CISC220 Fall 2009 James Atlas

1. CISC220Fall 2009James Atlas Nov 9: Heaps

2. Remaining Course Topics • Heaps • Hashing • Graphs

3. Heaps • Specialized Tree • Often are Binary Heaps • Satisfy Heap Property • if B is a child node of A, then key(A) ≥ key(B) [in a Max-Heap] • if B is a child node of A, then key(A)  key(B) [in a Min-Heap]

4. Binary Max Heap

5. Heap operations • insert: • adding a new key to the heap • delete-max or delete-min: • removing the root node • increase-key or decrease-key: • updating a key within a max- or min-heap, respectively • merge: • joining two heaps to form a valid new heap containing all the elements of both.

6. Heap Insert • Add the element on the bottom level of the heap. • Compare the added element with its parent; if they are in the correct order, stop. • If not, swap the element with its parent and return to the previous step.

7. Heap Insert (example) 1 2 3

8. Heap Delete • Replace root with last element • Find max (or min) between root and children • Swap if child > root, recursively do find max on subtree now rooted at new child

9. Heap Delete (example) 1 2

10. Increase/Decrease Key?

11. Implementations • Array? • Pointers?

13. Operation Running Times