Problem

Given an array of integers, find two numbers that add up to a given target number.
Example input: [1, 2, 3, 4, 5], target=5
Example output: [2, 3]

Solution

def find_two_numbers(array, target):
    
    This function takes an array of integers and a target number.
    It returns a list of two numbers that add up to the target number.
    
    # Create a dictionary to store the numbers in the array as keys and their indices as values.
    # This will allow us to look up the index of a number in the array in constant time.
    # This is the optimal solution because it takes O(n) time to create the dictionary and O(1) time to look up a number.
    # The total time complexity is O(n).
    num_dict = {}
    for i in range(len(array)):
        num_dict[array[i]] = i

    # Iterate through the array and check if the difference between the target number and the current number is in the dictionary.
    # If it is, return the current number and the difference.
    # This is the optimal solution because it takes O(n) time to iterate through the array and O(1) time to look up a number.
    # The total time complexity is O(n).
    for i in range(len(array)):
        if target - array[i] in num_dict:
            return [array[i], target - array[i]]

print(find_two_numbers([1, 2, 3, 4, 5], 5))