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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