这种特定方法的时间复杂度是多少？

Question

class Tower {
      public void moveDisks(int n, Tower Destination, Tower Buffer) {
         if (n > 0) {
            moveDisks(n-1, Buffer, Destination);
            moveTopto(Destination);
            Buffer.moveDisks(n-1, Destination, this);
        }
    }
}

Here is the code to the method I mentioned above. This is part of an algorithm that solves the classic Hanoi Tower problem. I just can't wrap my head around a time complexity for this as the it has quite a bit of recursion.

This is a method within the class Tower . moveTopto is O(1) , so shouldn't affect the runtime.

Answer 1

That depends on the time complexity of the moveTopto and buffer.moveTopto .

Basically to compute the complexity you will have to add the up the times. The time for n will be the time for n-1 , plus the time for moveTopto plus the time for buffer.moveTopto plus a constant. Now you see that it will have at least O(N) , but can have higher, especially if buffer.moveTopto have non-constant time complexity.

If you mean Buffer.moveTopto then the time would be about twice the time for n-1 , that is you would have t(n) = 2*t(n-1)+constant . That gives O(2^n) .

Answer 2

Good explanation of recursive algorithms complexity analysis Video Tutorial

PS. If you're too lazy to open the link and understand and just want the answer - complexity ~ O(2 ^ n)