Max Pair Sum in an Array - Practice Coding Problems

Max Pair Sum in an Array - Problem

Given an integer array nums, you need to find the maximum sum of a pair of numbers where both numbers share the same largest digit.

For example, in the number 2373, the digits are 2, 3, 3, and 7, where 7 is the largest digit. Two numbers can form a valid pair only if their largest digits are equal.

Goal: Return the maximum possible sum from such a pair, or -1 if no valid pair exists.

Example: For nums = [2536, 1613, 3103, 1730]
• 2536 → largest digit = 6
• 1613 → largest digit = 6
• 3103 → largest digit = 3
• 1730 → largest digit = 7
The pair (2536, 1613) both have largest digit 6, so the answer is 2536 + 1613 = 4149.

Input & Output

example_1.py — Basic Valid Pair

$ Input: nums = [2536, 1613, 3103, 1730]

› Output: 4149

💡 Note: Numbers 2536 and 1613 both have largest digit 6. Their sum 2536 + 1613 = 4149 is the maximum possible.

example_2.py — Multiple Valid Pairs

$ Input: nums = [51, 71, 17, 24]

› Output: 88

💡 Note: Numbers 51, 71, 17 all have largest digit 7. The maximum pair sum is 71 + 17 = 88.

example_3.py — No Valid Pairs

$ Input: nums = [1, 2, 3, 4]

› Output: -1

💡 Note: All numbers have different largest digits (1,2,3,4), so no valid pair can be formed.

Constraints

2 ≤ nums.length ≤ 100
1 ≤ nums[i] ≤ 10⁴
Each number has at least 1 digit

Visualization

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Understanding the Visualization

Assess Peak Skills

Find the largest digit (peak skill) for each number

Form Skill Groups

Group numbers with the same largest digit together

Find Best Teams

In each group with 2+ members, pair the two strongest

Key Takeaway

🎯 Key Insight: Instead of checking all possible pairs (O(n²)), we group numbers by their largest digit and only compare within each group, achieving O(n) time complexity.

Asked in

a Amazon 15 G Google 8 ⊞ Microsoft 6 f Meta 4

The optimal solution uses a hash table approach to group numbers by their largest digit in O(n) time. For each group with 2+ numbers, we find the two largest values and calculate their sum. The key insight is that we only need to track the best candidates for each largest digit group, avoiding the O(n²) comparison of all pairs.

Common Approaches

Approach	Time	Space	Notes
✓ Brute Force (Nested Loops)	O(n² × d)	O(1)	Check every possible pair and find the maximum sum among valid pairs
One-Pass Hash Table (Optimal)	O(n × d)	O(n)	Build hash map and find maximum pairs simultaneously in one pass

Brute Force (Nested Loops) — Algorithm Steps

Create a helper function to find the largest digit in a number
Use nested loops to check all possible pairs (i, j) where i < j
For each pair, find the largest digit of both numbers
If largest digits match, update the maximum sum
Return the maximum sum found, or -1 if no valid pair exists

Visualization

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Step-by-Step Walkthrough

Extract largest digits

For each number, find its largest digit

Compare all pairs

Check if largest digits of each pair match

Track maximum sum

Keep the highest sum found among valid pairs

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>

int getLargestDigit(int num) {
    int largest = 0;
    while (num > 0) {
        int digit = num % 10;
        if (digit > largest) {
            largest = digit;
        }
        num /= 10;
    }
    return largest;
}

int maxSum(int* nums, int n) {
    int maxSum = -1;
    
    for (int i = 0; i < n; i++) {
        for (int j = i + 1; j < n; j++) {
            if (getLargestDigit(nums[i]) == getLargestDigit(nums[j])) {
                int sum = nums[i] + nums[j];
                if (sum > maxSum) {
                    maxSum = sum;
                }
            }
        }
    }
    
    return maxSum;
}

int main() {
    int nums[] = {2536, 1613, 3103, 1730};
    int n = sizeof(nums) / sizeof(nums[0]);
    printf("%d\n", maxSum(nums, n));
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n² × d)

n² for checking all pairs, d for finding largest digit in each number

⚠ Quadratic Growth

Space Complexity

O(1)

Only using constant extra space for variables

✓ Linear Space

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Brute Force (Nested Loops) — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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