex(); // return 1
solution.pickIndex(); // return 0. It's returning the first element (index = 0) that has probability of 1/4.
Since this is a randomization problem, multiple answers are allowed so 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 <= 10000
1 <= w[i] <= 10^5
pickIndex
will be called at most10000
times.
ac: prefix sum
class Solution {
int[] prefixSum;
int upperLimit;
Random random;
public Solution(int[] w) {
prefixSum = new int[w.length + 1];
for (int i = 1; i < prefixSum.length; i++) {
prefixSum[i] = prefixSum[i-1] + w[i-1];
}
upperLimit = prefixSum[prefixSum.length-1];
int[] test = prefixSum;
random = new Random();
}
public int pickIndex() {
int r = random.nextInt(upperLimit);
int index = Arrays.binarySearch(prefixSum, r); // Return insertion index if exists, otherwise -(insertion index)-1;
return index >= 0 ? index : -index-1-1; // in "-(insertion index)-1" insertion index is the index of it after the insertion, so we find previous index.
}
}
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