Determine the Minimum Sum of a kavoiding Array
To construct a kavoiding array of length ( n ) with the minimum sum, start by placing the smallest available integers in the array. Keep in mind that the sum of any two numbers in the array should not equal ( k ).
 Initialize an empty list called
result
and a variablesum_result
set to 0.  Initialize a variable
current_number
set to 1.  Loop ( n ) times to fill the
result
array.  In each iteration, check if
current_number
added to any other number in theresult
array sums up to ( k ).  If it does, skip this number and check the next one.
 If it does not, append it to
result
and add its value tosum_result
.
Here’s the code:


Explanation
 We start by setting
current_number
to 1 because we are looking for positive integers.  We then loop ( n ) times to construct our
result
array.  Inside each loop, we check if adding
current_number
to any of the numbers already inresult
would sum to ( k ).  If it does, we skip this number and try the next one.
 If it doesn’t, we add it to
result
and move on to the next iteration of the loop.
The time complexity is ( O(n^2) ) because for each of the ( n ) numbers in result
, we potentially have to check all ( n ) numbers already in the array. This is acceptable for ( n \leq 50 ).