Maximum Product of Two Digits - Practice Coding Problems

Maximum Product of Two Digits - Problem

Math Sorting Easy

You are given a positive integer n. Return the maximum product of any two digits in n.

Note: You may use the same digit twice if it appears more than once in n.

Input & Output

Example 1 — Basic Case

$ Input: n = 253

› Output: 25

💡 Note: The digits are 2, 5, and 3. The maximum product is 5 × 5 = 25 (using digit 5 twice)

Example 2 — Single Digit Repeated

$ Input: n = 99

› Output: 81

💡 Note: The digits are 9 and 9. The maximum product is 9 × 9 = 81

Example 3 — Different Digits

$ Input: n = 1234

› Output: 12

💡 Note: The digits are 1, 2, 3, and 4. The maximum product is 4 × 3 = 12

Constraints

10 ≤ n ≤ 10⁹
n is a positive integer

Visualization

Tap to expand

Understanding the Visualization

Input

Given integer n = 253

Process

Extract digits [2,5,3] and find two largest: 5 and 5

Output

Maximum product = 5 × 5 = 25

Key Takeaway

🎯 Key Insight: The maximum product always comes from multiplying the two largest digits in the number

Asked in

G Google 25 a Amazon 15 f Facebook 12

The key insight is that the maximum product always comes from multiplying the two largest digits. The optimal approach tracks the first and second maximum digits in a single pass without sorting. Time: O(d), Space: O(1).

Common Approaches

Approach	Time	Space	Notes
✓ Brute Force - Check All Pairs	O(d²)	O(d)	Convert number to string and check every possible pair of digits
Optimized - Find Two Largest Digits	O(d)	O(d)	Extract digits, find the two largest ones, and multiply them
Mathematical - Track Two Largest	O(d)	O(1)	Track first and second maximum digits in a single pass without sorting

Brute Force - Check All Pairs — Algorithm Steps

Convert number to string to access individual digits
Use nested loops to check every pair of digits
Track the maximum product found

Visualization

Tap to expand

Step-by-Step Walkthrough

Extract Digits

Convert 253 to individual digits [2,5,3]

Check All Pairs

Test every combination: 2×2=4, 2×5=10, 2×3=6, 5×2=10, 5×5=25, 5×3=15, 3×2=6, 3×5=15, 3×3=9

Find Maximum

Maximum product is 25 from 5×5

Code -

solution.c — C

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

int solution(int n) {
    char digits[20];
    sprintf(digits, "%d", n);
    int maxProduct = 0;
    int len = strlen(digits);
    
    for (int i = 0; i < len; i++) {
        for (int j = 0; j < len; j++) {
            int product = (digits[i] - '0') * (digits[j] - '0');
            if (product > maxProduct) {
                maxProduct = product;
            }
        }
    }
    
    return maxProduct;
}

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

Time & Space Complexity

Time Complexity

⏱️

O(d²)

Nested loops over d digits, checking all d×d pairs

✓ Linear Growth

Space Complexity

O(d)

String conversion stores d digits

✓ Linear Space

25.0K Views

Medium Frequency

~10 min Avg. Time

890 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

Constraints

Visualization

Related Problems

Common Approaches

Brute Force - Check All Pairs — Algorithm Steps

Visualization

Code -

Time & Space Complexity

Select Compiler