Check If Array Pairs Are Divisible by k
The problem requires us to find if we can divide the array into exactly ( n / 2 ) pairs such that the sum of each pair is divisible by ( k ).
Here’s a way to approach the problem, starting simple and then going into more details:
Key Insight
The remainder when dividing a number by ( k ) will determine its compatibility with other numbers. We’ll have to match numbers with complementary remainders so that their sum is divisible by ( k ).
Algorithm
 Calculate Remainders: For each element in the array, calculate the remainder when dividing by ( k ), and keep track of the frequency of each remainder.
 Match Complementary Remainders: For each unique remainder ( r ), check if there are an equal number of elements that have a remainder of ( (k  r) ) or ( r ). These are complementary remainders.
 Special Case for Remainder 0: If there are numbers that are exactly divisible by ( k ) (remainder 0), then there should be an even number of them to form pairs.
Implementation
Python solution:


Example
For the input ( arr = [1,2,3,4,5,10,6,7,8,9], k = 5 ), the remainders are [0, 1, 1, 2, 2, 0, 1, 2, 3, 4]. By using the above method, we can find the pairs as described and return true.
Time Complexity
The time complexity of this solution is ( O(n + k) ), where ( n ) is the length of the array, and ( k ) is the given integer.
Summary
 Calculate the remainder of each number with ( k ) and count the occurrences.
 Match the complementary remainders.
 Special handling for remainder 0.
 Check if the solution works for each given example to validate the approach.