1. What makes a program easy to modify?
2. Describe the order of magnitude of the following code section using Big(O) notation.
j = 1;
While (j < N)
{
j = j * 2);
}
3. What are the benefits we accrue by using a Java interface construct to formally specify the logical level of ADTs?
4. Suppose we have a linked list of Strings, as defined in the textbook, named presidents. Suppose it contains three nodes, with the first node holding "Adams", the second node "Washington", and the third node "Kennedy". What would be output by the following code:
LLStringNode temp = presidents;
while (temp != null)
{
temp = temp.getLink();
}
System.out.println(temp.getInfo());
5. Suppose a collection object is defined to hold elements of class Object, and you use it to store String objects. Describe what you must do when you retrieve an object from the collection and intend to use it as a String.
6. Show what is written by the following segment of code, given that item1, item2, and item3 are int variables, and stack is an object that fits our abstract description of a stack. Assume that you can store and retrieve variables of type int on stack.
item1 = 1;
item2 = 0;
item3 = 4;
stack.push(item2);
stack.push(item1);
stack.push(item1 + item3);
item2 = stack.top();
stack.push (item3*item3);
stack.push(item2);
stack.push(3);
item1 = stack.top();
stack.pop();
System.out.println(item1 + " " + item2 + " " + item3);
while (!stack.isEmpty())
{
item1 = stack.top();
stack.pop();
System.out.println(item1);
}
7. Explain the relationship between dynamic storage allocation and recursion.
8. Analyze the factorial method and answer the following questions:
int factorial (int n)
{
if (n > 0)
return (n * factorial (n - 1));
else
if (n == 0)
return 1;
}
a. What is the base case?
b. What is the general case?
c. What are the constraints on the argument values?
d. What does the method do?
9. What are the three interfaces we defined related to our Queue ADT?
10. Describe in general terms the approach we use to implement an unbounded queue based on an array.
11. What does it mean for a class's equals and compareTo methods to be "consistent"?
12. Questions a-e below refer to the following figure:
a. What are the ancestors of node J?
b. What are the descendants of node T?
c. What are the descendants of node B?
d. What is the order in which the nodes are visited by a preorder traversal?
e. What is the order in which the nodes are visited by a postorder traversal?
13. If a heap is used to implement a priority queue, what is the Big O efficiency of the enqueue operation, assuming the size of the priority queue is N?
14. What would be the order of the following list after two iterations of the "inner" part of the Insertion Sort algorithm?
13 4 16 19 2 15 12 3 23 20
15. Suppose we are using Merge Sort to sort the following list of numbers. What would be the order of the list immediately before the execution of the merge method in the original (non-recursive) call to mergesort?
13 4 16 19 2 15 12 3 23 20
16. Programming Sorting Algorithms: For this section, use the Sorts.java test harness (provided by instructor).
a. Describe an approach to modifying the Sorts.java program so that after calling a sorting method the program prints out the number of swaps needed by the sorting method.
b. Implement your approach.
c. Test your new program by running the selectionSort method. Your program should report 49 swaps.
d. Now, modify your program to also output the number of comparisons (compares) needed. You must include one or more statements to increment your counter within the sorting methods themselves. For each of the listed methods, make and test the changes needed, and list both the number of swaps and the number of compares needed by the Sorts program to sort an array of 50 random integers.
selectionSort swaps:____ compares:____
bubbleSort swaps:____ compares:____
shortBubble swaps:____ compares:____
insertionSort swaps:____ compares:____
//----------------------------------------------------------------------------
// Sorts.java
//
// Test harness used to run sorting algorithms.
//----------------------------------------------------------------------------
import java.util.*;
import java.text.DecimalFormat;
public class Sorts
{
static final int SIZE = 50; // size of array to be sorted
static int[] values = new int[SIZE]; // values to be sorted
static void initValues()
// Initializes the values array with random integers from 0 to 99.
{
Random rand = new Random();
for (int index = 0; index < SIZE; index++)
values[index] = Math.abs(rand.nextInt()) % 100;
}
static public boolean isSorted()
// Returns true if the array values are sorted and false otherwise.
{
boolean sorted = true;
for (int index = 0; index < (SIZE - 1); index++)
if (values[index] > values[index + 1])
sorted = false;
return sorted;
}
static public void swap(int index1, int index2)
// Precondition: index1 and index2 are >= 0 and < SIZE.
//
// Swaps the integers at locations index1 and index2 of the values array.
{
int temp = values[index1];
values[index1] = values[index2];
values[index2] = temp;
}
static public void printValues()
// Prints all the values integers.
{
int value;
DecimalFormat fmt = new DecimalFormat("00");
System.out.println("The values array is:");
for (int index = 0; index < SIZE; index++)
{
value = values[index];
if (((index + 1) % 10) == 0)
System.out.println(fmt.format(value));
else
System.out.print(fmt.format(value) + " ");
}
System.out.println();
}
/////////////////////////////////////////////////////////////////
//
// Selection Sort
static int minIndex(int startIndex, int endIndex)
// Returns the index of the smallest value in
// values[startIndex]..values[endIndex].
{
int indexOfMin = startIndex;
for (int index = startIndex + 1; index <= endIndex; index++)
if (values[index] < values[indexOfMin])
indexOfMin = index;
return indexOfMin;
}
static void selectionSort()
// Sorts the values array using the selection sort algorithm.
{
int endIndex = SIZE - 1;
for (int current = 0; current < endIndex; current++)
swap(current, minIndex(current, endIndex));
}
/////////////////////////////////////////////////////////////////
//
// Bubble Sort
static void bubbleUp(int startIndex, int endIndex)
// Switches adjacent pairs that are out of order
// between values[startIndex]..values[endIndex]
// beginning at values[endIndex].
{
for (int index = endIndex; index > startIndex; index--)
if (values[index] < values[index - 1])
swap(index, index - 1);
}
static void bubbleSort()
// Sorts the values array using the bubble sort algorithm.
{
int current = 0;
while (current < (SIZE - 1))
{
bubbleUp(current, SIZE - 1);
current++;
}
}
/////////////////////////////////////////////////////////////////
//
// Short Bubble Sort
static boolean bubbleUp2(int startIndex, int endIndex)
// Switches adjacent pairs that are out of order
// between values[startIndex]..values[endIndex]
// beginning at values[endIndex].
//
// Returns false if a swap was made; otherwise, returns true.
{
boolean sorted = true;
for (int index = endIndex; index > startIndex; index--)
if (values[index] < values[index - 1])
{
swap(index, index - 1);
sorted = false;
}
return sorted;
}
static void shortBubble()
// Sorts the values array using the bubble sort algorithm.
// The process stops as soon as values is sorted.
{
int current = 0;
boolean sorted = false;
while ((current < (SIZE - 1)) && !sorted)
{
sorted = bubbleUp2(current, SIZE - 1);
current++;
}
}
/////////////////////////////////////////////////////////////////
//
// Insertion Sort
static void insertItem(int startIndex, int endIndex)
// Upon completion, values[0]..values[endIndex] are sorted.
{
boolean finished = false;
int current = endIndex;
boolean moreToSearch = true;
while (moreToSearch && !finished)
{
if (values[current] < values[current - 1])
{
swap(current, current - 1);
current--;
moreToSearch = (current != startIndex);
}
else
finished = true;
}
}
static void insertionSort()
// Sorts the values array using the insertion sort algorithm.
{
for (int count = 1; count < SIZE; count++)
insertItem(0, count);
}
/////////////////////////////////////////////////////////////////
//
// Merge Sort
static void merge (int leftFirst, int leftLast, int rightFirst, int rightLast)
// Preconditions: values[leftFirst]..values[leftLast] are sorted.
// values[rightFirst]..values[rightLast] are sorted.
//
// Sorts values[leftFirst]..values[rightLast] by merging the two subarrays.
{
int[] tempArray = new int [SIZE];
int index = leftFirst;
int saveFirst = leftFirst; // to remember where to copy back
while ((leftFirst <= leftLast) && (rightFirst <= rightLast))
{
if (values[leftFirst] < values[rightFirst])
{
tempArray[index] = values[leftFirst];
leftFirst++;
}
else
{
tempArray[index] = values[rightFirst];
rightFirst++;
}
index++;
}
while (leftFirst <= leftLast)
// Copy remaining items from left half.
{
tempArray[index] = values[leftFirst];
leftFirst++;
index++;
}
while (rightFirst <= rightLast)
// Copy remaining items from right half.
{
tempArray[index] = values[rightFirst];
rightFirst++;
index++;
}
for (index = saveFirst; index <= rightLast; index++)
values[index] = tempArray[index];
}
static void mergeSort(int first, int last)
// Sorts the values array using the merge sort algorithm.
{
if (first < last)
{
int middle = (first + last) / 2;
mergeSort(first, middle);
mergeSort(middle + 1, last);
merge(first, middle, middle + 1, last);
}
}
/////////////////////////////////////////////////////////////////
//
// Quick Sort
static int split(int first, int last)
{
int splitVal = values[first];
int saveF = first;
boolean onCorrectSide;
first++;
do
{
onCorrectSide = true;
while (onCorrectSide) // move first toward last
if (values[first] > splitVal)
onCorrectSide = false;
else
{
first++;
onCorrectSide = (first <= last);
}
onCorrectSide = (first <= last);
while (onCorrectSide) // move last toward first
if (values[last] <= splitVal)
onCorrectSide = false;
else
{
last--;
onCorrectSide = (first <= last);
}
if (first < last)
{
swap(first, last);
first++;
last--;
}
} while (first <= last);
swap(saveF, last);
return last;
}
static void quickSort(int first, int last)
{
if (first < last)
{
int splitPoint;
splitPoint = split(first, last);
// values[first]..values[splitPoint - 1] <= splitVal
// values[splitPoint] = splitVal
// values[splitPoint+1]..values[last] > splitVal
quickSort(first, splitPoint - 1);
quickSort(splitPoint + 1, last);
}
}
/////////////////////////////////////////////////////////////////
//
// Heap Sort
static int newHole(int hole, int lastIndex, int item)
// If either child of hole is larger than item this returns the index
// of the larger child; otherwise it returns the index of hole.
{
int left = (hole * 2) + 1;
int right = (hole * 2) + 2;
if (left > lastIndex)
// hole has no children
return hole;
else
if (left == lastIndex)
// hole has left child only
if (item < values[left])
// item < left child
return left;
else
// item >= left child
return hole;
else
// hole has two children
if (values[left] < values[right])
// left child < right child
if (values[right] <= item)
// right child <= item
return hole;
else
// item < right child
return right;
else
// left child >= right child
if (values[left] <= item)
// left child <= item
return hole;
else
// item < left child
return left;
}
static void reheapDown(int item, int root, int lastIndex)
// Precondition: Current root position is "empty".
//
// Inserts item into the tree and ensures shape and order properties.
{
int hole = root; // current index of hole
int newhole; // index where hole should move to
newhole = newHole(hole, lastIndex, item); // find next hole
while (newhole != hole)
{
values[hole] = values[newhole]; // move value up
hole = newhole; // move hole down
newhole = newHole(hole, lastIndex, item); // find next hole
}
values[hole] = item; // fill in the final hole
}
static void heapSort()
// Sorts the values array using the heap sort algorithm.
{
int index;
// Convert the array of values into a heap.
for (index = SIZE/2 - 1; index >= 0; index--)
reheapDown(values[index], index, SIZE - 1);
// Sort the array.
for (index = SIZE - 1; index >=1; index--)
{
swap(0, index);
reheapDown(values[0], 0, index - 1);
}
}
/////////////////////////////////////////////////////////////////
//
// Main
public static void main(String[] args)
{
initValues();
printValues();
System.out.println("values is sorted: " + isSorted());
System.out.println();
// make call to sorting method here (just remove //)
// selectionSort();
// bubbleSort();
// shortBubble();
// insertionSort();
// mergeSort(0, SIZE - 1);
// quickSort(0, SIZE - 1);
// heapSort();
printValues();
System.out.println("values is sorted: " + isSorted());
System.out.println();
}
}