Does Anybody Make Money Trading Options


import java.util.*;

class Solution 
    public List<Integer> findDisappearedNumbers(int[] nums) 
        Set<Integer> set = new HashSet<>();
        for (int num : nums) 
            set.add(num);
        
        List<Integer> result = new ArrayList<>();
        for (int i = 1; i <= nums.length; i++) 
            if (!set.contains(i)) 
                result.add(i);
            
        
        return result;
    

```The provided code is designed to find the missing numbers within a given array `nums` by leveraging a `HashSet` to track the existing numbers. The main idea is to first store all the numbers from the array `nums` into the `HashSet`, effectively creating a set of unique numbers that were present in the array. Then, the code iterates from 1 to the length of the array and checks for each number if it exists in the `HashSet`. If a number is not found in the `HashSet` during this iteration, it implies that the number is missing within the array `nums`, and it is added to the `result` list. Finally, the `result` list, which contains all the missing numbers, is returned as the result of the `findDisappearedNumbers` function.

Here's a breakdown of the code:

1. **Initialization**:
   - `Set<Integer> set = new HashSet<>();`: Create a `HashSet` called `set` to store unique numbers from the array `nums`.
   - `List<Integer> result = new ArrayList<>();`: Create an empty `ArrayList` called `result` to store the missing numbers.

2. **Loop**:
   - `for (int num : nums)`: Iterate through each element `num` in the input array `nums`.
     - `set.add(num);`: Add the current `num` to the `HashSet` to track the unique numbers present in `nums`.

3. **Missing Numbers Identification**:
   - `for (int i = 1; i <= nums.length; i++)`: Iterate through numbers from 1 to the length of the input array.
     - `if (!set.contains(i))`: Check if the current `i` is not present in the `HashSet`. If it's not, it implies that `i` is a missing number.
       - `result.add(i);`: Add the missing number `i` to the `result` list.

4. **Return Missing Numbers**:
   - The function returns `result`, which contains the list of missing numbers within the input array `nums`.

This code efficiently identifies and collects the missing numbers in the given array using the `HashSet` to track unique numbers and the second loop to identify the missing ones.

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