Time complexity of the fastest algorithm for this case
I think it's not optimal but here's a lower bound: you have to move at least $\lfloor\frac{n}{3}\rfloor$ elements.

Split $A$ into blocks of $3$: {$A[1],A[2],A[3]$}, {$A[4],A[5],A[6]$}, ...

The claim is you have to move at least one element from each block. Otherwise, assume the block {$A[k],A[k+1],A[k+2]$} is kept unchanged. Since $A$ is sorted, $\min(A[k],A[k+2])&lt;A[k+1]&lt;\max(A[k],A[k+2])$, which violates your constraint. So the problem takes $\Omega(n)$. Combine this with your $O(n)$ approach we get $\Theta(n)$.