Infix Notation is the mathematical notation scheme
we all
learned as children. For example: (4 * 5) + (36 / 4) - 5. This application solves equations in
infix notation.
$ calculator
Press Enter to quit.
Enter an arithmetic equation in infix notation: (4 * 5) + (36 / 4) - 5
( 4 * 5 ) + ( 36 / 4 ) - 5 = 24
Enter an arithmetic equation in infix notation:
$
It can handle both missing and extra spaces in its input:
$ calculator
Press Enter to quit.
Enter an arithmetic equation in infix notation: 8--7 +8++7
8 - -7 + 8 + +7 = 30
Enter an arithmetic equation in infix notation:
$
The input equation is pretty-printed and solved. Input may contain the alternate operators x, ÷, and −. These are swapped for the symbols *, /, and - supported by C++.
The debug mode shows the algorithm in action:
$ calculator -d
Press Enter to quit.
Enter an arithmetic equation in infix notation: (8−−7)+(9×+1)−−3.4−4÷7*2^2
( 8 - -7 ) + ( 9 * +1 ) - -3.4 - 4 / 7 * 2 ^ 2
Pushed ( onto operator stack. Size = 1
Pushing 8 onto value stack. Size = 1
Pushed - onto the operator stack. Size = 2
Pushing -7 onto value stack. Size = 2
operator -, operand_l 8, operand -7
Pushing 15 onto value stack. Size = 1
Pushed + onto the operator stack. Size = 1
Pushed ( onto operator stack. Size = 2
Pushing 9 onto value stack. Size = 2
Pushed * onto the operator stack. Size = 3
Pushing 1 onto value stack. Size = 3
operator *, operand_l 9, operand 1
Pushing 9 onto value stack. Size = 2
operator +, operand_l 15, operand 9
Pushing 24 onto value stack. Size = 1
Pushed - onto the operator stack. Size = 1
Pushing -3.4 onto value stack. Size = 2
operator -, operand_l 24, operand -3.4
Pushing 27.4 onto value stack. Size = 1
Pushed - onto the operator stack. Size = 1
Pushing 4 onto value stack. Size = 2
Pushed / onto the operator stack. Size = 2
Pushing 7 onto value stack. Size = 3
operator /, operand_l 4, operand 7
Pushing 0.571429 onto value stack. Size = 2
Pushed * onto the operator stack. Size = 2
Pushing 2 onto value stack. Size = 3
Pushed ^ onto the operator stack. Size = 3
Pushing 2 onto value stack. Size = 4
operator ^, operand_l 2, operand 2
Pushing 4 onto value stack. Size = 3
operator *, operand_l 0.571429, operand 4
Pushing 2.28571 onto value stack. Size = 2
operator -, operand_l 27.4, operand 2.28571
Pushing 25.1143 onto value stack. Size = 1
( 8 - -7 ) + ( 9 * +1 ) - -3.4 - 4 / 7 * 2 ^ 2 = 25.11
Enter an arithmetic equation in infix notation:
$
The test mode calculator -t runs a map full of equations in debug mode
and reports any
errors.
Bjarne Stroustrup uses the challenge of writing a calculator as an instructional exercise in “Programming: Principles and Practice Using C++, Second Edition”. This gave me the inspiration for the project.
Dave Matuszek is the designer of the algorithm used in this application. All algorithm design credit goes to him. Naturally any implementation blame should go to the author.