How to Find the Maximum Number of k-Sum Pairs?

Finding pairs in an array that sum up to a particular value is a common problem that often comes up in technical interviews. Interviewers want to assess your problem-solving skills and your understanding of data structures and algorithms. This article will walk you through the concept of k-sum pairs, provide sample interview questions, and illustrate the methods to solve them effectively.

What are k-Sum Pairs?

A k-sum pair refers to a pair of numbers in an array whose sum equals a given value ( k ). The objective is to determine how many such pairs exist in the array.

For example, if the array is [1, 2, 3, 4, 3, 5] and ( k = 6 ), the pairs that sum up to ( k ) are:

• (1, 5)
• (2, 4)
• (3, 3)

In this case, there are three k-sum pairs.

Interview Questions on k-Sum Pairs

Sample Question 1:

Given an array of integers and a target sum ( k ), write a function that determines the number of unique pairs that sum up to ( k ).

Example Input:

PythonCopy code
array = [1, 2, 3, 4, 3, 5]
k = 6

Expected Output:

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3

Answer Approach:

To solve this problem, keep track of the numbers you've seen and use a set to store the pairs. Here’s how you can implement it in Python:

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def count_k_sum_pairs(array, k):
    seen = set()
    pairs = set()

    for number in array:
        target = k - number
        if target in seen:
            pairs.add((min(number, target), max(number, target)))
        seen.add(number)

    return len(pairs)

# Example usage
array = [1, 2, 3, 4, 3, 5]
print(count_k_sum_pairs(array, 6))  # Output: 3

This code utilizes a set to check if the complement of the current number exists while looping through the array. Each pair is stored in a sorted manner in pairs to ensure uniqueness.

Sample Question 2:

You are given a sorted array of integers and a target sum ( k ). How many unique pairs in the array sum up to ( k )?

Example Input:

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array = [1, 2, 3, 4, 4, 5]
k = 6

Expected Output:

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3

Answer Approach:

For a sorted array, you can use a two-pointer technique for an efficient solution:

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def count_k_sum_pairs_sorted(array, k):
    left, right = 0, len(array) - 1
    count = 0

    while left < right:
        current_sum = array[left] + array[right]
        if current_sum == k:
            count += 1
            left += 1
            right -= 1
            
            # Skip duplicates
            while left < right and array[left] == array[left - 1]:
                left += 1
            while left < right and array[right] == array[right + 1]:
                right -= 1
        
        elif current_sum < k:
            left += 1
        else:
            right -= 1

    return count

# Example usage
array = [1, 2, 3, 4, 4, 5]
print(count_k_sum_pairs_sorted(array, 6))  # Output: 3

This approach runs in ( O(n) ) time since each pointer only moves through the list once, making it much more efficient for large datasets.

Key Takeaways

Knowing how to handle variations of the k-sum pair problem can greatly enhance your problem-solving skills during interviews. Understanding both hash-based and two-pointer methods allows you to tackle these challenges confidently. Being prepared with a variety of examples is essential for demonstrating your approach clearly in an interview setting.