Time Complexity of the makeEmpty() of the Top-Down splay tree

Question

In this implementation of a splay tree, the listed time complexity of the makeEmpty() function (which removes all elements) is O(n). It is implemented as follows:

 while( !isEmpty( ) )
 {
     findMax( );        // Splay max item to root
     remove( root->element );
 }

Given that both findMax and remove might have time complexity proportional to the height of the tree, why will this take O(n) time in the worst-case?

Thanks!

score 3 · Accepted Answer · answered Nov 10 '13 at 07:34

Three words: The Sequential Access Theorem.

http://www.wseas.us/e-library/conferences/cairns2001/papers/632.pdf

Because the above loop repeatedly removes the maximum value, it effectively visits all of the elements in sequence, and so I'm pretty certain the sequential access theorem applies.

Time Complexity of the makeEmpty() of the Top-Down splay tree

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