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Find the Sum of Encrypted Integers

Difficulty: Easy

Problem Description

You are given an integer array nums containing positive integers. We define a function encrypt such that encrypt(x) replaces every digit in x with the largest digit in x. For example, encrypt(523) = 555 and encrypt(213) = 333. Return the sum of encrypted elements.

Key Insights

  • The encryption of a number involves identifying the maximum digit and replacing all digits with this maximum digit.
  • The sum of encrypted integers can be computed by applying the encryption to each integer and accumulating the results.
  • The constraints are manageable, allowing for simple iteration and string manipulation.

Space and Time Complexity

Time Complexity: O(n * k), where n is the number of integers in nums and k is the maximum number of digits in the largest integer (which is at most 3). Space Complexity: O(1), as we are using a constant amount of extra space.

Solution

To solve this problem, we can iterate over each integer in the nums array, convert each integer to a string to analyze its digits, find the maximum digit, and then construct the encrypted version of the integer. Finally, we sum all the encrypted integers and return the result.

Code Solutions

def encrypt(x):
    # Convert the integer to string to analyze digits
    s = str(x)
    # Find the maximum digit
    max_digit = max(s)
    # Create the encrypted number by repeating the maximum digit
    encrypted_number = int(max_digit) * len(s)
    return encrypted_number

def sum_of_encrypted_integers(nums):
    total_sum = 0
    for num in nums:
        total_sum += encrypt(num)
    return total_sum

# Example usage
print(sum_of_encrypted_integers([1, 2, 3]))  # Output: 6
print(sum_of_encrypted_integers([10, 21, 31]))  # Output: 66
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