#1281

Easy

auto_awesomeMath-driven solution strategy

LeetCode Problem Workspace

Subtract the Product and Sum of Digits of an Integer

Calculate the difference between the product and sum of an integer's digits using a simple math-driven approach for efficiency.

math

Problem Statement

Given an integer n, calculate the product of its digits and the sum of its digits, then return the result of subtracting the sum from the product. Ensure your solution handles all digits without missing any and works efficiently for the full range of allowed integers.

For example, if n = 234, the product of digits is 2 * 3 * 4 = 24, the sum is 2 + 3 + 4 = 9, and the final result is 24 - 9 = 15. The integer n will always satisfy 1 <= n <= 10^5.

Examples

Example 1

Input: n = 234

Output: 15

Product of digits = 2 * 3 * 4 = 24 Sum of digits = 2 + 3 + 4 = 9 Result = 24 - 9 = 15

Example 2

Input: n = 4421

Output: 21

Product of digits = 4 * 4 * 2 * 1 = 32 Sum of digits = 4 + 4 + 2 + 1 = 11 Result = 32 - 11 = 21

Constraints

1 <= n <= 10^5

Solution Approach

Digit Extraction and Iteration

Iterate through each digit by repeatedly dividing and taking the remainder by 10, updating both product and sum variables. This ensures every digit is included and avoids errors from string conversion.

Product and Sum Calculation

Maintain running totals for product and sum while iterating through digits. Start product at 1 and sum at 0, then for each digit multiply into product and add to sum.

Compute Final Result

Subtract the computed sum from the product after all digits are processed. Return this difference as the final output.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

Time complexity is O(d) where d is the number of digits in n, since each digit is processed once. Space complexity is O(1) because only two integer variables are used regardless of n's size.

What Interviewers Usually Probe

Ask candidates to handle each digit efficiently without converting to arrays unnecessarily.
Check if the solution correctly initializes the product to 1 to avoid zeroing out the result.
Probe understanding of basic number manipulation and iteration over digits in an integer.

Common Pitfalls or Variants

Common pitfalls

Initializing the product incorrectly as 0 instead of 1, causing the final result to always be zero.
Skipping digits when using division and modulo incorrectly in the loop.
Using excessive extra space instead of simple integer tracking for product and sum.

Follow-up variants

Compute the difference for very large integers requiring optimized iteration or string handling.
Return both product and sum separately instead of their difference for additional insight into digit composition.
Handle negative integers by considering absolute values or separate sign handling.

FAQ

What is the most efficient way to subtract the product and sum of digits of an integer?

Iterate through each digit using modulo and division, maintain a running product and sum, and subtract sum from product at the end.

Can I convert the integer to a string to solve this problem?

Yes, converting to a string is valid, but direct modulo/division iteration is more memory efficient and aligns with the math-driven pattern.

What are common mistakes when solving this problem?

Common mistakes include initializing the product as 0, skipping digits in the loop, or miscalculating the subtraction order.

Does this approach work for the maximum constraint n = 100000?

Yes, iterating through at most 6 digits is efficient, keeping both time and space complexity minimal.

Why is this called a math-driven solution strategy?

Because the solution relies on fundamental digit arithmetic—product and sum operations—rather than data structures or advanced algorithms.

terminal

Solution

Solution 1: Simulation

We use two variables $x$ and $y$ to record the product of the digits and the sum of the digits respectively. At the beginning, $x=1,y=0$.

1

2

3

4

class Solution:
    def subtractProductAndSum(self, n: int) -> int:
        nums = list(map(int, str(n)))
        return prod(nums) - sum(nums)

Continue Practicing

#1276 number of burgers with no waste of ingredients #1290 convert binary number in a linked list to integer #1295 find numbers with even number of digits