# 5. Find All Duplicates in an Array

Given an integer array `nums` of length `n` where all the integers of `nums` are in the range `[1, n]` and each integer appears **once** or **twice**, return *an array of all the integers that appears **twice***.

**Example 1:**

```
Input: nums = [4,3,2,7,8,2,3,1]
Output: [2,3]
```

**Example 2:**

```
Input: nums = [1,1,2]
Output: [1]
```

**Example 3:**

```
Input: nums = [1]
Output: []
```

## Solution: (Hashset)&#x20;

Basic solution extra space of O(n)

## Solution: (Optimized)

**Approach:**\
**when find a number i, flip the number at position i-1 to negative.**\
**if the number at position i-1 is already negative, i is the number that occurs twice.**

```cpp
class Solution
{
public:
    vector<int> findDuplicates(vector<int> &nums)
    {

        vector<int> res;

        for (int i = 0; i < nums.size(); i++)
        {

            int idx = abs(nums[i]) - 1;
            if (nums[idx] < 0)
            {
                res.push_back(idx+1);
            }
            nums[idx] = nums[idx] * -1;
        }

        return res;
    }
};
```

**Time Complexity: O(n) , Space Complexity: O(1)**
