# CMP-‐338 Name: Midterm Spring 2015 Solutions Midterm

## CMP-‐338 Name: Midterm Spring 2015 Solutions Midterm

CMP-­‐338   Midterm  Spring  2015                                                                                        Solutions   Version 1 Name...

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CMP-­‐338   Midterm  Spring  2015

Solutions   Version 1

Name:____________________________________

1. (3 Points) The  keyword  ______  is  used  in  the  class  declaration  of  a  subclass  to  indicate  its  superclass. a. inherits b. extends c. implements d. super 2. (3 Points) Assuming a linked list of n nodes, the code fragment: Node curr = head; while (curr != null) { System.out.println(curr.getItem()); curr.setNext(curr.getNext()); } // end while

requires ______ assignments. a. n b. n – 1 c. n + 1 d. 1 3. (3 Points) If a problem of size n requires time that is directly proportional to n, the problem is ______. a. O(1) b. O(n) c. O(n2) d. O(2n) 4. (3 Points) In ______, the left and right subtrees of any node have heights that differ by at most 1. a. all trees b. all binary tress c. n-ary trees d. balanced binary trees     5. (3 Points) In an array based representation of a complete binary tree, which of the following represents the left child of node tree[i]? a. tree[i+2] b. tree[i–2] c. tree[2*i+1] d. tree[2*i+2] 6. (3 Points) A graph is ______ if it has at least one pair of vertices without a path between them. a) complete b) disconnected c) connected d) full Version 1

CMP-­‐338   Midterm  Spring  2015

Solutions   Version 1

7. (20 Points) Given the following ListInterface: public interface ListInterface { public void add(Object obj); public boolean add(Object obj, int index); public Object getObject(int index); public boolean remove(int index); }

The correct array-based implementation: public class ArrayList implements ListInterface { private int tail = 0; private Object[] arrayList = new Object[10000]; private void moveElementsToAdd(int begin, int end) { for ( int i = end ; i >= begin ; i-- ) { arrayList[i+1] = arrayList[i]; } } private void moveElementsToRemove(int begin, int end) { for ( int i = begin ; i <= end ; i++ ) { arrayList[i-1] = arrayList[i]; } } public void add(Object obj) { if (tail < arrayList.length) { arrayList[tail++] = obj; } } public boolean add(Object obj, int index) { if ((index <= tail) && (tail < arrayList.length)) { moveElementsToAdd(index, tail-1); arrayList[index] = obj; tail++; return true; } return false; } public Object getObject(int index) { if (index < tail) { return arrayList[index]; } return null; } public boolean remove(int index) { if (index < tail) { moveElementsToRemove(index+1, tail-1); tail--; return true; } return false; } }

Name:____________________________________

CMP-­‐338   Midterm  Spring  2015

Solutions   Version 1

Name:____________________________________

8. (40 Points) The correct BinarySearchTree implementation is: public class BinarySearchTree implements BinarySearchTreeInterface { private TreeNode root = null; @Override public boolean isEmpty() { return (root == null); } @Override public void makeEmpty() { root = null; } @Override public void insert(TreeItem item) { root = insertItem(root, item); } private TreeNode insertItem(TreeNode node, TreeItem newItem) { TreeNode newSubtree; if (node == null) { node = new TreeNode(newItem); return node; } if (newItem.compareTo(node.getItem()) < 0) { newSubtree = insertItem(node.getLeftChild(), newItem); node.setLeftChild(newSubtree); return node; } else { newSubtree = insertItem(node.getRightChild(), newItem); node.setRightChild(newSubtree); return node; } }

@Override public TreeItem retrieve(int key) { return retrieveItem(root, key); } private TreeItem retrieveItem(TreeNode node, int key) { TreeItem treeItem; TreeItem compareItem = new TreeItem(key); if (node == null) { treeItem = null; } else if (compareItem.compareTo(node.getItem()) == 0) { treeItem = node.getItem(); } else if (compareItem.compareTo(node.getItem()) < 0) { treeItem = retrieveItem(node.getLeftChild(), key); } else { treeItem = retrieveItem(node.getRightChild(), key); } return treeItem; } }

CMP-­‐338   Midterm  Spring  2015

Solutions   Version 1

9. (20 Points) The correct method for merging two arrays: public void merge(T[]a, T[]b, T[]c) { int firstA = 0; int lastA = a.length - 1; int firstB = 0; int lastB = b.length - 1; int cIindex = 0; while ((firstA <= lastA) && (firstB <= lastB)) { if (a[firstA].compareTo(b[firstB]) < 0) { c[cIindex] = a[firstA++]; } else { c[cIindex] = b[firstB++]; } cIindex++; } // end while while (firstA <= lastA) { c[cIindex++] = a[firstA++] ; } // end while

while (firstB <= lastB) { c[cIindex++] = b[firstB++]; } // end while }

Name:____________________________________

CMP-­‐338   Midterm  Spring  2015

Solutions   Version 1

Name:____________________________________

10. (16 Points) The following list of numbers: 20, 15, 35, 10, 5, 3, 19, 22, 30, 45, 2, 6, 42, 55, 17 inserted in the given order into: a. (4 Points) Into a Binary Search Tree produces the following tree:

b. (4 Points) Into a 2-3 Tree produces the following tree:

CMP-­‐338   Midterm  Spring  2015

Solutions   Version 1

Name:____________________________________

c. (4 Points) Into a 2-3-4 Tree produces the following tree:

d. (4 Points) The numbers in the following order produces a full Binary Search Tree: 19, 6, 3, 2, 5, 15, 10, 17, 35, 22, 20. 30, 45, 42, 55

CMP-­‐338   Midterm  Spring  2015

Solutions   Version 2

Name:____________________________________

1. (3 Points) A superclass method can be accessed by a subclass, even though it has been overridden by the subclass, by using the ______ reference. a. super b. final c. static d. new 2.

(3 Points) Assuming

a linked list of n nodes, the code fragment:

Node curr = head; while (curr != null) { System.out.println(curr.getItem()); curr.setNext(curr.getNext()); } // end while

requires ______ comparisons. a. n b. n – 1 c. n + 1 d. 1 3. (3 Points) The value of which of the following growth-rate functions grows the fastest? a. O(n) b. O(n2) c. O(1) d. O(log2n)   4. (3 Points) In a ______ of height h, all nodes that are at a level less than h have two children each. a. general tree b. binary tree c. full binary tree d. complete binary tree 5. (3 Points) ) In an array based representation of a complete binary tree, which of the following represents the right child of node tree[i]? a. tree[i+2] b. tree[i–2] c. tree[2*i+1] d. tree[2*i+2] 6. (3 Points) The edges in a ______ indicate a direction. a. graph b. multigraph c. digraph d. spanning tree

CMP-­‐338   Midterm  Spring  2015

Solutions   Version 2

Name:____________________________________

7. (20 Points) Given the following ListInterface, the correct reference-based implementation is: public interface ListInterface { public void add(Object obj); public boolean add(Object obj, int index); public Object getObject(int index); public boolean remove(int index); }

public boolean add(Object obj, int index) { boolean rc = false; Node newNode = new Node(obj); Node curNode = head; if (index == 0) { if (head == null) { tail = newNode; } newNode.setNext(head); head = newNode; listSize++; rc = true; } else if (index == listSize) { add(obj); rc = true; } else if (index < listSize) { for ( int j = 1 ; j < index ; j++ ) { curNode = curNode.getNext(); } newNode.setNext(curNode.getNext()); curNode.setNext(newNode); listSize++; rc = true; } return rc;

//--------------------------------------------------public class Node { private Object object; private Node next; public Node(Object object) { this.object = object; this.next = null; } public Node getNext() { return next; } public void setNext(Node next) { this.next = next; } public Object getObject() { return object; } }

}

//---------------------------------------------------

public boolean remove(int index) { boolean result = false; Node curNode = head; Node prevNode = null;

public class LinkedList implements ListInterface { private Node head = null; private Node tail = null; private int listSize = 0;

if (index < listSize) { if (index == 0) { head = head.getNext(); result = true; } else { for ( int i = 0 ; i < index ; i++ ) { prevNode = curNode; curNode = curNode.getNext(); } prevNode.setNext(curNode.getNext()); if (index == (listSize - 1)) { tail = prevNode; } result = true; } listSize--; } return result;

public void add(Object obj) { Node newNode = new Node(obj); if (head == null) { head = newNode; } else { tail.setNext(newNode); } tail = newNode; listSize++; } public Object getObject(int index) { Object obj = null; Node curNode = head; if (index < listSize && head != null) { for ( int i = 0 ; i < index ; i++) { curNode = curNode.getNext(); } obj = curNode.getObject(); } return obj; }

} }

CMP-­‐338   Midterm  Spring  2015

Solutions   Version 2

Name:____________________________________

8. (40 Points) The correct BinarySearchTree implementation is: public class BinarySearchTree implements BinarySearchTreeInterface { private TreeNode root = null; @Override public boolean isEmpty() { return (root == null); } @Override public void makeEmpty() { root = null; } @Override public void insert(TreeItem item) { root = insertItem(root, item); } private TreeNode insertItem(TreeNode node, TreeItem newItem) { TreeNode newSubtree; if (node == null) { node = new TreeNode(newItem); return node; } if (newItem.compareTo(node.getItem()) < 0) { newSubtree = insertItem(node.getLeftChild(), newItem); node.setLeftChild(newSubtree); return node; } else { newSubtree = insertItem(node.getRightChild(), newItem); node.setRightChild(newSubtree); return node; } }

@Override public TreeItem retrieve(int key) { return retrieveItem(root, key); } private TreeItem retrieveItem(TreeNode node, int key) { TreeItem treeItem; TreeItem compareItem = new TreeItem(key); if (node == null) { treeItem = null; } else if (compareItem.compareTo(node.getItem()) == 0) { treeItem = node.getItem(); } else if (compareItem.compareTo(node.getItem()) < 0) { treeItem = retrieveItem(node.getLeftChild(), key); } else { treeItem = retrieveItem(node.getRightChild(), key); } return treeItem; } }

CMP-­‐338   Midterm  Spring  2015

Solutions   Version 2

9. (20 Points) The correct method for merging two arrays: public void merge(T[]a, T[]b, T[]c) { int firstA = 0; int lastA = a.length - 1; int firstB = 0; int lastB = b.length - 1; int cIindex = 0; while ((firstA <= lastA) && (firstB <= lastB)) { if (a[firstA].compareTo(b[firstB]) < 0) { c[cIindex] = a[firstA++]; } else { c[cIindex] = b[firstB++]; } cIindex++; } // end while while (firstA <= lastA) { c[cIindex++] = a[firstA++] ; } // end while

while (firstB <= lastB) { c[cIindex++] = b[firstB++]; } // end while }

Name:____________________________________

CMP-­‐338   Midterm  Spring  2015

Solutions   Version 2

Name:____________________________________

10. (16 Points) The following list of numbers: 25, 16, 33, 22, 10, 8, 7, 9, 5, 12, 29, 31, 40, 44, 30 inserted in the given order into: a. (4 Points) Into a Binary Search Tree produces the following tree:

b. (4 Points) Into a 2-3 Tree produces the following tree:

CMP-­‐338   Midterm  Spring  2015

Solutions   Version 2

Name:____________________________________

c. (4 Points) Into a 2-3-4 Tree produces the following tree:

d. (4 Points) The numbers in the following order produces a full Binary Search Tree: 22, 9, 7, 5, 8, 12, 10, 16, 31, 29, 25, 30, 40, 33, 44