1. CSE 12 – Basic Data Structures Cynthia Bailey Lee Some slides and figures adapted from Paul Kube’s CSE 12 CS2 in Java Peer Instruction Materials by Cynthia Lee is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. Based on a work at http://peerinstruction4cs.org. Permissions beyond the scope of this license may be available at http://peerinstruction4cs.org.Cynthia LeeCreative Commons Attribution-NonCommercial 4.0 International Licensehttp://peerinstruction4cs.org

2. Today’s Topics 1. Heap implementation issues  Heap uniqueness  Heapsort in place  HW suggestions 2. Back to generic binary trees  In-order traversal  Pre-order traversal  Post-order traversal  Level-order traversal (also called “breadth-first”) 2

3. Reading quiz!

4. 1. A node in a binary tree may have ___ children A. 0 B. 1 C. 2 D. 3 E. Other/none of the above/more than one of the above Reading quiz!

5. 2. A preorder traversal visits the current node, performs a preorder traversal of its ___ subtree and then performs a preorder traversal of the its ___ subtree. A. right, right B. left, right C. left, left D. right, left Reading quiz!

6. 3. A full binary tree is a tree in which every node other than the leaves has ____ children. A. 0 B. 1 C. 2 D. 3 E. Other/none of the above/more than one of the above Reading quiz!

7. Heap uniqueness

8. TRUE OR FALSE  There is only one configuration of a valid min-heap containing the elements {34, 22, 3, 9, 18} A. TRUE B. FALSE

9. Heap outcomes by insert order Create a MIN-heap by inserting the elements, one by one, in the order given below for the first letter of your last name :  A-F: {3, 9, 18, 22, 34}  G-L: {3, 33, 18, 9, 34}  M-R: {9, 22, 18, 3, 34}  S-Z: {18, 22, 3, 9, 34}

10. Heap outcomes by insert order Create a MIN-heap by inserting the elements, one by one, in the order given below for the first letter of your last name :  A-F: {18, 9, 34, 3, 22}  G-L: {3, 18, 22, 9, 34}  M-R: {22, 9, 34, 3, 18}  S-Z: {34, 3, 9, 18, 22}

11. How many distinct min-heaps are possible for the elements {3, 9, 18, 22, 34} ? A. 1 B. 2-4 C. 5-8 D. 5! (5 factorial) E. Other/none/more

12. Heapsort

13. Heapsort is super easy 1. Insert unsorted elements one at a time into a heap until all are added 2. Remove them from the heap one at a time. We will always be removing the next biggest[smallest] item from the max-heap[min-heap], so the items come out in sorted order! THAT’S IT!

14. Example: using heapsort to print an array in sorted order (note: this is not the in- place version you need for HW) public static void printSorted(String[] unsortedlist) { Heap heap = new Heap (); for (int i=0; i<unsortedlist.length; i++) { heap.add(unsortedlist[i]); } while (!heap.isEmpty()) { System.out.println(heap.remove()); }

15. Implementing heapsort Devil’s in the details

16. We can do the entire heapsort in place in one array  Unlike mergesort, we don’t need a separate array for our workspace  We can do it all in place in one array (the same array we were given as input)

17. Build heap by inserting elements one at a time:

18. Sort array by removing elements one at a time:

19. Build heap by inserting elements one at a time IN PLACE:

20. Sort array by removing elements one at a time IN PLACE:

21. Important tip!  The in-place approach will not work if your test to see if index i is past the end of the heap is to check if heaparray[i] is null.  Things will be in the array that are NOT in the heap!  You need to keep track of an int size (in addition to an int capacity ) in order to check where the heap ends!

22. Binary tree traversals

23. Binary trees  Recall from last time, a binary tree is any tree where each node has 0, 1, or 2 children  That’s the only restriction  Recall: heaps are a special case of binary trees, and they have two additional restrictions

24. Trees vs. Lists  Lists have an obvious ordering  1 st element is first, 2 nd element is second, …  Trees don’t  More than one reasonable order

25. Pre-order traversal preorder(node) { if (node != null){ visit this node preorder(node.left) preorder(node.right) } A. D B E A F C G B. A B D E C F G C. A B C D E F G D. D E B F G C A E. Other/none/more

26. Post-order traversal postorder(node) { if (node != null){ postorder(node.left) postorder(node.right) visit this node } A. D B E A F C G B. A B D E C F G C. A B C D E F G D. D E B F G C A E. Other/none/more

27. In-order traversal inorder(node) { if (node != null){ inorder(node.left) visit this node inorder(node.right) } A. D B E A F C G B. A B D E C F G C. A B C D E F G D. D E B F G C A E. Other/none/more