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Lecture 22:Applications 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 arrayName[intExp]; where intExp is any expression that evaluates to a positive integer

Example: int num[5];

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#include <iostream>#include <iomanip>using namespace std;const int arraySize = 10;

void fill_Array(double list[], int listSize) {

for(int i=0; i<listSize; ++i) cin>>list[i];

}

void print_Array(double list[], int listSize){

for(int i=0; i<listSize; ++i) cout<<setw(5)<<list[i];

}

void copy_Array(const double listOne[], double listTwo[], int listOneSize) {

for(int i=0; i<listOneSize; ++i) listTwo[i] = listOne[i];

}

int indexLargestElement(double list[], int listSize){

int maxIndex = 0;for (int i = 0; i < listSize; i++) if ( list[maxIndex] < list[i] ) maxIndex = i;

return maxIndex; }int main(){

double listA[arraySize]={0};double listB[arraySize];

fill_Array(listA, arraySize);print_Array(listA, arraySize);copy_Array(listA, listB, arraySize);cout<<“The position of the largest element in listA is: ” << indexLargestElement(listA, 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 arrayName[intexp1][intexp2];where intexp1 and intexp2 are expressions yielding positive integer values

Example: double sales[10][5];

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Accessing Array Components The syntax to access a component of a two-dimensional array is:

arrayName[indexexp1][indexexp2]where indexexp1 and indexexp2 are expressions yielding nonnegative integer values

Example: sales[5][3]=25.75;

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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 < columns; col++) matrix[row][col] = 0;

The following for loop inputs data in row 4 of matrix:row = 4;for(col = 0; col < columns; col++) cin>>matrix[row][col];

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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 < rows; row++){

for(col = 0; col < columns; col++){ matrix[row][col] = 0;}

}

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#include <iostream>#include <iomanip>using namespace std;const int MAXI = 10;const int MAXJ = 15;

void init_matrix(double matrix[MAXI][MAXJ]) {

for(int i=0; i<MAXI; ++i) for(int j=0; j<MAXJ; ++j)

matrix[i][j]=i+j;}

void print_matrix(double matrix[MAXI][MAXJ]){

for(int i=0; i<MAXI; ++i){ for(int j=0; j<MAXJ; ++j)

cout<<setw(5)<<matrix[i][j]; cout<<endl;}

}

double sum_matrix(double matrix[MAXI][MAXJ]){

double sum=0.0;for(int i=0; i<MAXI; ++i) for(int j=0; j<MAXJ; ++j)

sum = sum + matrix[i][j];return sum;

}

int main(){

double matrix[MAXI][MAXJ];double sum;

init_matrix(matrix);print_matrix(matrix);sum = sum_matrix(matrix);

cout<<"The sum of all the elements of matrix is "<<sum<<endl;}

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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:

1. Search for a given item

2. Sort the list

3. Insert an item in the list

4. Delete an item from the list

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Searching

To search a list, you need1. The list (array) containing the list2. List length3. Item to be found

After the search is completed4. If found,

Report “success” Location where the item was found

5. 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 < listLength; loc++) if (list[loc] == searchItem)

return loc;

return -1;}

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Sorting a List: Bubble Sort

Suppose list[0]...list[n - 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, list[index] and list[index + 1]

If list[index] is greater than list[index + 1], then swap them

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void bubbleSort(int list[], int length){ int temp; int i, j;

for (i = 0; i < length - 1; i++) { for (j = 0; j < length - 1 - i; j++) if (list[j] > list[j + 1]) { temp = list[j]; list[j] = list[j + 1]; list[j + 1] = temp; } }}

Bubble Sort Algorithm

for i = 0 to n-1 do        for j = 0 to n - i - 1 do        if list[j] > list[j+1] then         Swap(list[j] , list[j+1])

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#include <iostream>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 << "After sorting, the list elements are:" << endl; //Line 4

for (i = 0; i < 10; i++) //Line 5 cout << list[i] << " "; //Line 6

cout << endl; //Line 7

return 0; //Line 8}

void bubbleSort(int list[], int length){ int temp; int counter, index;

for (counter = 0; counter < length - 1; counter++) { for (index = 0; index < length - 1 - counter; index++) if (list[index] > list[index + 1]) { temp = list[index]; list[index] = list[index + 1]; list[index + 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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void selectionSort(int list[], int length){ int index;

int smallestIndex;int minIndex;int temp;

for (index = 0; index < length - 1; index++) {

//Step asmallestIndex = index;

for (minIndex = index + 1; minIndex < length; minIndex++)

if (list[minIndex] < list[smallestIndex])smallestIndex = minIndex;

//Step b temp = list[smallestIndex];

list[smallestIndex] = list[index];list[index] = temp;

}}

Selection Sort Algorithm

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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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int seqOrderedSearch(const int list[], int listLength, int searchItem){ int loc; //Line 1 bool found = false; //Line 2

for (loc = 0; loc < listLength; loc++) //Line 3 if (list[loc] >= searchItem) //Line 4 {

found = true; //Line 5 break; //Line 6

} if (found) //Line 7 if (list[loc] == searchItem) //Line 8

return loc; //Line 9 else //Line 10

return -1; //Line 11else //Line 12 return -1; //Line 13

}

Sequential Search on an Ordered List

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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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int binarySearch(const int list[], int listLength, int searchItem){

int first = 0;int last = listLength - 1;int mid;

bool found = false;

while(first <= last && !found){

mid = (first + last) / 2;

if(list[mid] == searchItem)found = true;

else if(list[mid] > searchItem)

last = mid - 1; else

first = mid + 1;}

if(found) return mid;

else return -1;

}

Binary Search

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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!