How do you solve Max Pair Sum in an Array on LeetCode?

Max Pair Sum in an Array (LeetCode #2815) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(n) space complexity. Key insight: Using a hash map can significantly reduce the number of comparisons needed.

What is the brute force solution for Max Pair Sum in an Array?

The brute force approach for Max Pair Sum in an Array is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach checks every possible pair of numbers to see if they share the same largest digit. If they do, we calculate their sum and track the maximum sum found. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Max Pair Sum in an Array?

Max Pair Sum in an Array uses the following concepts: Array, Hash Table. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Max Pair Sum in an Array?

Always clarify the problem requirements before jumping into coding. Think about edge cases, such as when all numbers have different largest digits. Explain your thought process while coding to show your understanding.

What are common mistakes when solving Max Pair Sum in an Array?

Not considering the case where no pairs exist, leading to incorrect outputs. Forgetting to check if there are at least two numbers in a group before calculating the sum.

#2815

Max Pair Sum in an Array

Easy

ArrayHash TableHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log n)
Space	O(1)	O(n)

💡

Intuition

Time O(n log n)Space O(n)

We can optimize the solution by using a hash map to group numbers by their largest digit. This allows us to find pairs efficiently without checking every combination.

⚙️

Algorithm

4 steps

1Step 1: Create a hash map where the key is the largest digit and the value is a list of numbers that have that largest digit.
2Step 2: Iterate through the array and populate the hash map.
3Step 3: For each entry in the hash map, if there are at least two numbers, calculate the sum of the two largest numbers and update the maximum sum.
4Step 4: Return the maximum sum found or -1 if no valid pairs exist.

solution.py18 lines

1# Full working Python code
2
3def maxPairSum(nums):
4    from collections import defaultdict
5
6    def largest_digit(num):
7        return max(int(d) for d in str(num))
8
9    digit_map = defaultdict(list)
10    for num in nums:
11        digit_map[largest_digit(num)].append(num)
12
13    max_sum = -1
14    for numbers in digit_map.values():
15        if len(numbers) > 1:
16            numbers.sort(reverse=True)
17            max_sum = max(max_sum, numbers[0] + numbers[1])
18    return max_sum

ℹ

Complexity note: The time complexity is O(n log n) due to sorting the lists of numbers in the hash map. The space complexity is O(n) because we store all numbers in the hash map.

1Using a hash map can significantly reduce the number of comparisons needed.
2Sorting the groups allows us to easily find the two largest numbers.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.