528. Random-Pick-with-Weight

difficulty: Medium

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Given an array w of positive integers, where w[i] describes the weight of index i(0-indexed), write a function pickIndex which randomly picks an index in proportion to its weight.

For example, given an input list of values w = [2, 8], when we pick up a number out of it, the chance is that 8 times out of 10 we should pick the number 1 as the answer since it's the second element of the array (w[1] = 8).

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.

Method One

分析一下如何按权重随机。 假设我们有 index 0 1 2 3 4 value 1 2 3 4 5 那么我们建一个长度为15的线段，那么就知道如果能均匀的落在这个线段上， 那么我们就按权重落在 index 上了。 比如 index 0 1 2 3 4 range 0-1 1-3 3-6 6-10 10-15 注意区间的开闭需要具体问面试官，其实无所谓。 如果我们产生一个 0到1之间的随机数，乘以总长度，那就是随机的按权重选了。 即 target = Math.random() * totalSum. 如果 target = 4.5， 用我最爱的普通二分查找直到停止的模板，我们知道 left = 2, right = 1. 这里我们显然应该返回 left.

class Solution {
    private int[] prefixSum;
    private int totalSum;

    public Solution(int[] w) {
        this.prefixSum = new int[w.length];

        int curSum = 0;
        for(int i = 0; i < w.length; i++) {
            curSum += w[i];
            prefixSum[i] = curSum;
        }

        this.totalSum = curSum;
    }

    public int pickIndex() {
        double target = this.totalSum * Math.random();
        int left = 0;
        int right = prefixSum.length - 1;
        while( left <= right ) {
            int pivot = left + (right - left ) / 2;
            int curVal = prefixSum[pivot];
            if(curVal < target ) {
                left = pivot + 1;
            }else {
                right = pivot - 1;
            }
        }
        return left;
    }
}
​
/**
 * Your Solution object will be instantiated and called as such:
 * Solution obj = new Solution(w);
 * int param_1 = obj.pickIndex();
 */
​