Minimum swaps to reach permuted array with at most 2 positions left swaps allowed

Given a permuted array of length N of first N natural numbers, we need to tell the minimum number of swaps required in the sorted array of first N natural number to reach given permuted array where a number can be swapped with at most 2 positions left to it. If it is not possible to reach permuted array by above swap condition then print not possible. 

Examples:

Input : arr = [1, 2, 5, 3, 4]
Output : 2
We can reach to above-permuted array in total 2 swaps as shown below,
[1, 2, 3, 4, 5] -> [1, 2, 3, 5, 4] -> [1, 2, 5, 3, 4]

Input : arr[] = [5, 1, 2, 3, 4]
Output : Not Possible
It is not possible to reach above array just by swapping numbers 2 positions left to it.

We can solve this problem using inversions. As we can see that if a number is at a position which is more than 2 places away from its actual position then it is not possible to reach there just by swapping with elements at 2 left positions and if all element satisfy this property (there are <=2 elements smaller than it on the right) then answer will simply be a total number of inversions in the array because that many swaps will be needed to transform the array into permuted array. 

We can find the number of inversions in N log N time using merge sort technique explained here so total time complexity of solution will be O(N log N) only. 

2

Time Complexity: O(N*logN)
Auxiliary Space: O(logN)