sol6 - 6.851 Advanced Data Structures (Spring10) Prof. Erik...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
6.851 Advanced Data Structures (Spring’10) Prof. Erik Demaine Dr. Andr´ e Schulz TA: Aleksandar Zlateski Problem 6 Sample Solutions Dynamizing static search structures. (a) To perform a successor search we start from the root node, perform a search for a successor and follow the link to it’s left until we reach a leaf node. The runtime recurrence is then: T ( n ) = S (Θ( n 1 /c )) + T (Θ( n 1 - 1 /c )) For fusion trees we have: T ( n ) = O (log ω n 1 /c ) + T (Θ( n 1 - 1 /c )) T ( n ) = O ( c - 1 log ω n ) + O ( c - 1 log ω n 1 - 1 /c + T (Θ( n (1 - 1 /c ) 2 ))) Hence T ( n ) = O ( X i =0 c - 1 log ω n (1 - 1 /c ) i ) = O ( X i =0 c - 1 (1 - 1 /c ) i log ω n ) T ( n ) = O ( c - 1 c log ω n ) = O (log ω n ) (b) The space reccurence is: C ( n ) = Θ( n 1 /c )( C ( n (1 - 1 /c ) )+1). Since we have Θ( n 1 /c ) subtrees of size O ( n (1 - 1 /c ) ) plus Θ( n 1 /c ) for the space at the current level. We see that the reccurence solves to C ( n ) = O ( n ). (c) We will constrain the number of nodes in a subtree rooted at a node at depth
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.
Ask a homework question - tutors are online