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# 398 Random Pick Index

## 398. [Random Pick Index](https://leetcode.com/problems/random-pick-index/description/)

## 1. Question

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);
```

## 2. Implementation

**(1) Reservoir Sampling**

```java
class Solution {
    Random rand;
    int[] nums;

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

    public int pick(int target) {
        int res = -1;
        int count = 0;

        for (int i = 0; i < nums.length; i++) {
            if (nums[i] == target && rand.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);
 */
```

## 3. Time & Space Complexity

**Reservoir Sampling:** 时间复杂度O(n), 空间复杂度O(n)