Copyright © 2012 Pearson Education, Inc. Chapter 7 One Dimensional Arrays.

Copyright © 2012 Pearson Education, Inc.

Chapter 7

One Dimensional Arrays


OutlineObjectives

1. Arrays

2. Problem Solving Applied: Hurricane Categories

3. Statistical Measurements

4. Problem Solving Applied: Speech Signal Analysis

5. Sorting and Search Algorithms

6. Problem Solving Applied: Tsunami Warning Systems

7. Character Strings

8. The string class

9. The vector class

10.Problem Solving Applied: Calculating Probabilities


ObjectivesDevelop problem solutions in C++ containing:• One-dimensional arrays and vectors• Programmer-defined modules for statistical analysis of

data• Functions that sort data and search data• Functions that calculate the probability of an event• Character strings and string objects• Functions defined in the header files cstring and string• Custom header files

Arrays


Arrays Defined

• An array is a data structure for storing a contiguous block of data.

• All data elements in an array must be of the same type.

• Individual elements of the array are specified using the array name and an offset.

• In C++ the offset of the first element is always 0 (zero).


Array Definition Syntax


Syntax:data_type identifier[ [array_size] ] [= initialization_list ]; //array_size must be an integer constant

Examplesint data[5]; //allocates consecutive memory for 5 integer valueschar vowels[5] = {‘a', ‘e', ‘i', ‘o', ‘u'}; //allocates and initializesdouble t[100] = {0.0}; //allocates and initialized all values to 0.0

Valid Referencescout << vowels[0];cout << t[2];

Invalid Referencescout << vowel[5]; //invalid offset.cout << t[-1]; //invalid offset

7

Initializing Arrays

Initializing array elements (initialization=>declaration)char vowels[5] = {'a', 'e', 'i', 'o', 'u'};bool ansKey[] ={true, true, false, true, false, false};char word[] = "Hello";

vowels'a' 'e' 'i' 'o' 'u'

true falsefalsetruefalsetrue

ansKey

word'H' 'e' 'l' 'l' 'o' '\0'

Accessing Array Elements

• Offsets are used to access individual elements of an array.

• General format:array_identifier[offset]

• Examplefor (int i=0; i<=7; ++i)m[i] = double(i) + 0.5;

• Integer expressions may be used as offsets.– i.e. offset does not need to be constant


Avoiding Bugs

• C++ does not enforce array bounds!– Invalid references are NOT reported by the

compiler.– May or may not result in run-time error.

• E.g. segmentation fault, bus error, etc.• More often than not no run-time error occurs.

– Such errors are often difficult to identify.– Results in unpredictable program behavior.


Operator Precedence


Precedence Operator Associativity

1 () [] Innermost First

2 Unary operators: + - ++ -- ! (type) Right to left

3 * / % Left to right

4 + - Left to right

5 < <= > => Left to right

6 == != Left to right

7 && Left to right

8 || Left to right

9 ? : Right to left

10 = += -= *= /= %= Right to left

11 , Left to right

Functions and Arrays

• An array identifier, without subscripts, references the starting address(first element) of the array.

• In C++, arrays are passed by reference (i.e. the starting address is passed, no size information)

• Arrays in C++ do not know their size.

• Generally we specify an additional parameter representing the number of elements in the array.


Example

#include <iostream>using namespace std;const int MAXSIZE=20;void ReadArr(double a[], int& count, istream& in);int FindMin(const double a[], int count);

int main() { double darr[MAXSIZE]; int cnt=0, position=0; ReadArr(darr, cnt, cin); position = FindMin(darr, cnt); cout << "The smallest value in the array is " << darr[position] << endl;}


Example

// This function inputs values into an array until EOF // or array limit reachedvoid ReadArray(double a[], int& count, istream& in) {

double temp;count = 0;in >> temp;while ( (count < MAXSIZE) && !in.eof() ) {

a[count] = temp;++count;in >> temp;

}}


Example

//This function returns the offset of the smallest//value in an array

int FindMin(const double a[], int size) { int offsetOfMin = 0;

for (int i=1; i<size; ++i) {if (a[i] < a[offsetOfMin] ) {

offsetOfMin = i; } //end if } //end for

return offsetOfMin;} //end FindMin


Problem Solving Applied: Hurricane Categories


Hurricane Categories

• The Saffir-Simpson scale of hurricane intensities is used to classify hurricanes according to the amount of damage that the storm is likely to generate if it hits a populated area.


CategoryWind Speed

(mph)Storm Surge

(feet)Expected Property

Damage

1 74-95 4-5 Minimal

2 96-110 6-8 Moderate

3 111-130 9-12 Extensive

4 131-155 13-18 Extreme

5 155+ 18+ Catastrophic

Problem Solving Applied: Hurricane Categories


Statistical Measurements


Statistical Measurements

• Data collected from engineering experiments often have statistical properties that change from one data set to another.– E.g. sin(60) is always the same, but the miles

per gallon a vehicle consumes varies depending on type of driving, temperature, etc…


Simple Statistical Analyses

• Simple statistical analyses often involve computing properties of a data set such as:– Minimum value– Maximum value– Mean (average) value– Median (middle) value


Recall…


int FindMin(const double a[], int size) { int offsetOfMin = 0; for (int i=1; i<size; ++i) { if (a[i] < a[offsetOfMin] ) { offsetOfMin = i; } //end if } //end for return offsetOfMin;} //end FindMin


Question

• Given the previous algorithm for finding the offset of the minimum element of a data set, how can you modify it to find:– The offset of maximum element?– The value of the minimum element?– The value of the maximum element?


Offset of Maximum


int FindMin(const double a[], int size) { int offsetOfMin = 0; for (int i=1; i<size; ++i) { if (a[i] > a[offsetOfMin] ) { offsetOfMin = i; } //end if } //end for return offsetOfMin;} //end FindMin


Simply changing the relational operator in the FindMin algorithm with yield an algorithm that finds the offset of the maximum value!Note that identifiers are not meaningful to the compiler… identifiers are used only to uniquely identify (and type) variables.

Min and Max Offsets

//This function returns the //offset of the smallest//value in an array

int FindMin(const double a[], int size) { int offsetOfMin = 0; for (int i=1; i<size; ++i) { if (a[i] < a[offsetOfMin] ) { offsetOfMin = i; } //end if } //end for return offsetOfMin;} //end FindMin


//This function returns the //offset of the largest//value in an array

int FindMax(const double a[], int size) { int offsetOfMax = 0; for (int i=1; i<size; ++i) { if (a[i] > a[offsetOfMax] ) { offsetOfMax = i; } //end if } //end for return offsetOfMax;} //end FindMax

Min and Max Values

//This function returns the //value of the smallest//element in an array

double FindMinVal(const double a[], int size) { int offsetOfMin = 0; for (int i=1; i<size; ++i) { if (a[i] < a[offsetOfMin] ) { offsetOfMin = i; } //end if } //end for return a[offsetOfMin];} //end FindMinVal


//This function returns the //value of the largest//element in an array

double FindMaxVal(const double a[], int size) { int offsetOfMax = 0; for (int i=1; i<size; ++i) { if (a[i] > a[offsetOfMax] ) { offsetOfMax = i; } //end if } //end for return a[offsetOfMax];} //end FindMaxVal

Min and Max Values

//This function returns the //value of the smallest//element in an array

double FindMinVal(const double a[], int size) { return a[FindMin(a,size)];} //end FindMinVal


//This function returns the //value of the largest//element in an array

double FindMaxVal(const double a[], int size) { return a[FindMax(a,size)];} //end FindMaxVal

Computing the Mean

//This function computes the mean of a dataset //contained in an array. // Mean = Sum(all array elements)/sizedouble Mean(const double a[], int size) { double sum(0);

//compute the sum for (int i=0; i<size; ++i) sum += a[i];

//return the mean return sum/size;} //end Mean


Variance

• One of the most important statistical measurements for a data set is variance.

where σ2 is the variance and μ is the mean of all values x0, x1, … , xn-1.

Note – standard deviation is just σ.Copyright © 2012 Pearson Education, Inc.

Computing the Variance

//This function computes the variance of a dataset//contained in an array.

double Variance(const double a[], int n) { double sum(0), mu = mean(a,n);

//compute the sum for (int i=0; i<n; ++i) sum += (a[i]-mu)*(a[i]-mu);

//return the mean return sum/(n-1);} //end Variance


Custom Header Files

• Frequently used classes and functions may be stored in separate files to easily include them in other programs.

• Define code ‘libraries’• Header file named “library_name.h”• Implementation file named “library_name.cpp”• To use the library, #include “library_name.h” and

be sure the linker can find the implementation file.


stat_lib.h

//This header defines commonly used statistical //functions

#pragma once

int FindMin(const double [], int);int FindMax(const double [], int);double FindMinVal(const double [], int);double FindMaxVal(const double [], int);double Mean(const double [], int);double Variance(const double [], int);double StandardDeviation(const double [], int);


Problem Solving Applied: Speech Signal Analysis


Sorting and Searching Algorithms


Sorting Algorithms

• Sorting algorithms arrange the data into either ascending or descending order, based on the values in the array.

• Sorting algorithms to be discussed– Selection sort


Selection Sort Algorithm

• Find minimum value, place it in the first position.

• Find next minimum value, place it in the second position.

• Continue doing this until you have placed the second to the largest value in the second to the last position.


Selection Sort//This function sorts the array with n elements//into ascending order using selection sortvoid Sort(const double a[], int n) { double temp; int m; for (int k=0; k<=n-2; ++k) { //find position of smallest element beginning at k m = k; for (int j=k+1; j < n-1; ++j) if (a[j] < a[m]) m = j; //exchange smallest value with value at k temp = x[m]; x[m] = x[k]; x[k] = temp; } //end for (k)} //end Sort


Searching Algorithms

• Search algorithms are groupedaccording to those that required an ordered dataset and those that do not (i.e. unordered datasets).– Unordered datasets searched sequentially.– Ordered datasets may be searched

sequentially, however binary searches are more efficient.


Searching Unordered Datasets

• Simple Sequential Search– Examine each element starting with the first one until:

• a match is found.• end of the list is reached.

• Sequential search can be implemented as:– a function which returns true if item in the list, false if

item is not in the list.– a function which returns the location of the item if

found, or –1 if not found.


Searching Ordered Datasets

• Modified Sequential Search:– examine every element in the list until:

• item is found.• list element is larger/smaller than the item you are searching

for (search fails).

• Binary Search– Examine middle element:

• if element equals item, item found, return location.• if element is larger than item ignore bottom of list.• if element is smaller than item ignore top of list.

– Repeat until:• item is found.• top and bottom cross over (search failed).


Example of Binary Search for 48


7059564337282214115arr[top] arr[bot]

arr[mid] arr[bot]arr[top]

4337arr[top] arr[bot]

mid is 5

43arr[6]

arr[mid]

mid is 6

mid is 7 7059564337

43

arr[top]arr[bot]

Problem Solving Applied: Tsunami Warning

Systems


Character Strings


C-style Character Strings

• A C style strings is defined as a sequence of characters, terminated by the null character.

• When declaring a character array to store a C style string, memory must be allocated for the null character ('\0').

• Literal string constants are enclosed within double quote marks: "a string".


C-style String Input• Recall that the input operator (>>) skips

whitespace .• To input strings with embedded whitespace , the

getline() function can be used as illustrated:char phrase[SIZE];cin.getline(phrase, SIZE);

• The getline() function reads up to SIZE-1 characters from the input stream and will insert the null character.

• getline() is a member function of what class?


C-style String Functions• The Standard C++ library contains a set of

predefined functions that operate on C style strings.

• These functions are defined in the header file:cstring

• Commonly used string functions:– strlen()– strcpy()– strcat()– strcmp()


C-style String Example

#include <iostream>#include <cstring> //strcmp(), strcpy(), strcat()uses namespace std;void main() { char str1[30] = "John", str2[30] = "Johnson"; char phrase[20] = "'s shirt was green", sentence[30]; if (strcmp(str1,str2) < 0) strcpy (sentence, str1);//puts "John" into sentence else strcpy (sentence,str2);//puts "Johnson” into sentence strcat(sentence, phrase);//append phrase to sentence cout << "Sentence is: " << sentence << endl;}


Avoiding Bugs• The null character ( ‘\0’ ) must always

mark the end of the string.– If there is no null character, functions will

produce invalid references that can be difficult to identify (remember that C-style strings are 1D arrays of characters).

• String sizes are fixed.– Input operator does NOT ‘know’ what the array

size is; input may result in overflow of the array (invalid references).


The string Class


The String Class

• The string class implements the concept of a character string.

• A string object can increase and decrease its size dynamically.

• Numerous operators and methods are defined in the string class.


Common Methods of the string Class

– size( )– empty( )– substr (int start, int len)– c_str()


Operators Overloaded for the string Class

• relational operators – < > == <= >=

• concatenation– + +=

• assignment– =


String Class Example

#include <iostream>#include <string> //string classuses namespace std;void main() { string str1 = "John", str2 = "Johnson"; string phrase = "'s shirt was green", sentence; if ( str1< str2 ) sentence = str1;//puts "John" into sentence else sentence = str2;//puts "Johnson” into sentence sentence += phrase; //append phrase to sentence cout << "Sentence is: " << sentence << endl;}


The vector Class


The vector Class

• Predefined type included in theStandard Template Library

• Provides a generic implementation of the array concept.

• Vectors can increase and decrease its size dynamically.

• Numerous operators and methods are defined on vectors.


vector Examples

vector<char> v1;

//Define vector of type char, capacity 0.

vector<int> v2(10);

//Define v2 with capacity for 10 integers.

vector<string> v3(n);

//Define v3 with capacity for n strings.

vector<double> v4(n,1.0);

//Define v4 with capacity for n doubles.

//Initialize each element to 1.0.


Common Methods of the vector Class

– back()– begin()– capacity()– empty( )– end()– erase()– insert()– pop_back()– pop_front()– resize( ) – size( )


Passing string and vectorInstances to Functions

• Unlike arrays, objects of vector andstring types are passed by value to functions.– Thus a copy is made of the arguments to the function

call, and changes made to the formal parameter will NOT affect the argument value.

• Pass string and vector objects by reference to allow the function to alter the argument.

• Pass string and vector objects by const reference to avoid copying potentially large datasets.


Standard Template Library Algorithms

• Classes defined in the C++ STL are supported by a collection of top-level functions.– Defined in <algorithm>– Algorithms include search, sort,

random_shuffle, copy, random_sample, partition, transform, and others.

• See http://www.sgi.com/tech/stl/table_of_contents.html for STL documentation.


http://www.sgi.com/tech/stl/table_of_contents.html

Problem Solving Applied: Calculating Probabilities




Notation indicates that every CardDeck

has 52 Cards

Flowchart forCalculating Probabilities


Copyright © 2012 Pearson Education, Inc. Chapter 7 One Dimensional Arrays.

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Transcript of Copyright © 2012 Pearson Education, Inc. Chapter 7 One Dimensional Arrays.