Find the Sum of Encrypted Integers

Find the Sum of Encrypted Integers

1. What is this problem about?

The Find the Sum of Encrypted Integers interview question is a numeric transformation and summation task. "Encrypting" an integer involves identifying its largest digit and replacing all other digits in that number with that largest digit. For example, the number 123 becomes 333 (since 3 is the largest). You are given an array of integers and need to return the sum of all their encrypted versions.

2. Why is this asked in interviews?

Companies like Larsen & Toubro use this Find the Sum of Encrypted Integers coding problem as a basic competency check. It tests your ability to manipulate digits of a number, use simple loops, and perform basic aggregation. It evaluations your proficiency in Math interview patterns and clean code structure for repetitive tasks.

3. Algorithmic pattern used

This problem follows the Digit Extraction and Reconstruction pattern.

• For each number:
  1. Find the maximum digit: Convert to string or use % 10 and / 10 repeatedly.
  2. Count the number of digits.
  3. Build the encrypted number: For $D$ digits and max digit $M$, the encrypted number is $M imes (11\dots1)$ ($D$ times).
• Sum: Accumulate these values in a global total.

4. Example explanation

Array: [10, 21, 31]

• 10: Max digit is 1. Two digits. Encrypted: 11.
• 21: Max digit is 2. Two digits. Encrypted: 22.
• 31: Max digit is 3. Two digits. Encrypted: 33. Sum: $11 + 22 + 33 = 66$.

5. Common mistakes candidates make

• String Conversion Overhead: Using strings excessively for a purely mathematical problem. While fine for small arrays, math is more efficient.
• Maximum Digit Logic: Forgetting to handle the digit 0 correctly (though not an issue for positive integers).
• Reconstruction error: Hardcoding the number of digits instead of calculating it for each number.

6. Interview preparation tip

Practice digit manipulation! Be able to extract digits and rebuild numbers mathematically using powers of 10. This is a foundational Math interview pattern that appears in many "String vs Math" scenarios.