Max Number of K-Sum Pairs

Problem Description

You are given an integer array nums and an integer k. In one operation, you can pick two numbers from the array whose sum equals k and remove them from the array. Return the maximum number of operations you can perform on the array.

Key Insights

• The problem can be approached using a hash table to count the frequency of each number in the array.
• For each number num, the complement needed to form a pair that sums to k is k - num.
• We can use the counts of num and its complement to determine how many pairs can be formed.
• Care must be taken when num is equal to its complement, to ensure we only count pairs appropriately.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(n)

Solution

To solve the problem, we can utilize a hash table (or dictionary) to keep track of the frequency of each number in the array. The algorithm follows these steps:

1. Count the occurrences of each number in the array using a hash table.
2. Iterate through the unique numbers in the hash table.
3. For each number, calculate its complement (k - num).
4. Determine the number of pairs that can be formed using the counts of the number and its complement.
5. Update the counts accordingly and sum the total pairs formed.

Code Solutions