1. Nov 2, 2001CSE 373, Autumn 20011 Hash Table example 0 1 2 3 4 5 6 7 8 9 + marking deleted items + choice of table size

2. Nov 2, 2001CSE 373, Autumn 20012 Priority Queue ADT Checkout line at the supermarket Printer queues operations: insert, deleteMin insertdeleteMin 6 2 15 23 12 18 45 3 7

3. Nov 2, 2001CSE 373, Autumn 20013 Simple implementations of the Priority Queue ADT insertdeleteMin list sorted list BST AVL tree (overkill?)

4. Nov 2, 2001CSE 373, Autumn 20014 Binary heaps Structure property Perfect binary tree – all leaves are at the same depth. 25 92 215 11 3071013 16 131922 height h 2 h+1 – 1 nodes 2 h – 1 non-leaves 2 h leaves

5. Nov 2, 2001CSE 373, Autumn 20015 Complete binary tree of height h For h = 0, just a single node. For h = 1, left child or two children. For h  2, either –the left subtree of the root is perfect with height h-1 and the right is complete with height h-1, OR –the left is complete with height h- 1 and the right is perfect with height h-2.

6. Nov 2, 2001CSE 373, Autumn 20016 Structure, continued Informally: A perfect binary tree of height h-1 with leaves added at height h in the leftmost positions. N-node heap of height h: h =  log N  2 h  N  2 h+1 - 1

7. Nov 2, 2001CSE 373, Autumn 20017 Representing Complete Binary Trees G ED CB A JKHI F L From node i, left child: right child: parent: 1 23 45 67 98101112 ABCDEFGHIJKL 012345678910111213 implicit (array) implementation:

8. Nov 2, 2001CSE 373, Autumn 20018 Why is it better? no pointers (space). *2, /2, + are faster operations than dereferencing a pointer. can get to parent easily Can we use the implicit representation for binary search trees?