pemdas.py

inputs = [
    '1 + 1',
    '2 * 2',
    '1 + 2 * 3',
    '( 1 + 2 ) * 3'
]

def pemdas(s):
    ops = { op: p for p, l in enumerate(['+-', '*/']) for op in l }
    ostk = []
    out = []
    for tok in s.split(' '):
        if tok.isdigit():
            out.append(tok)
        elif tok in ops:
            while ostk and ostk[-1] not in '()' and ops[tok] <= ops[ostk[-1]]:
                out.append(ostk.pop())
            ostk.append(tok)
        elif tok == '(':
            ostk.append(tok)
        elif tok == ')':
            while ostk[-1] != '(':
                out.append(ostk.pop())
            ostk.pop()
    while ostk:
        out.append(ostk.pop())
    stk = []
    for v in out:
        if v.isdigit():
            stk.append(int(v))
        elif v in ops:
            stk.append({
                '+': lambda x, y: x + y,
                '-': lambda x, y: x - y,
                '*': lambda x, y: x * y,
                '/': lambda x, y: x / y,
            }[v](stk.pop(), stk.pop()))
    return stk[0]

print '\n'.join(str(pemdas(i)) for i in inputs)