Subtract the Product and Sum of Digits of an Integer

Subtract the Product and Sum of Digits of an Integer - Problem

Math Easy

Imagine you have a number and you want to perform a simple mathematical operation on its individual digits. Given an integer n, your task is to:

Calculate the product of all its digits (multiply them together)
Calculate the sum of all its digits (add them together)
Return the difference between the product and sum (product - sum)

For example, if n = 234:

Product of digits: 2 × 3 × 4 = 24
Sum of digits: 2 + 3 + 4 = 9
Difference: 24 - 9 = 15

This problem tests your ability to extract individual digits from a number and perform basic arithmetic operations.

Input & Output

example_1.py — Basic Case

$ Input: n = 234

› Output: 15

💡 Note: Product of digits: 2 × 3 × 4 = 24. Sum of digits: 2 + 3 + 4 = 9. Difference: 24 - 9 = 15.

example_2.py — Single Digit

$ Input: n = 4

› Output: 0

💡 Note: Product of digits: 4. Sum of digits: 4. Difference: 4 - 4 = 0.

example_3.py — Contains Zero

$ Input: n = 4021

› Output: -7

💡 Note: Product of digits: 4 × 0 × 2 × 1 = 0. Sum of digits: 4 + 0 + 2 + 1 = 7. Difference: 0 - 7 = -7.

Visualization

Tap to expand

Understanding the Visualization

Start with Number

Begin with the input number n

Extract Last Digit

Use n % 10 to get the rightmost digit

Update Calculations

Multiply product and add to sum with current digit

Remove Digit

Use n / 10 to remove the processed digit

Repeat Until Empty

Continue until n becomes 0

Calculate Difference

Return product - sum

Key Takeaway

🎯 Key Insight: Mathematical digit extraction using modulo and division is more efficient than string conversion, requiring only O(1) space while maintaining O(d) time complexity.

Time & Space Complexity

Time Complexity

⏱️

O(d)

Where d is the number of digits in n. We process each digit exactly once.

✓ Linear Growth

Space Complexity

O(1)

We only use a constant amount of extra space for variables.

✓ Linear Space

Constraints

1 ≤ n ≤ 10⁵
n is a positive integer
No negative numbers or zero as input

Asked in

a Amazon 35 ⊞ Microsoft 28 G Google 22 f Meta 18

The optimal approach uses mathematical operations to extract digits without string conversion. Use modulo (% 10) to get the last digit and integer division (/ 10) to remove it, processing each digit exactly once in O(d) time and O(1) space.

Common Approaches

Approach	Time	Space	Notes
✓ String Conversion Approach	O(d)	O(d)	Convert number to string and iterate through characters
Mathematical Digit Extraction (Optimal)	O(d)	O(1)	Use modulo and division to extract digits without string conversion

String Conversion Approach — Algorithm Steps

Convert the integer n to a string
Initialize product to 1 and sum to 0
Iterate through each character in the string
Convert each character back to integer
Update product by multiplying with current digit
Update sum by adding current digit
Return product - sum

Visualization

Tap to expand

Step-by-Step Walkthrough

Convert to String

Convert integer 234 to string '234'

Process Each Character

Iterate through '2', '3', '4' and convert each back to integer

Calculate Product and Sum

Product: 2×3×4=24, Sum: 2+3+4=9

Return Difference

Return 24-9=15

Code -

solution.c — C

#include <stdio.h>
#include <string.h>

int subtractProductAndSum(int n) {
    char strN[20];
    sprintf(strN, "%d", n); // Convert number to string
    
    int product = 1;
    int digitSum = 0;
    
    // Iterate through each character (digit)
    for (int i = 0; i < strlen(strN); i++) {
        int digit = strN[i] - '0'; // Convert character to integer
        product *= digit;
        digitSum += digit;
    }
    
    return product - digitSum;
}

int main() {
    int n;
    scanf("%d", &n);
    printf("%d\n", subtractProductAndSum(n));
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(d)

Where d is the number of digits in n. We process each digit once.

✓ Linear Growth

Space Complexity

O(d)

We create a string representation of the number, which takes O(d) space.

✓ Linear Space

Constraints

1 ≤ n ≤ 10⁵
n is a positive integer
No negative numbers or zero as input

52.0K Views

Medium Frequency

~8 min Avg. Time

2.2K Likes

Ln 1, Col 1

Smart Actions

💡 Explanation

AI Ready

💡 Suggestion Tab to accept Esc to dismiss

// Output will appear here after running code

Code Editor Closed

Click the red button to reopen

Input & Output

Visualization

Time & Space Complexity

Related Problems

Constraints

Common Approaches

String Conversion Approach — Algorithm Steps

Visualization

Code -

Time & Space Complexity

Constraints

Select Compiler