1. DEAPS By: Michael Gresenz Austin Forrest

2. Deaps A deap is a double-ended heap that supports the double-ended priority operations of insert, delete-min, and delete-max. Similar to min-max heap but deap is faster on these operations by a constant factor, and the algorithms are simpler.

3. Deaps A deap is a complete binary tree that is either empty or satisfies the following properties: –The root contains no element –The left subtree is a min heap. –The right subtree is a max heap. –If the right subtree is not empty, then let i be any node in the left subtree. Let j be the corresponding node in the right subtree. If such a j does not exist, then let j be the node in the right subtree that corresponds to the parent of i. The key in node i is less than or equal to that of j.

4. Modules Insert –Insert a new element with an arbitrary value Delete min –Delete an element with minimum key Delete max –Delete an element with maximum key

5. 8 10 7 2540 1519 45 7 9 30 8 5 20 Min heap Max heap 小 大 5 < 45 ; 10 <25 ; 8 <40; 15 < 20; 19 < 25; 9 < 40; 30 < 40

6. Insert Similar to normal insert into heap The new value when inserted into deap, if it is in the left subtree will move up using a compare for a min heap and if it is in the right subtree it will move up using a compare for a max heap

7. 8 10 7 2540 1519 45 7 9 30 8 5 20 Deaps-Insert 4 4

8. 8 5 7 2540 1510 45 7 9 30 8 4 20 Deaps-Insert 60 1960

9. Delete min Deletes the min value in heap Rearranges the heap so it is still a min heap in left subtree and max heap in right subtree

10. Delete max Deletes the max value in heap Rearranges the heap so it is still a min heap in left subtree and max heap in right subtree

11. Testing Random number generator Symbols Letters Zero Try to ensure that the program doesn’t crash