Parse-Tree-Calculator

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A basic scientific calculator built in HTML, SASS, and Vanilla JavaScript.

Usage

This calculator can perform all expected operations:

• Basic Arithmetic
• Decimals
• Parenthesis to organize priority
• Basic trigonometry (sin, cos, tan)

Additonal Information

• There is implied multiplication between opening parenthesis.
  (e.g. 5(2+3) will evaluate to 5*(2+3))
• When using trig functions, there is no implied multiplication, and you must place a '*' sign in between expressions.
  (e.g., 5*sin(3) not 5sin3)
• You can input negative numbers by simply placing a '-' before the number.
• You can only input expressions with the buttons.
• If there is data in the input field, the 'C' button will clear only input, otherwise it will clear the result field.
• You can position the cursor to insert/delete at any place in the input field.

Invalid Input

• Input that cannot be evaluated, such as '2**', will return the user 'NaN'.
• Input that does not allow the parse tree to be made, such as unclosed parenthesis, will log an error to the console, and return the user nothing.

Implementation Details

Tokenizing

Before an expression is evaluated, it must be tokenzed first so 'buildTree()' knows how to build the tree. Each component of the expression is typed as either a "Literal", "Operator, "Left Parenthesis", "Right Parenthesis, or "Function", and assigned a value.
Here's an example of the token array of '5(sin(5)+2)':

Parse Tree Formation

This calculator uses a parse tree to implement order of operations. The tree is built by pushing operators to the top of the tree, while inserting literals to the lowest free node. Below is an example.
Expression: 5+2*6.
Insert: '5': .
Insert: '+': .
Insert: '2': .
Insert: '*': .
Now you'll notice the order of expressions is incorrect. To fix this, we simply right rotate the tree: .
Insert '6': .

Parenthesis

Parenthesis are handled by creating a new tree when an an opening parenthesis is found. When a closing parenthesis is found, the tree returned and evaluated, being inserted back into the tree as a number. Since this is done recursively, nested parenthesis work just fine.

Functions

When a trig function is encountered, it is put into a stack. It is popped from the stack when the next literal is encountered, and the result of function and the literal is inserted into the tree.