Subtract the Product and Sum of Digits of an Integer

Subtract the Product and Sum of Digits of an Integer

What is this problem about?

This is a straightforward mathematical problem where you are given an integer n. You need to calculate the product of all its individual digits and the sum of all its individual digits. The final answer is the result of subtracting the sum from the product. For example, if the input is 234, the product is 2 * 3 * 4 = 24, and the sum is 2 + 3 + 4 = 9. The result would be 24 - 9 = 15.

Why is this asked in interviews?

Though it appears simple, this question is common in initial screening rounds at companies like Microsoft and Google. It tests a candidate's ability to handle basic arithmetic in a programming context and their knowledge of how to decompose a number into its digits. It's a test of "clean code" and handling edge cases like zeros within the digits.

Algorithmic pattern used

The algorithmic pattern here is "Digit Extraction using Modulo and Division." To get the last digit of a number, you use n % 10. To "remove" that last digit and move to the next one, you use integer division n / 10. You repeat this process in a loop until the number becomes zero, updating your running product and running sum at each step.

Example explanation

Consider the number 1024.

• Step 1: Last digit is 1024 % 10 = 4. Sum = 4, Product = 4. Remaining number = 102.
• Step 2: Last digit is 102 % 10 = 2. Sum = 4 + 2 = 6, Product = 4 * 2 = 8. Remaining number = 10.
• Step 3: Last digit is 10 % 10 = 0. Sum = 6 + 0 = 6, Product = 8 * 0 = 0. Remaining number = 1.
• Step 4: Last digit is 1 % 10 = 1. Sum = 6 + 1 = 7, Product = 0 * 1 = 0. Remaining number = 0. Final Result: Product (0) - Sum (7) = -7.

Common mistakes candidates make

1. Integer Overflow: In some languages, the product of digits can exceed the maximum value of a 32-bit integer, although the constraints for this specific problem usually prevent that.
2. Initializing Product incorrectly: Starting the product at 0 instead of 1 will result in the final product always being 0.
3. Handling Zero: If the input number is 0, the sum is 0 and the product is 0. Some candidates might overthink this case or fail to enter the loop.

Interview preparation tip

Decomposing a number into its digits is a "bread and butter" skill for coding interviews. Ensure you are comfortable doing this without converting the number to a string, as using mathematical operations (% and /) is generally more memory-efficient and often preferred by interviewers.