This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: n1 moves are required to assemble a puzzle with n pieces. 6. Give a recursive denition of P m ( n ), the product of the integer m and the nonnegative integer n . 7. A full binary tree is a graph dened through the following recursive denition. Basis step: A single vertex is a full binary tree. Inductive step: If T 1 and T 2 are disjoint full binary trees with roots r 1 , r 2 , respectively, the the graph formed by starting with a root r , and adding an edge from r to each of the vertices r 1 ,r 2 is also a full binary tree. Draw all full binary trees that can be obtain by applying the inductive step at most 3 times (full binary trees of level 3). Use structural induction to show that n ( T ) 2 h ( T )+ 1, where n ( T ) denotes the number of vertices in T , and h ( T ) denotes the height of T . 2...
View
Full
Document
 Fall '09
 MarniMishna

Click to edit the document details