# Random Pick Index

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);
```

## Note

水槽采样

Reservior Sampling: when we get the Nth digit, we should generate 0-1 random number. if this random number is less than 1/N, we replace pre-digit to N. if random number is larger than 1/N, than keep pre-digit.

We should get 0-N random number and use 1 to decide replace or keep pre-digit.

## Code

```java
class Solution {

    private int[] nums;
    private Random rdm;

    public Solution(int[] nums) {
        this.nums = nums;
        rdm = new Random();
    }

    public int pick(int target) {
        int winner = -1;
        int j = 0;
        for (int i = 0; i < nums.length; i++) {
            if (nums[i] == target) {
                if (rdm.nextInt(++j) == 0) {
                    winner = i;
                } else winner = winner;
            }
        }
        return winner;
    }
}
```
