1 c++ classes and data structures jeffrey s. childs chapter 2 overloaded operators, class templates,...
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1
C++ Classes and Data StructuresJeffrey S. Childs
Chapter 2Overloaded Operators, Class
Templates, and Abstraction
Jeffrey S. Childs
Clarion University of PA
© 2008, Prentice Hall
2
Binary Operators
• A binary operator acts upon two operands
x + a
binary operator
operands
3
Overloaded Operators
• The operands can be constants, variables, or objects
• If one or more of the operands are objects, the operator must be an overloaded operator
• An overloaded operator calls a function, which carries out the operation
4
1 struct CarType {2 string maker;3 int year;4 float price;
5 bool operator >( int num ) 6 { if ( price > num ) return true; return false; }6 };7
8 int main( )9 {
10 CarType myCar;...
16 if ( myCar > 2000 )17 cout << “My car is more than 2000!” << endl;18 return 0;19 }
Example
5
The Function Call
• “myCar > 2000” is the function call
• The operator > function is called for the myCar object
• The right operand is always passed as a parameter into the function
6
1 struct CarType {2 string maker;3 int year;4 float price;
5 bool operator >( int num ) 6 { if ( price > num ) return true; return false; }6 };7
8 int main( )9 {
10 CarType myCar;...
16 if ( myCar > 2000 )17 cout << “My car is more than 2000!” << endl;18 return 0;19 }
Right Operand
7
1 struct CarType {2 string maker;3 int year;4 float price;5 bool operator >( int num ) 6 { if ( price > num ) return true; else return false; }7 bool operator >( CarType car ) 8 { if ( price > car.price ) return true; else return false; }9 };
Adding Another Overloaded Operator > for
“myCar > yourCar”
8
struct CarType {string maker;int year;float price;bool operator >( int num ) { if ( price > num ) return true; else
return false; }bool operator >( CarType car ) { if ( price > car.price ) return true; else
return false; }float operator +( CarType car ) { return price + car.price; }
};
Adding an Overloaded Operator + for “myCar + yourCar”
9
Where to Place Overloaded Operator Functions
• If the left operand is an object of a struct, place the overloaded operator within the struct definition (as shown previously)
• If the left operand is not an object, place the overloaded operator directly underneath the struct definition
10
struct CarType {string maker;int year;float price;...float operator +( CarType car ) { return price + car.price; }
};
bool operator <( int num, CarType car ) { if ( num < car.price ) return true; else
return false; }
Adding an Overloaded Operator for “2000 < myCar”
11
struct Check {float checkAmount;int checkNum;string date;string receiver;
};
A Check Struct for the Checkbook Class
(to Replace float)
12
class Checkbook{public:
void setBalance( float amount );bool writeCheck( float amount ); void deposit( float amount );float getBalance( );float getLastCheck( );float getLastDeposit( );
private:float balance;float lastCheck;float lastDeposit;
};
The First Class
13
class Checkbook {public:
void setBalance( float amount );bool writeCheck( Check amount ); void deposit( float amount );float getBalance( );Check getLastCheck( );float getLastDeposit( );
private:float balance;Check lastCheck;float lastDeposit;
};
The Second Class
Check struct placed hereNecessary, so the compiler knows what “Check” is
14
Class Templates
• Instead of making different classes for different data types, we can make one class template.
• A class template is a blueprint for making a class.
• The client uses one line of code to have the compiler make a class from the class template.
• The client can make his/her own Check struct for the Checkbook, and place it in the main program.
15
class Checkbook {public:
void setBalance( float amount );
bool writeCheck( Check amount ); void deposit( float amount );float getBalance( );
Check getLastCheck( );float getLastDeposit( );
private:float balance;
Check lastCheck;float lastDeposit;
};
Making a Class TemplateCheck struct placed here
First, we don’t need the Check struct here – the client can make it the way they want in the main program (the compiler will see it before it makes the class)
16
class Checkbook {public:
void setBalance( float amount );
bool writeCheck( Check amount ); void deposit( float amount );float getBalance( );
Check getLastCheck( );float getLastDeposit( );
private:float balance;
Check lastCheck;float lastDeposit;
};
Making a Class Template (cont.)
17
class Checkbook {public:
void setBalance( float amount );
bool writeCheck( Check amount ); void deposit( float amount );float getBalance( );
Check getLastCheck( );float getLastDeposit( );
private:float balance;
Check lastCheck;float lastDeposit;
};
Making a Class Template (cont.)
Now, we need a special line of code to tell the compiler this is a class template
18
template <class DataType>class Checkbook {public:
void setBalance( float amount );
bool writeCheck( Check amount ); void deposit( float amount );float getBalance( );
Check getLastCheck( );float getLastDeposit( );
private:float balance;
Check lastCheck;float lastDeposit;
};
Making a Class Template (cont.)
Now, we need a special line of code to tell the compiler this is a class template
19
template <class DataType>class Checkbook {public:
void setBalance( float amount );
bool writeCheck( Check amount ); void deposit( float amount );float getBalance( );
Check getLastCheck( );float getLastDeposit( );
private:float balance;
Check lastCheck;float lastDeposit;
};
Making a Class Template (cont.)
you can think of DataType as a “variable name” for a data type – its value can be “float” or “Check” or anything else the client would like it to be
20
template <class DataType>class Checkbook {public:
void setBalance( float amount );
bool writeCheck( Check amount ); void deposit( float amount );float getBalance( );
Check getLastCheck( );float getLastDeposit( );
private:float balance;
Check lastCheck;float lastDeposit;
};
Making a Class Template (cont.)
Now, since we are using a more general DataType, we use it for the type wherever appropriate
21
template <class DataType>class Checkbook {public:
void setBalance( float amount );
bool writeCheck( Check amount ); void deposit( float amount );float getBalance( );
Check getLastCheck( );float getLastDeposit( );
private:float balance;
Check lastCheck;float lastDeposit;
};
Making a Class Template (cont.)
22
template <class DataType>class Checkbook {public:
void setBalance( float amount );
bool writeCheck( DataType amount ); void deposit( float amount );float getBalance( );
Check getLastCheck( );float getLastDeposit( );
private:float balance;
Check lastCheck;float lastDeposit;
};
Making a Class Template (cont.)
23
template <class DataType>class Checkbook {public:
void setBalance( float amount );
bool writeCheck( DataType amount ); void deposit( float amount );float getBalance( );
Check getLastCheck( );float getLastDeposit( );
private:float balance;
Check lastCheck;float lastDeposit;
};
Making a Class Template (cont.)
24
template <class DataType>class Checkbook {public:
void setBalance( float amount );
bool writeCheck( DataType amount ); void deposit( float amount );float getBalance( );
DataType getLastCheck( );float getLastDeposit( );
private:float balance;
Check lastCheck;float lastDeposit;
};
Making a Class Template (cont.)
25
template <class DataType>class Checkbook {public:
void setBalance( float amount );
bool writeCheck( DataType amount ); void deposit( float amount );float getBalance( );
DataType getLastCheck( );float getLastDeposit( );
private:float balance;
Check lastCheck;float lastDeposit;
};
Making a Class Template (cont.)
26
template <class DataType>class Checkbook {public:
void setBalance( float amount );
bool writeCheck( DataType amount ); void deposit( float amount );float getBalance( );
DataType getLastCheck( );float getLastDeposit( );
private:float balance;
DataType lastCheck;float lastDeposit;
};
Making a Class Template (cont.)
27
template <class DataType>class Checkbook {public:
void setBalance( float amount );
bool writeCheck( DataType amount ); void deposit( float amount );float getBalance( );
DataType getLastCheck( );float getLastDeposit( );
private:float balance;
DataType lastCheck;float lastDeposit;
};
Making a Class Template (cont.)
Finally, we add a line to include the implementation file (not done in an ordinary class)
28
template <class DataType>class Checkbook {public:
void setBalance( float amount );
bool writeCheck( DataType amount ); void deposit( float amount );float getBalance( );
DataType getLastCheck( );float getLastDeposit( );
private:float balance;
DataType lastCheck;float lastDeposit;
};
#include “checkbook.cpp”
Making a Class Template (cont.)
Finally, we add a line to include the implementation file (not done in an ordinary class)
29
template <class DataType>class Checkbook {public:
void setBalance( float amount );
bool writeCheck( DataType amount ); void deposit( float amount );float getBalance( );
DataType getLastCheck( );float getLastDeposit( );
private:float balance;
DataType lastCheck;float lastDeposit;
};
#include “checkbook.cpp”
Making a Class Template (cont.)
The client can also have the compiler make more than one class from the class template, each having a different type for DataType
30
18 template <class DataType>19 void Checkbook<DataType>::setBalance( float amount )20 {21 balance = amount;22 }
The Implementation File for a Class Template
In a class template, we don’t include the class specification file at the top of the implementation file.
31
23 template <class DataType>24 bool Checkbook<DataType>::writeCheck( DataType amount )25 {26 if ( amount > balance )27 return false;28 balance -= amount;29 lastCheck = amount;30 return true;31 }
The Implementation File for a Class Template (cont.)
32
23 template <class DataType>24 bool Checkbook<DataType>::writeCheck( DataType amount )25 {26 if ( amount > balance )27 return false;28 balance -= amount;29 lastCheck = amount;30 return true;31 }
The Implementation File for a Class Template (cont.)
If the client wants to use a Check struct for DataType, we have some overloaded operators here…
33
23 template <class DataType>24 bool Checkbook<DataType>::writeCheck( DataType amount )25 {26 if ( amount > balance )27 return false;28 balance -= amount;29 lastCheck = amount;30 return true;31 }
The Implementation File for a Class Template (cont.)
struct assignment is allowed
34
32 template <class DataType>33 void Checkbook<DataType>::deposit( float amount )34 {35 balance += amount;36 lastDeposit = amount;37 }3839 template <class DataType>40 float Checkbook<DataType>::getBalance( ) 41 {42 return balance;43 }
The Implementation File for a Class Template (cont.)
35
61 template <class DataType>62 DataType Checkbook<DataType>::getLastCheck( )63 {64 return lastCheck;65 }6667 template <class DataType>68 float Checkbook<DataType>::getLastDeposit( )69 {70 return lastDeposit;71 }
The Implementation File for a Class Template (cont.)
36
// checkbook.h – a class template for a Checkbook, where the// check is any data type
// to use an object for the DataType, overload the following // operators:// > left operand: object right operand: float// used to compare the amount of the check in the// struct object with the balance// -= left operand: float right operand: object// used to subtract the amount of the check in the// struct object from the balance
Example of Comments for a Class Template
Place these comments above the class template
37
1 #include <iostream>2 #include <iomanip>3 #include <string>4 #include "checkbook.h"56 using namespace std;
Program Using the Class Template
Needed in the main program for both classes and class templates
38
7 struct MyCheck {8 float amt;9 int checkNum;10 string checkComment;11 bool operator >( float bal ) 12 { if ( amt > bal ) return true; return false; }13 };1415 void operator -=( float & bal, MyCheck ch ) 16 { bal -= ch.amt; }
Program Using the Class Template (cont.)
from writeCheck:
26 if ( amount > balance )
from writeCheck:
28 balance -= amount;
39
17 int main( )18 {19 Checkbook<float> johnsCheckbook;20 Checkbook<MyCheck> susansCheckbook;2122 MyCheck susansCheck;23 float amount;24 bool johnsCheckAccepted = false, 25 susansCheckAccepted = false;
Program Using the Class Template (cont.)
40
26 johnsCheckbook.setBalance( 1000 );27 susansCheckbook.setBalance( 2000 );2829 cout << "John, your balance is $1000.00." << endl;30 cout << "Susan, your balance is $2000.00." << endl;
Program Using the Class Template (cont.)
41
31 cout << "John, enter your check amount: $";32 cin >> amount;33 if ( johnsCheckbook.writeCheck( amount ) ) {34 cout << "Your check was accepted." << endl;35 johnsCheckAccepted = true;36 }37 else38 cout << 39 “Check amount is higher than balance” << endl;
Program Using the Class Template (cont.)
42
40 cout << "Susan, enter the check number for your check: ";41 cin >> susansCheck.checkNum;42 cin.ignore( );43 cout << "Please also enter any comment you wish” << 44 “ to make about the check: “ << endl;45 getline( cin, susansCheck.checkComment );46 cout << "Susan, enter your check amount: $";47 cin >> susansCheck.amt;
Program Using the Class Template (cont.)
43
48 if ( susansCheckbook.writeCheck( susansCheck ) ) {49 cout << "Your check was accepted." << endl;50 susansCheckAccepted = true;51 }52 else53 cout << 54 “Check amount is higher than balance” << endl;
Program Using the Class Template (cont.)
44
55 cout << fixed << showpoint << setprecision( 2 );56 cout << "John, your balance is: $" <<
57 johnsCheckbook.getBalance( ) << endl;58 if ( johnsCheckAccepted )59 cout << "Your last check amount is: $" << 60 johnsCheckbook.getLastCheck( ) << endl;61 cout << "Susan, your balance is: $" << 62 susansCheckbook.getBalance( ) << endl;
Program Using the Class Template (cont.)
45
63 if ( susansCheckAccepted ) {64 MyCheck testSusansCheck;65 testSusansCheck = susansCheckbook.getLastCheck( );66 cout << "Your last check amount was: $" <<67 testSusansCheck.amt << endl;68 cout << "for check number: " << 69 testSusansCheck.checkNum << endl;70 cout << "with check comment: " << 71 testSusansCheck.checkComment << endl;72 }7374 return 0;75 }
Program Using the Class Template (cont.)
46
Stack
• A stack is a data structure
• It is like a stack of plates, except it is a stack of data
• It can be a stack of int’s, a stack of float’s, a stack of strings, a stack of struct objects, etc.– why class templates are used for data
structures
47
Push
• Push means place a new data element at the top of the stack
17
5
11
3
48
Push (cont.)
17
5
11
3
• Push means place a new data element at the top of the stack
49
Push (cont.)
17
5
11
3
• Push means place a new data element at the top of the stack
50
Push (cont.)
17
5
11
3
• Push means place a new data element at the top of the stack
51
Pop
• Pop means take a data element off the top of the stack
17
5
11
3
52
Pop (cont.)
• Pop means take a data element off the top of the stack
17
5
11
3
53
Pop (cont.)
• Pop means take a data element off the top of the stack
17
5
11
3
54
Pop (cont.)
• Pop means take a data element off the top of the stack
17
5
11
3
55
Peek
• Peek means retrieve the top of the stack without removing it
17
5
11
3
56
Peek (cont.)
• Peek means retrieve the top of the stack without removing it
17
5
11
3
3
57
Peek (cont.)
• Peek means retrieve the top of the stack without removing it
17
5
11
3
3
58
Abstraction• Abstraction occurs when we use something
without thinking about the details of how it works– Driving a car– The string class
• An abstract data type (ADT) is a data type that contains both data and functions (operations on data); we use the functions without thinking about how they work
• The stack is an abstract data type• Abstraction makes large program development
much easier
59
Chapter 2 Exercises
• A stack is often used as an aid in more complex algorithms
• For example, stacks can be used in expression evaluation
• Consider the problem of having the user enter an expression to be evaluated– must account for operator precedence: 5 + 2 * 3– may be an indefinite number of nested parentheses:
( ( 5 + 2 ) * 3 + 4 ) / 5• Ordinarily, this would be a very difficult problem,
but an algorithm using stacks makes it easy
60
Chapter 2 Exercises (cont.)
• First, a stack is used to convert an infix expression to a postfix expression
• Then, a stack is used to evaluate the postfix expression
• The following slides show how…
61
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 )
Postfix Expression:
Stack
Infix to Postfix Conversion
62
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 )
Postfix Expression:
First, we push an ‘(‘ onto an empty stack.
Infix to Postfix Conversion (cont.)
63
Stack(
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 )
Postfix Expression:
First, we push an ‘(‘ onto an empty stack.
Infix to Postfix Conversion (cont.)
64
( Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 )
Postfix Expression:
Then, we append a ‘)’ to the infix expression
Infix to Postfix Conversion (cont.)
65
( Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:
Then, we append a ‘)’ to the infix expression
Infix to Postfix Conversion (cont.)
66
( Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:
Then, we read “tokens” from the infix expression, performing actions based on what we read.
Infix to Postfix Conversion (cont.)
67
Infix to PostfixConversion (cont.)
• If the token is a ‘(‘, we push it on the stack• If the token is a number, we append it to the
postfix expression• If the token is a ‘)’, we pop the stack and append
each popped token to the postfix expression, until we pop a ‘(‘
• If the token is an operator, then while the top of the stack is an operator with precedence greater than or equal to the token, we pop the stack and append the popped operator to the postfix expression; when we are done popping, we push the token onto the stack
68
( Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:
Infix to Postfix Conversion (cont.)
69
(
(
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:
Infix to PostfixConversion (cont.)
70
(
(
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:
Infix to PostfixConversion (cont.)
71
(
(5
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:
Infix to PostfixConversion (cont.)
72
(
(
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5
Infix to PostfixConversion (cont.)
73
(
(
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5
Not even an operator here, so we don’t pop anything.
Infix to PostfixConversion (cont.)
74
(
(
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5
Infix to PostfixConversion (cont.)
75
(
(
+
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5
Infix to PostfixConversion (cont.)
76
(
(
+
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5
Infix to PostfixConversion (cont.)
77
(
(
+
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3
Infix to PostfixConversion (cont.)
78
(
(
+
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3
Infix to PostfixConversion (cont.)
79
(
(
+
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3
This is an operator, but its precedence is less than *, so we don’t pop.
Infix to PostfixConversion (cont.)
80
(
(
+
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3
Infix to PostfixConversion (cont.)
81
(
(
+
*
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3
Infix to PostfixConversion (cont.)
82
(
(
+
*
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3
Infix to PostfixConversion (cont.)
83
(
(
+
*
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3 2
Infix to PostfixConversion (cont.)
84
(
(
+
*
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3 2
Infix to PostfixConversion (cont.)
85
(
(
+
*Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3 2
Infix to PostfixConversion (cont.)
86
(
(
+
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3 2 *
Infix to PostfixConversion (cont.)
87
(
(+
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3 2 *
Infix to PostfixConversion (cont.)
88
(
(
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3 2 * +
Infix to PostfixConversion (cont.)
89
((
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3 2 * +
Infix to PostfixConversion (cont.)
90
( Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3 2 * +
Infix to PostfixConversion (cont.)
91
( Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3 2 * +
Infix to PostfixConversion (cont.)
92
(
-
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3 2 * +
Infix to PostfixConversion (cont.)
93
(
-
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3 2 * +
Infix to PostfixConversion (cont.)
94
(
-
(
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3 2 * +
Infix to PostfixConversion (cont.)
95
(
-
(
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3 2 * +
Infix to PostfixConversion (cont.)
96
(
-
(
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3 2 * + 6
Infix to PostfixConversion (cont.)
97
(
-
(
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3 2 * + 6
Infix to PostfixConversion (cont.)
98
(
-
(
/
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3 2 * + 6
Infix to PostfixConversion (cont.)
99
(
-
(
/
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3 2 * + 6
Infix to PostfixConversion (cont.)
100
(
-
(
/
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3 2 * + 6 2
Infix to PostfixConversion (cont.)
101
(
-
(
/
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3 2 * + 6 2
Infix to PostfixConversion (cont.)
102
(
-
(
/
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3 2 * + 6 2
Infix to PostfixConversion (cont.)
103
(
-
(
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3 2 * + 6 2 /
Infix to PostfixConversion (cont.)
104
(
-
(
+
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3 2 * + 6 2 /
Infix to PostfixConversion (cont.)
105
(
-
(
+
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3 2 * + 6 2 /
Infix to PostfixConversion (cont.)
106
(
-
(
+
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3 2 * + 6 2 / 7
Infix to PostfixConversion (cont.)
107
(
-
(
+
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3 2 * + 6 2 / 7
Infix to PostfixConversion (cont.)
108
(
-
(
+
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3 2 * + 6 2 / 7
Infix to PostfixConversion (cont.)
109
(
-
(
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3 2 * + 6 2 / 7 +
Infix to PostfixConversion (cont.)
110
(
-(
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3 2 * + 6 2 / 7 +
Infix to PostfixConversion (cont.)
111
(
-
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3 2 * + 6 2 / 7 +
Infix to PostfixConversion (cont.)
112
(
-
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3 2 * + 6 2 / 7 +
Infix to PostfixConversion (cont.)
113
(-
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3 2 * + 6 2 / 7 +
Infix to PostfixConversion (cont.)
114
( Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Infix to PostfixConversion (cont.)
115
( Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Infix to PostfixConversion (cont.)
116
Stack
Infix Expression:( 5 + 3 * 2 ) – ( 6 / 2 + 7 ) )
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Infix to PostfixConversion (cont.)
117
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Stack
Postfix ExpressionEvaluation
118
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Stack
When evaluating a postfix expression, a number encountered is simply pushed onto the stack.
Postfix ExpressionEvaluation (cont.)
119
5 Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
120
5 Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
121
5
3
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
122
5
3
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
123
5
3
2
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
124
5
3
2
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
125
5
3
2
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
When an operator is encountered, it is used to perform an operation on the top 2 elements of the stack – in the following slides, take careful note of how it is done…
Postfix ExpressionEvaluation (cont.)
126
5
32
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
127
53 2
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
128
53 2*
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
129
53 2*
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Was the topmost element – order can be important here!
Postfix ExpressionEvaluation (cont.)
130
56
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
131
5
6
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
132
5
6
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
133
56 Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
134
5 6 Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
135
5 6+ Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
136
11 Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
137
11 Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
138
11 Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
139
11
6
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
140
11
6
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
141
11
6
2
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
142
11
6
2
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
143
11
62
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
144
11
6 2
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
145
11
6 2/
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
146
11
3
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
147
11
3
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
148
11
3
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
149
11
3
7
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
150
11
3
7
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
151
11
37
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
152
11
3 7
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
153
11
3 7+
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
154
11
10
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
155
11
10
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
156
11
10
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
157
11
10
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
158
11 10
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
159
11 10-
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
160
1
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
161
1 Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
162
1 Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)
163
1
Answer:
Stack
Postfix Expression:5 3 2 * + 6 2 / 7 + -
Postfix ExpressionEvaluation (cont.)