Lecture 22:Applications of Arrays

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Lecture 22Applications of Arrays

• Introduction to Computer Science
• Spring 2006

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Contents

• Review of Arrays
• Application of Arrays

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Contents

• Review of Arrays
• Application of Arrays

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Arrays

• Array - a collection of a fixed number of
  elements
• All the elements of an array must be the same
  data type
• The elements of an array are stored sequentially
  in memory.
• One-dimensional array - an array in which the
  components are arranged in a list form
• The syntax for declaring a one-dimensional array
  is
• dataType arrayNameintExp
• where intExp is any expression that
  evaluates to a positive integer
• Example int num5

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include ltiostreamgt include ltiomanipgt using
namespace std const int arraySize 10 void
fill_Array(double list, int listSize)
for(int i0 iltlistSize i)
cingtgtlisti void print_Array(double list,
int listSize) for(int i0 iltlistSize i)
coutltltsetw(5)ltltlisti void
copy_Array(const double listOne, double
listTwo, int listOneSize) for(int i0
iltlistOneSize i) listTwoi
listOnei int indexLargestElement(double
list, int listSize) int maxIndex 0 for
(int i 0 i lt listSize i) if
( listmaxIndex lt listi )
maxIndex i return maxIndex int
main() double listAarraySize0 double
listBarraySize fill_Array(listA,
arraySize) print_Array(listA,
arraySize) copy_Array(listA, listB,
arraySize) coutltltThe position of the largest
element in listA is ltlt indexLargestElement(list
A, arraySize)
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Two-Dimensional Arrays

• Two-dimensional Array a collection of a fixed
  number of components arranged in two dimensions
• The syntax for declaring a two-dimensional array
  is
• dataType arrayNameintexp1intexp2
• where intexp1 and intexp2 are expressions
  yielding positive integer values

• Example double sales105

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Accessing Array Components

• The syntax to access a component of a
  two-dimensional array is
• arrayNameindexexp1indexexp2
• where indexexp1 and indexexp2 are expressions
  yielding nonnegative integer values
• Example sales5325.75

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Processing Two-Dimensional Arrays Row
processing and Column processing

• We can process a particular row or column of a
  two-dimensional array as a one-dimensional array
• use algorithms similar to processing
  one-dimensional arrays
• For example
• the following for loop initializes row four to
  zero
• row 4
• for(col 0 col lt columns col)
• matrixrowcol 0
• The following for loop inputs data in row 4 of
  matrix
• row 4
• for(col 0 col lt columns col)
• cingtgtmatrixrowcol

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Processing Two-Dimensional Arrays Entire Array

• We can process the entire array by using nested
  for loop
• Example
• The following nested for loop initialize the
  entire matrix
• for(row 0 row lt rows row)
• for(col 0 col lt columns col)
• matrixrowcol 0

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include ltiostreamgt include ltiomanipgt using
namespace std const int MAXI 10 const int
MAXJ 15 void init_matrix(double
matrixMAXIMAXJ) for(int i0 iltMAXI
i) for(int j0 jltMAXJ
j) matrixijij void
print_matrix(double matrixMAXIMAXJ) for(int
i0 iltMAXI i) for(int
j0 jltMAXJ j) coutltltsetw(5)ltltmatrixij
coutltltendl double
sum_matrix(double matrixMAXIMAXJ) double
sum0.0 for(int i0 iltMAXI i)
for(int j0 jltMAXJ j) sum sum
matrixij return sum int
main() double matrixMAXIMAXJ double
sum init_matrix(matrix) print_matrix(matrix)
sum sum_matrix(matrix) coutltlt"The sum of
all the elements of matrix is "ltltsumltltendl
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Contents

• Review of Arrays
• Application of Arrays
• sequential search algorithm
• bubble sort algorithm
• selection sort algorithm
• binary search algorithm

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List Processing

• List a set of values of the same type
• Basic list operations
• Search for a given item
• Sort the list
• Insert an item in the list
• Delete an item from the list

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Searching

• To search a list, you need
• The list (array) containing the list
• List length
• Item to be found
• After the search is completed
• If found,
• Report success
• Location where the item was found
• If not found, report failure

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Sequential Search

• Sequential search search a list for an item
• Compare search item with other elements until
  either
• Item is found
• List has no more elements left
• Average number of comparisons made by the
  sequential search equals half the list size
• Good only for very short lists

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int seqSearch(const int list, int listLength,
int searchItem) int loc for (loc 0 loc
lt listLength loc) if (listloc
searchItem) return loc return -1
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Sorting a List Bubble Sort

• Suppose list0...listn - 1 is a list of n
  elements, indexed 0 to n 1
• Bubble sort algorithm
• In a series of n - 1 iterations, compare
  successive elements, listindex and listindex
  1
• If listindex is greater than listindex 1,
  then swap them

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Bubble Sort Algorithm
for i 0 to n-1 do        for j 0 to n - i -
1 do        if listj gt listj1 then        
Swap(listj , listj1)
void bubbleSort(int list, int length) int
temp int i, j for (i 0 i lt length -
1 i) for (j 0 j lt length -
1 - i j) if (listj gt listj
1) temp
listj listj listj 1
listj 1 temp

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include ltiostreamgt using namespace std void
bubbleSort(int list, int length) int
main() int list 2, 56, 34, 25, 73, 46,
89, 10, 5, 16 //Line 1 int i

//Line 2
bubbleSort(list, 10)
//Line 3 cout ltlt
"After sorting, the list elements are" ltlt endl
//Line 4 for (i 0 i
lt 10 i) //Line 5
cout ltlt listi ltlt " "
//Line 6 cout ltlt endl
//Line 7 return
0
//Line 8 void bubbleSort(int list, int
length) int temp int counter, index
for (counter 0 counter lt length - 1
counter) for (index 0 index
lt length - 1 - counter index) if
(listindex gt listindex 1)
temp listindex
listindex listindex 1
listindex 1 temp
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Sorting a List Selection Sort

• Selection sort rearrange list by selecting an
  element and moving it to its proper position
• Find the smallest (or largest) element and move
  it to the beginning (end) of the list

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Sorting a List Selection Sort (continued)

• On successive passes, locate the smallest item in
  the list starting from the next element

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Selection Sort Algorithm
void selectionSort(int list, int length)
int index int smallestIndex int
minIndex int temp for (index 0 index lt
length - 1 index) //Step
a smallestIndex index for (minIndex
index 1 minIndex lt length minIndex) if
(listminIndex lt listsmallestIndex) smalles
tIndex minIndex //Step b temp
listsmallestIndex listsmallestIndex
listindex listindex temp
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Sorting a List Insertion Sort
The insertion sort algorithm sorts the list by
moving each element to its proper place.
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Sequential Search on an Ordered List

• General form of sequential search algorithm on a
  sorted list

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Sequential Search on an Ordered List
int seqOrderedSearch(const int list, int
listLength, int searchItem) int
loc //Line 1 bool found false //Line
2 for (loc 0 loc lt listLength
loc) //Line 3 if (listloc gt
searchItem) //Line 4 found
true //Line 5 break //Line 6
if (found) //Line 7 if
(listloc searchItem) //Line 8 return
loc //Line 9 else //Line 10
return -1 //Line 11 else //Line 12
return -1 //Line 13
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Binary Search

• Binary search can be applied to sorted lists
• Uses the divide and conquer technique
• Compare search item to middle element
• If search item is less than middle element,
  restrict the search to the lower half of the list
• Otherwise search the upper half of the list

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Binary Search
int binarySearch(const int list, int
listLength, int searchItem) int first
0 int last listLength - 1 int mid bool
found false while(first lt last
!found) mid (first last) /
2 if(listmid searchItem) found
true else if(listmid gt searchItem)
last mid - 1 else first mid
1 if(found) return mid else
return -1
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Binary Search (continued)

• Every iteration cuts size of search list in half
• If list L has 1000 items
• At most 11 iterations needed to determine if an
  item x is in list
• Every iteration makes 2 key (item) comparisons
• Binary search makes at most 22 key comparisons to
  determine if x is in L
• Sequential search makes 500 key comparisons
  (average) to if x is in L for the same size list

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End of lecture 22

• Thank you!