隨機選取一個數的下標（蓄水池抽樣）Random Pick Index

問題：

Given an array of integers with possible duplicates, randomly output the index of a given target number. You can assume that the given target number must exist in the array.

Note:
The array size can be very large. Solution that uses too much extra space will not pass the judge.

Example:

int[] nums = new int[] {1,2,3,3,3};
Solution solution = new Solution(nums);
// pick(3) should return either index 2, 3, or 4 randomly. Each index should have equal probability of returning.
solution.pick(3);
// pick(1) should return 0. Since in the array only nums[0] is equal to 1.
solution.pick(1);

解決：

① 蓄水池抽樣。

class Solution { //345ms
    int[] nums;
    public Solution(int[] nums) {
        this.nums = nums;
    }
    Random random = new Random();
    public int pick(int target) {
        List<Integer> index = new ArrayList<>();
        for (int i = 0;i < nums.length;i ++){
            if (nums[i] == target){
                index.add(i);
            }
        }
        return index.get(random.nextInt(index.size()));
    }
}
/**
 * Your Solution object will be instantiated and called as such:
 * Solution obj = new Solution(nums);
 * int param_1 = obj.pick(target);
 */

② 同理

class Solution {//310ms
    int[] nums;
    Random random;
    public Solution(int[] nums) {
        this.nums = nums;
        random = new Random();
    }
    public int pick(int target) {
        int count = 0;
        int res = 0;
        for (int i = 0;i < nums.length;i ++){
            if (nums[i] != target) continue;
            if (random.nextInt(++ count) == 0){
                res = i;
            }
        }
        return res;
    }
}
/**
 * Your Solution object will be instantiated and called as such:
 * Solution obj = new Solution(nums);
 * int param_1 = obj.pick(target);
 */