CSE 12 – Basic Data StructuresCynthia Bailey Lee

Some slides and figures adapted from Paul Kube’s CSE 12

                          

CS2 in Java Peer Instruction Materials by Cynthia Lee is

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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”)

Reading quiz!

1. A node in a binary tree may have ___ children

A. 0 B. 1C. 2D. 3E. Other/none of the above/more than

one of the above

Reading quiz!

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, rightB. left, rightC. left, leftD. right, left

Reading quiz!

3. A full binary tree is a tree in which every node other than the leaves has  ____ children.

A. 0B. 1C. 2D. 3E. Other/none of the above/more than

one of the above

Reading quiz!

Heap uniqueness

TRUE OR FALSE There is only one configuration of a valid

min-heap containing the elements {34, 22, 3, 9, 18}

A. TRUEB. FALSE

Heap outcomes by insert orderCreate 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}

Heap outcomes by insert orderCreate 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}

How many distinct min-heaps are possible for the elements {3, 9, 18, 22, 34} ?

A. 1B. 2-4C. 5-8D. 5! (5 factorial)E. Other/none/more

Heapsort

Heapsort is super easy1. Insert unsorted elements one at a time

into a heap until all are added2. 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!

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<String> heap = new Heap<String>();for (int i=0; i<unsortedlist.length; i++) {

heap.add(unsortedlist[i]);}while (!heap.isEmpty()) {

System.out.println(heap.remove());}

}

Implementing heapsortDevil’s in the details

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)

Build heap by inserting elements one at a time:

Sort array by removing elements one at a time:

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

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

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!

Binary tree traversals

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

Trees vs. Lists Lists have an

obvious ordering 1st element is

first, 2nd element is second, …

Trees don’t More than one

reasonable order

Pre-order traversalpreorder(node) { if (node != null){

visit this node preorder(node.left) preorder(node.right)

}}

A. D B E A F C GB. A B D E C F G C. A B C D E F G

D. D E B F G C AE. Other/none/more

Post-order traversalpostorder(node) { if (node != null){

postorder(node.left) postorder(node.right)visit this node

}}

A. D B E A F C GB. A B D E C F G C. A B C D E F G

D. D E B F G C AE. Other/none/more

In-order traversalinorder(node) { if (node != null){

inorder(node.left)visit this node inorder(node.right)

}}

A. D B E A F C GB. A B D E C F G C. A B C D E F G

D. D E B F G C AE. Other/none/more