Maximum Product of Two Digits

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: 16

💡 Note: The digits are 1, 2, 3, and 4. The maximum product is 4 × 4 = 16

Constraints

10 ≤ n ≤ 10⁹
n is a positive integer

Visualization

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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

✓ Brute Force - Check All Pairs

⏱️ Time: O(d²) Space: O(d)

Extract all digits from the number and systematically check every possible pair to find the maximum product. This ensures we don't miss any combination.

Mathematical - Track Two Largest

⏱️ Time: O(d) Space: O(1)

Instead of sorting all digits, we can track the largest and second largest digits in a single pass. This is more space efficient and avoids the sorting overhead.

Optimized - Find Two Largest Digits

⏱️ Time: O(d) Space: O(d)

Since we want maximum product, we only need the two largest digits. Extract all digits, find the largest and second largest, then multiply them together.

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

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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

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Input & Output

Constraints

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Related Problems

Common Approaches

Brute Force - Check All Pairs — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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