Expression Parser - Bauer-Samelson algorithm as described in BYTE magazine 1976-02

ExpressionParser.py

```
# Expression Parser - Bauer-Samelson algorithm as described in BYTE magazine 1976-02
# Python implementation: Rick Companje, 30 July 2022
# usage: main("20+4*(5-(6-3))/8")

import math,re

def precedence_check(operators,c):
    if not operators or operators[-1] == '(':
        return True
    else:
        order = "^*/+-"
        return order.find(operators[-1]) > order.find(c)

def unstack(operators, operands):
    op = operators.pop()
    b = operands.pop()
    a = 0 if op=="U" else operands.pop() # a=0 when unary operator

    if op=="^": #power
      operands.append(a**b)
    elif op=="*":
      operands.append(a*b)
    elif op=="/":
      operands.append(int(a/b))
    elif op=="+":
      operands.append(a+b)
    elif op in "U-":
      operands.append(a-b)

def parse(s,vars={}):
    # keywords = ["sin"]
    operands = []
    operators = []
    pc = "" #prev char

    # token=""
    # tokenType=""

    for c in s:
        if c==")":
            while operators[-1]!="(":
                unstack(operators,operands)
            operators.pop() #remove (
        if c.isnumeric():
            if pc.isnumeric():
                operands[-1] = int(str(operands[-1])+c)
            else:
                operands.append(int(c))
        if c.isalpha():
            operands.append(vars[c])
        elif c=="(":
            operators.append(c)
        elif c in "^+*/-":
            if c=="-" and not pc.isnumeric(): 
                # print("unary")
                operators.append("U") #unary
            else:
                while not precedence_check(operators,c):
                    unstack(operators,operands)
                operators.append(c)

        # print(c,"\t",operands,"\t",operators)
        pc=c # prev char for multidigit numbers

    while operators:
        # print(operators,operands)
        unstack(operators,operands)

    return operands[-1]

vars = {
    "t": 10,
    "i": 85,
    "x": 5,
    "y": 5
}

print(parse("t*(i/y)",vars))
```

TODO: add support for unary operators such as the - in -5 and -3:

-5-(-3-4)

TODO2: add support for variables:

-8*(y-x)+t

TODO3: functions like sin()

sin(t)

BYTE magazine 1976-02