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RandomPickWithWeight.java
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RandomPickWithWeight.java
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package Leetcode;
/**
* @author kalpak
*
* You are given an array of positive integers w where w[i] describes the weight of ith 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 most 10000 times.
*/
public class RandomPickWithWeight {
int[] cumulativeWeights;
public RandomPickWithWeight(int[] w) {
cumulativeWeights = new int[w.length];
// build up the array
cumulativeWeights[0] = w[0];
for(int i = 1; i < w.length; i++)
cumulativeWeights[i] = cumulativeWeights[i-1] + w[i];
}
public int pickIndexLinearSearch() {
int target = (int)(cumulativeWeights[cumulativeWeights.length - 1] * Math.random());
for(int i = 0; i < cumulativeWeights.length; i++) {
if(target < cumulativeWeights[i])
return i;
}
return -1;
}
public int pickIndex() {
int target = (int)(cumulativeWeights[cumulativeWeights.length - 1] * Math.random());
int result = -1;
int left = 0;
int right = cumulativeWeights.length - 1;
while(left <= right) {
int mid = left + (right - left)/2;
if (target < cumulativeWeights[mid]) {
result = mid; // we got a candidate. But check if we can do better. So go left
right = mid - 1;
} else {
left = mid + 1;
}
}
return result;
}
public static void main(String[] args) {
RandomPickWithWeight obj = new RandomPickWithWeight(new int[]{1, 3});
System.out.println(obj.pickIndex());
System.out.println(obj.pickIndex());
System.out.println(obj.pickIndex());
System.out.println(obj.pickIndex());
}
}