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1. Find the Integer Added to Array I-out

You’re given an initial array of n integers and another array of n+1 integers which contains all the original integers plus one additional integer. Write a function to find the additional integer that was added.

Clarifying Questions

1. What kind of values can the integers in the array take? They can be any valid integer values, both positive and negative, and can also include zero.

2. Are the integers in the arrays unique? Yes, all integers in the initial array are unique.

3. Can we assume the arrays are valid (i.e. the second array always has exactly one more integer)? Yes, you can assume the input is always valid as per the problem statement.

4. Is there any specific order for the output? No, just return the additional integer.

Strategy

To find the additional integer, several strategies can be used, such as sorting the arrays and comparing, using a hash map to count occurrences, etc. However, a more optimal way is to use the properties of sums:

1. Calculate the sum of the original array.
2. Calculate the sum of the array with the extra integer.
3. The difference between the sum of the array with the extra integer and the sum of the original array will give the additional integer.

This approach is optimal in terms of both time and space complexities.

Time Complexity

• Time Complexity: (O(n)), where (n) is the number of elements in the original array since we are just performing sums which are (O(n)) operations.
• Space Complexity: (O(1)), since we are only using a constant amount of extra space for the sums.

Code

Here is the Python implementation of the described approach:

def find_added_integer(original, extended):
    # Calculate the sum of the original and the extended arrays
    sum_original = sum(original)
    sum_extended = sum(extended)
    
    # The difference will be the added integer
    added_integer = sum_extended - sum_original
    
    return added_integer

# Example Usage:
original = [3, 1, 2, 4]
extended = [3, 1, 2, 4, 5]
print(find_added_integer(original, extended)) # Output: 5

Explanation

1. We calculate the sum of the original array.
2. We calculate the sum of the extended array.
3. The difference between those sums is the additional integer that was added to the array.

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