Find the Maximum Number of K-Sum Pairs Possible

Introduction

Finding the maximum number of k-sum pairs possible, is an important problem in the field of computer programming and is used to solve complex problems which involve the sum of multiple elements. The problem mainly involves finding the maximum number of pairs which add up to a given number k.

Understanding K-Sum Pairs

For a given array with 'n' elements, we have to find maximum number of pairs which sum upto a given number 'k'. For example, given an array {2,5,7,11,14,17} and given a number 'k' as 34, the maximum number of pairs is 3 i.e. {2,17}, {7,11}, {11, 14}.

Requirements

In order to solve this problem, we must first understand the basics of a sorted array:

• A sorted array is an array that has its elements arranged in increasing order, i.e. from the smallest to the largest.
• An array may contain duplicate elements but all the elements must be in increasing order.

We should also understand the binary search algorithm: A binary search algorithm is an efficient algorithm used to find an element's position in a given sorted array. It works by beginning with an element in the middle of an array and comparing it to the desired element. If the element is higher than the desired element, then the algorithm moves to the lower half of the array and searches the element there; if the element is lower than the desired element, then the algorithm moves to the upper half of the array and searches the element there.

Algorithm

The algorithm for finding the maximum number of ‘k-sum’ pairs possible in a given array is as follows:

1. Sort the array elements.
2. Initialize two variables left and right, both pointing to the first and last indexes of the array, respectively.
3. While the left and right variables don't meet, add the elements pointed to by left and right variables and compare the sum to given number ‘k’.
4. If the sum is greater than ‘k’, then decrement the right variable (i.e. move right variable one index to left).
5. If the sum is lesser than ‘k’, then increment the left variable (i.e. move left variable one index to right).
6. If the sum is equal to ‘k’, then add left and right element to the output list and then increment and decrement respective variables.
7. Repeat steps 4, 5 and 6 until left and right variable cross each other.

Source Code

Let us take a look at the source code for finding the maximum number of ‘k-sum’ pairs possible in a given array in Python programming language:

def maxKsumPairs(arr, k): 
    # Sort the array 
    arr.sort() 
   
    # Initializing two index variables to find the maximum sum pair 
    l = 0
    r = len(arr) - 1
  
    # Initialize maximum ksum pairs count 
    ksum_pairs = 0
  
    # Take an empty set to store pairs 
    pairs = set() 
  
    # Traverse array elements while l < r 
    while l < r: 
        # Compare sum of current pair with given sum k 
        if (arr[l] + arr[r] == k): 
            ksum_pairs += 1
            pairs.add((arr[l], arr[r]))
    
            # Move both left and right pointers one step towards each other 
            l += 1
            r -= 1
        elif (arr[l] + arr[r] < k):
            l += 1
        else:
            r -= 1
  
    print("Maximum k-sum pairs are %d" %ksum_pairs)
    for element in pairs:
        print("Pair (%d, %d)" %element)
 
# Driver Code 
arr = [2, 5, 7, 11, 14, 17] 
k = 34
  
maxKsumPairs(arr, k) # Maximum k-sum pairs are 3 
# Pair (2, 17) 
# Pair (7, 11) 
# Pair (14, 11)

FAQ

What Is the Maximum Number of K-Sum Pairs Possible?

The maximum number of k-sum pairs possible for a given array is determined by the size of the array and the value of k. The maximum number of k-sum pairs is equal to the size of the array minus one.

How Can We Determine the Maximum Number of K-Sum Pairs Possible?

The maximum number of k-sum pairs possible can be determined by using a sorted array and the binary search algorithm. This algorithm works by beginning with an element in the middle of an array and comparing it to the desired element. If the element is higher than the desired element, then the algorithm moves to the lower half of the array and searches the element there; if the element is lower than the desired element, then the algorithm moves to the upper half of the array and searches the element there.

What Are the Advantages of K-Sum Pairs?

There are multiple advantages of k-sum pairs:

• K-sum pairs can be used to solve complex problems that involve the sum of multiple elements.
• It is a fast and efficient algorithm for finding the maximum number of k-sum pairs possible in a given array.
• K-sum pairs can be used to reduce the time complexity of computation in computer programming and thus, improve performance.
• K-sum pairs can also be used to find the smallest and largest elements in a given array.

What Is the Time Complexity of K-Sum Pairs Algorithm?

The time complexity of K-sum pairs algorithm is O(n). This means that the algorithm has a linear time complexity, which means that the time taken to execute the algorithm will increase in proportion to the size of the input array.

Conclusion

K-sum pairs is an important problem in computer programming and is used to solve complex problems that involve the sum of multiple elements. In this article, we discussed the requirements, algorithm, source code, and the advantages and time complexity of k-sum pairs. With this article, you should now have a better understanding of k-sum pairs and be able to implement it in your programming language of choice.