Description

Project #1

Calculator

For this project you need to implement a scientific calculator program. This calculator should be able to read mathematical expressions and assignments, compute the result of the expressions and execute the assignments.
Expressions.
A mathematical expression can be made up of numbers, variables, mathematical operations, and parentheses. Some examples of mathematical expressions:
x 2.3+4*3-2
x (0.4 + 2)* (4 – 12.5) x 2^2 +(4-3) ^ (2 *(1-3) ) x (count+ 1)^(growth/10) x x^(0-y)^2 x (((((1+2)+3)+4)+5)+6) x 2+3-4-2+2*3/4*5+6-7 x (2/(3 * 4)) ^ 2
In order to compute the result of an expression you need to find out the value of variables used in the expression (if any), and calculate the final value of the expression based on the operators. Assignments.
An assignment is made up of a variable and an expression and is used to store the result of the expression in the variable. The format of an assignment is let <variable-name> = <expression> and the given variable could be used in any expression after this assignment.
Variables.
The variables’ names are strings of alphabetical characters, i.e. ‘a’ to ‘z’ and ‘A’ to ‘Z’. You should use a hash-map to store the values of the variables. Note that the names of the variables are case-sensitive, in other words Count and count are two different variables and can have different values. The names quit and let will not be used as variables since they are reserved to signal the termination of the program and declaration of the variables. Some examples of assignments:
x let x = 2 x let count = 0 x let bIGVaLuE = 2^2^(2+2^(2+2*2)) x let count = count + 1
x let AVeryVeryLongVariableNameIsUsedInThisAssignment = (count + 47)* bigValue

Numbers.
x 1 + 1.0 + 1.1 + 0.1 Operators.
Your program should support the following five operators.
x +: Addition. x -: Subtraction. x *: Multiplication.
x /: Division. x ^: Exponentiation.

Example expression:
x 3 + 3 x 3 – 3 x 3 * 3 x 3 / 3 x 3 ^ 3
Operator Precedence.
Operator precedence determines the order of the operations in the absence of the parentheses. For example, in the expression 2 + 3 * 4 the result would be different based on which operator we are computing first. Operator precedence clears up this ambiguity. For instance, in the same example, since we know that * has a higher precedence than +, we will compute the subexpression 3 * 4 first. In other words, the expressions 2 + 3 * 4 and 2 + (3 * 4) are equivalent.
Op. Precedence Example Exp. Equivalent Exp.
^ 3 (Highest) 2^3 (2^3)
* 2 2 * 4 ^ 2 * 3 (2 * (4 ^ 2) * 3)
/ 2 4 / 2 ^ 4 (4 / (2 ^ 4))
+ 1 (Lowest) 2 + 4 * 3 + 2 ^ 3 * 4 (2 + (4 * 3) + ((2 ^ 3) * 4))
– 1 (Lowest) 4 – 2 * 3 ^ 4 (4 – (2 * (3 ^ 4)))

Operator Associativity.
Operator associativity determines the order of multiple operations of the same precedence in the absence of the parentheses. For example, in the expression 4 / 2 * 2 the result would be different based on which operator we are computing first. Operator associativity clears up this ambiguity. For instance, in the same example, since we know that the operators * and / are associative from left to right, we will compute the sub-expression 4 / 2 first. In other words, the expressions 4 / 2 * 2 and (4 / 2) * 2 are equivalent.
Op. Associativity Example Exp. Equivalent Exp.
^ right to left 2 ^ 3 ^ 4 ^ 5 (2 ^ (3 ^ (4 ^ 5)))
* , / left to right 2 * 3 / 4 * 5 (((2 * 3) / 4) * 5)
+ , – left to right 2 – 3 – 4 + 5 (((2 – 3) – 4) + 5)

The following table contains a few more examples regarding the precedence and associativity of the operators.
Example Exp. Equivalent Exp.
2 – 3 * 4 + 5 ((2 – (3 * 4)) + 5)
2 + 3 * 4 / 5 – 6 * 7 ^ 8 ^ 9 * 10 ((2 + ((3 * 4) / 5)) – ((6 * (7 ^ (8 ^ 9))) * 10))
Parentheses.
The parentheses will always override the order of the operations, regardless of the precedence and/or the associativity of the operators.
Whitespaces.
x e^2+2.3 x e ^ 2 + 2.3 x e^2 + 2.3 x e ^ 2+2.3 x e^ 2+ 2.3 x e ^2+ 2.3
Error Handling.
You do not need to check the expression for any syntax errors. The expressions are never malformed, i.e. they will not contain errors such as two consecutive operators, two numbers without any operators, undefined constants, etc., but you still need to check and report two possible errors. One is the division-by-zero error which happens if some number is being divided by zero in the expression. The other is the undeclared-variable error which happens if the expression is using a variable that has not been declared in a previous assignment.
Input/Output.
Each line of input contains an expression or an assignment. If the input is an assignment your program should compute the result of the right hand side expression and update the value of the left hand side variable. Nothing should be printed for assignment. If the input is an assignment, your program should compute the result of the expression and print the result to the output. The result is either a number, the string “Division-By-Zero” if there is a division-by-zero error in the expression, or the string “Undeclared-Variable” if there is an undeclared-variable error in the expression. The final line of input will be the string “quit”, and after your program reads that line it should terminate without printing anything. An example running of the program (input is black, output is blue):
2 + 4 / 2
4
2.3 + 2.7 ^ 2
9.59
4 + 3 / (2 – 4 / 2)
Division-By-Zero
2 + 3 * 2 – 4 * 10
-32
4 / myVar
Undeclared-Variable let myVar = 4
4 / myVar
1
let myVar = myVar ^ myVar
myVar 256
let x = (2 + 4*12 – (14-6)*2)
myVar – x*2
188
14 + (2 – y) ^ 12
Undeclared-Variable quit

Notes.
x For questions, please use the Canvas discussion board.
x You can use C++11’s unordered_map instead of implementing your own hash map. There will be a bonus (up to 10 points) for those who implement their own hash map correctly. The TAs will not assist with your bonus hash map implementation and it will be graded strictly.
x Your code is going to be compiled with GCC. It’s your responsibility to make sure there are no compile errors. If your code generates compile errors, you will receive no credit. x Calculating an expression is 𝑂(𝑛) with 𝑛 being the number of characters in the expression.