Download Monday, March 23, 2009 - Lynbrook Computer Science

Monday, March 23, 2009
Announcements
 ACSL – Free Response: April 3, Written: April 6
 Prefix, Infix, Postfix - 2
 Data Structures - 2
 Digital Electronics - 2
 USACO US Open – April 23
 No proctoring required this year
 Qualification round to the USAICO Summer Cam
 CML Computer Contest – April 27 @ Lunch
 Team Contest
 25 questions, 40 minutes
Final USACO Standings
 Gold Division Qualifiers (Finalists)
 Johnny Ho (2013)
 Tony Ho (2010)
 Silver Division Qualifiers (Semi-finalists)
 Brandon Liu (2010)
 Ritik Malhotra (2010)
 David Liu (2010)
 Felix Sung (2010)
 Patrick Lin (2011)
Data Structures
 Some terminology to know:
 Parent node = the node directly above the current one
 Child node = the node(s) directly below the current one
 Tree, Heap, etc. = types of data structures
 Level = 1 + level of parent (root is level 0)
 Height = maximum level of the data structure
 Root = topmost node, level 0
 Leaf = nodes without children nodes
 Internal path length = sum of all the levels of the nodes
Data Structures Continued
 For trees:
 Left child node is smaller than the parent node
 Right child node is larger than the parent node
 For heaps:
 Parent node is larger than the child nodes
Tree:
Heap:
Sample Problem #1
 Consider the binary search tree that is formed
from the letters S N O W F L A K E, in that
order. Now consider the binary search tree built
from the letter in reverse order (that is, the letters
E K A L F W O N S, in that order). Both trees
have 9 nodes. What is the sum of the internal path
lengths of the two trees?
 Remember: Internal path length = sum of all the
levels of the nodes
Solution
 Step 1: Draw the binary search trees
 Step 2: Count the level for each node, and add it up for
each tree separately (20 and 23 respectively)
 Step 3: Add them up to get your answer (20 + 23) = 43
Sample Problem #2
 Consider the following heap of 10 distinct letters:
 List all the letters that could replace the ?
 Remember:
 Left child node is smaller than the parent node
 Right child node is larger than the parent node
Solution
 Remember, every node in a heap must be larger than
its children
 ? must be smaller than S, larger than G and L.
 Leaves 6 possibilities: M, N, O, P, Q, R
 Two of those are already in heap: Q and N, so they can’t
be the ?
 The answer thus is:
M, O, P, R