Given a positive integer N, arrange the integers 1 to N such the position of the average of two numbers (if present) falls outside the two numbers. For example, for a[i] and a[j], if b = (a[i] + a[j])/2, then if a[k] = b, k < i or k > j. Hint :- If the average of two numbers is not an integer then we can assume that they do not have an average.

One possible solution  i can think of is  divide the array in two parts , odd and even , sort them and use be.low algo , like if we have the array say N=10 and array is 3 10 2 7 5 3 4 6 9 8 1 after dividing and sorting
array will be 1 3 5 7 9 2 4 6 8 10
now calculate length of even and odd list ,if length is odd,then divide it into 2 equal parts and align alone one middle value like
1 3 5 7 9 2 4 6 8 10
now swap all values of two list except first value based on middle if each sub-list
1 7 5 3 9 2 8 6 4 10

i have not coded it yet so feel free to comment if it fails for any test case :)