Tag Archives: postfix

C++ || Multi Digit, Decimal & Negative Number Infix To Postfix Conversion & Evaluation

The following is sample code which demonstrates the implementation of a multi digit, decimal, and negative number infix to postfix converter and evaluator using a Finite State Machine

REQUIRED KNOWLEDGE FOR THIS PROGRAM

How To Convert Infix To Postfix
How To Evaluate A Postfix Expression
What Is A Finite State Machine?

Using a Finite State Machine, the program demonstrated on this page has the ability to convert and evaluate a single digit, multi digit, decimal number, and/or negative number infix equation. So for example, if the the infix equation of (19.87 * ~2) was entered into the program, the converted postfix expression of 19.87 ~2* would display to the screen, as well as the final evaluated answer of -39.74.

NOTE: In this program, negative numbers are represented by the “~” symbol.

This program has the following flow of control:

• Get an infix expression from the user
• Convert the infix expression to postfix
• Use a Finite State Machine to isolate all of the math operators, multi digit, decimal, negative and single digit numbers that are found in the postfix expression
• Evaluate the postfix expression using the tokens found from the above step
• Display the evaluated answer to the screen

The above steps are implemented below.


QUICK NOTES:
The highlighted lines are sections of interest to look out for.

The code is heavily commented, so no further insight is necessary. If you have any questions, feel free to leave a comment below.

The following is sample output.

====== RUN 1 ======

==== Infix To Postfix Conversion & Evaluation ====

Math Operators:
+ || Addition
- || Subtraction
* || Multiplication
/ || Division
% || Modulus
^ || Power
$ || Square Root
s || Sine
c || Cosine
t || Tangent
~ || Negative Number

Sample Infix Equation: ((s(~4^5)*1.4)/($(23+2)-~2.8))*(c(1%2)/(7.28*.1987)^(t23))

Please enter an Infix expression: 12/3*9

The Infix expression = 12/3*9
The Postfix expression = 12 3 /9*

Calculations:
12/3 = 4
4*9 = 36

Final answer = 36

====== RUN 2 ======

==== Infix To Postfix Conversion & Evaluation ====

Math Operators:
+ || Addition
- || Subtraction
* || Multiplication
/ || Division
% || Modulus
^ || Power
$ || Square Root
s || Sine
c || Cosine
t || Tangent
~ || Negative Number

Sample Infix Equation: ((s(~4^5)*1.4)/($(23+2)-~2.8))*(c(1%2)/(7.28*.1987)^(t23))

Please enter an Infix expression: ~150.89996 - 87.56643

The Infix expression = ~150.89996 - 87.56643
The Postfix expression = ~150.89996 87.56643-

Calculations:
-150.9-87.5664 = -238.466

Final answer = -238.466

====== RUN 3 ======

==== Infix To Postfix Conversion & Evaluation ====

Math Operators:
+ || Addition
- || Subtraction
* || Multiplication
/ || Division
% || Modulus
^ || Power
$ || Square Root
s || Sine
c || Cosine
t || Tangent
~ || Negative Number

Sample Infix Equation: ((s(~4^5)*1.4)/($(23+2)-~2.8))*(c(1%2)/(7.28*.1987)^(t23))

Please enter an Infix expression: ((s(~4^5)*1.4)/($(23+2)-~2.8))*(c(1%2)/(7.28*.1987)^(t23))

The Infix expression = ((s(~4^5)*1.4)/($(23+2)-~2.8))*(c(1%2)/(7.28*.1987)^(t23))
The Postfix expression = ~4 5^ s1.4* 23 2+ $~2.8-/ 1 2% c7.28 .1987* 23t^/*

Calculations:
-4^5 = -1024
sin(-1024) = 0.158533
0.158533*1.4 = 0.221947
23+2 = 25
√25 = 5
5--2.8 = 7.8
0.221947/7.8 = 0.0284547
1%2 = 1
cos(1) = 0.540302
7.28*0.1987 = 1.44654
tan(23) = 1.58815
1.44654^1.58815 = 1.79733
0.540302/1.79733 = 0.300614
0.0284547*0.300614 = 0.00855389

Final answer = 0.00855389

C++ || Stack Based Postfix Evaluation (Single Digit)

This page consists of another homework assignment which was presented in a C++ Data Structures course. While the previously discussed program dealt with converting Infix expressions to Postfix, this program will demonstrate exactly how to evaluate them.

NOTE: Want to convert & evaluate multi digit, decimal, and negative numbers? Click here!

REQUIRED KNOWLEDGE FOR THIS PROGRAM

What Is Postfix?
How To Convert Infix To Postfix Equations
Stack Data Structure
Cin.getline
How To Evaluate Postfix Expressions
The Order Of Operations
#include "ClassStackType.h"

The title of this page is called – “Stack Based Postfix Evaluation (Single Digit).” Why “single digit?” The program demonstrated on this page has the ability to evaluate a postfix equation, but it only has the ability to evaluate single digit values. What do I mean by that? Consider the infix equation: 5+2. When that expression is converted to postfix, it will come out to be: 52+, and the answer will be 7 (5+2=7). But what if we have an equation like 12+2? When that expression is converted to postfix, it will come out to be: 122+. The postfix conversion is correct, but when you try to evaluate the expression, we do not know if the math operation should be 12+2 or 1+22, it can be read either way.

Question: So why is this program being displayed if it only works for single digits?
Answer: Because it demonstrates the process of evaluating postfix equations very well.

Want to convert & evaluate multi digit, decimal, and negative numbers? Click here!

Before we get into things, here is a helpful algorithm for evaluating a postfix expression in pseudo code:

Once you understand the process of converting from infix to postfix, adding the ability to evaluate multiple digits within this program should be doable.

======= POSTFIX EVALUATION =======

This program uses a custom template.h class. To obtain the code for that class, click here.


QUICK NOTES:
The highlighted lines are sections of interest to look out for.

Want to convert & evaluate multi digit, decimal, and negative numbers? Click here!

The code is heavily commented, so no further insight is necessary. If you have any questions, feel free to leave a comment below.

Once compiled, you should get this as your output
(Note: the code was compile three separate times to display different output)

====== RUN 1 ======

==== Postfix Evaluation ====

Math Operators:
+ || Addition
- || Subtraction
* || Multiplication
/ || Division
% || Modulus
^ || Power
$ || Square Root

Sample Postfix Equation: 45^14*232+$2-/12%24*/*

Please enter a postfix expression: 1 2 + 5 6 + /
The postfix expression = 1 2 + 5 6 + /

Calculations:
1+2 = 3
5+6 = 11
3/11 = 0.272727
Final answer = 0.272727

====== RUN 2 ======

==== Postfix Evaluation ====

Math Operators:
+ || Addition
- || Subtraction
* || Multiplication
/ || Division
% || Modulus
^ || Power
$ || Square Root

Sample Postfix Equation: 45^14*232+$2-/12%24*/*

Please enter a postfix expression: 35*76^+
The postfix expression = 35*76^+

Calculations:
3*5 = 15
7^6 = 117649
15+117649 = 117664
Final answer = 117664

====== RUN 3 ======

==== Postfix Evaluation ====

Math Operators:
+ || Addition
- || Subtraction
* || Multiplication
/ || Division
% || Modulus
^ || Power
$ || Square Root

Sample Postfix Equation: 45^14*232+$2-/12%24*/*

Please enter a postfix expression: 45^4*32+$2-/12%24*/*
The postfix expression = 45^4*32+$2-/12%24*/*

Calculations:
4^5 = 1024
1024*4 = 4096
3+2 = 5
√5 = 2.23607
2.23607-2 = 0.236068
4096/0.236068 = 17350.9
1%2 = 1
2*4 = 8
1/8 = 0.125
17350.9*0.125 = 2168.87
Final answer = 2168.87

C++ || Stack Based Infix To Postfix Conversion (Single Digit)

This page consists of another homework assignment which was presented in a C++ Data Structures course. No matter which institution you attend, it seems every instructor assigns a program similar to this at one time or another.

Want to evaluate a postfix expression? Click here.

Want to convert & evaluate multi digit, decimal, and negative numbers? Click here!

REQUIRED KNOWLEDGE FOR THIS PROGRAM

What Is Infix?
What Is Postfix?
Stack Data Structure
Cin.getline
How To Convert To Postfix
The Order Of Operations
#include "ClassStackType.h"

The program demonstrated on this page has the ability to convert a normal infix equation to postfix equation, so for example, if the user enters the infix equation of (1*2)+3, the program will display the postfix result of 12*3+.

Before we get into things, here is a helpful algorithm for converting from infix to postfix in pseudo code:

======= INFIX TO POSTFIX CONVERSION =======

This program uses a custom template.h class. To obtain the code for that class, click here.


QUICK NOTES:
The highlighted lines are sections of interest to look out for.

Want to convert & evaluate multi digit, decimal, and negative numbers? Click here!

The code is heavily commented, so no further insight is necessary. If you have any questions, feel free to leave a comment below.

Want to evaluate a postfix expression? Click here for sample code.

Once compiled, you should get this as your output
(Note: the code was compile three separate times to display different output)

====== RUN 1 ======

==== Infix to Postfix Conversion ====

Math Operators:
+ || Addition
- || Subtraction
* || Multiplication
/ || Division
% || Modulus
^ || Power
$ || Square Root

Sample Infix Equation: (((4^5)*14)/($(23+2)-2))*(1%2)/(2*4)

Please enter an infix expression: ((a+b)+c)/(d^e)
The Infix expression = ((a+b)+c)/(d^e)
The Postfix expression = ab+c+de^/

====== RUN 2 ======

==== Infix to Postfix Conversion ====

Math Operators:
+ || Addition
- || Subtraction
* || Multiplication
/ || Division
% || Modulus
^ || Power
$ || Square Root

Sample Infix Equation: (((4^5)*14)/($(23+2)-2))*(1%2)/(2*4)

Please enter an infix expression: (3*5)+(7^6)
The Infix expression = (3*5)+(7^6)
The Postfix expression = 35*76^+

====== RUN 3 ======

==== Infix to Postfix Conversion ====

Math Operators:
+ || Addition
- || Subtraction
* || Multiplication
/ || Division
% || Modulus
^ || Power
$ || Square Root

Sample Infix Equation: (((4^5)*14)/($(23+2)-2))*(1%2)/(2*4)

Please enter an infix expression: (((4^5)*14)/($(23+2)-2))*(1%2)/(2*4)
The Infix expression = (((4^5)*14)/($(23+2)-2))*(1%2)/(2*4)
The Postfix expression = 45^14*232+$2-/12%24*/*