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# After stumbling through my first technical screen, I'm going to drill
# algorithms for implementing evaluators for a toy expression language:
# e.g. 2 + 13 * 3 + 5 * 2
#
# As of now, I'm aware of a few algorithms for solving this:
# - DONE: Convert infix expression to Polish notation and evaluate the Polish
# notation.
# - DONE: Evaluate the tokens using two stacks and avoid converting it.
# - DONE: Create a tree of depth two to encode the operator precedence and
# evaluate that AST.
# - TODO: Convert the infix expression to a prefix expression
# - TODO: Write a recursive descent parser and evaluate the AST.
operators = {
'*': 1,
'+': 0,
}
def tokenize(xs):
result = []
i = 0
while i < len(xs):
current = xs[i]
if current == ' ':
i += 1
continue
elif current in operators.keys():
result.append(current)
i += 1
else:
i += 1
while i < len(xs) and xs[i] in {str(n) for n in range(10)}:
current += xs[i]
i += 1
result.append(int(current))
return result
# Convert infix to postfix; evaluate postfix
# I believe this is known as the Shunting-Yards algorithm
def postfix(tokens):
result = []
s = []
for token in tokens:
if type(token) == int:
result.append(token)
else:
while s and operators[token] < operators[s[-1]]:
result.append(s.pop())
s.append(token)
while s:
result.append(s.pop())
return result
def do_evaluate_with_polish_notation(tokens):
s = []
for token in tokens:
if token == '*':
s.append(s.pop() * s.pop())
elif token == '+':
s.append(s.pop() + s.pop())
else:
s.append(token)
return s[-1]
def evaluate_with_polish_notation(expr):
tokens = tokenize(expr)
print("Tokens: {}".format(tokens))
pn = postfix(tokens)
print("Postfix: {}".format(pn))
result = do_evaluate_with_polish_notation(pn)
print("Result: {}".format(result))
return result
# Evaluate Tokens
def apply_operator(op, a, b):
if op == '*':
return a * b
elif op == '+':
return a + b
def do_evaluate_tokens(tokens):
vals = []
ops = []
for token in tokens:
if type(token) == int:
vals.append(token)
elif token == '*':
ops.append(token)
elif token == '+':
while ops and operators[token] < operators[ops[-1]]:
vals.append(apply_operator(ops.pop(), vals.pop(), vals.pop()))
ops.append(token)
else:
raise Exception("Unexpected token: {}".format(token))
while ops:
vals.append(apply_operator(ops.pop(), vals.pop(), vals.pop()))
return vals[-1]
def evaluate_tokens(expr):
tokens = tokenize(expr)
print("Tokens: {}".format(tokens))
result = do_evaluate_tokens(tokens)
print("Result: {}".format(result))
return result
# Ad Hoc Tree
def parse(tokens):
result = []
series = []
for token in tokens:
if type(token) == int:
series.append(token)
elif token == '*':
continue
elif token == '+':
result.append(series)
series = []
else:
raise Exception("Unexpected token: {}".format(token))
result.append(series)
return result
def product(xs):
result = 1
for x in xs:
result *= x
return result
def do_evaluate_ad_hoc_tree(ast):
return sum([product(xs) for xs in ast])
def evaluate_ad_hoc_tree(expr):
tokens = tokenize(expr)
print("Tokens: {}".format(tokens))
ast = parse(tokens)
print("AST: {}".format(ast))
result = do_evaluate_ad_hoc_tree(ast)
print("Result: {}".format(result))
return result
# Recursive Descent Parser
# expression -> addition ;
# addition -> multiplication ( "+" multiplication )* ;
# multiplication -> terminal ( "*" terminal )* ;
# terminal -> NUMBER ;
class Parser(object):
def __init__(self, tokens):
self.tokens = tokens
self.i = 0
# mutations
def advance(self):
self.i += 1
def consume(self):
result = self.curr()
self.advance()
return result
# predicates
def match(self, x):
if self.curr() == x:
self.advance()
return True
return False
def tokens_available(self):
return self.i < len(self.tokens)
# getters
def prev(self):
return self.tokens[self.i - 1]
def curr(self):
return self.tokens[self.i] if self.tokens_available() else None
def next(self):
return self.tokens[self.i + 1]
def parse_expression(tokens):
parser = Parser(tokens)
return parse_addition(parser)
def parse_addition(parser):
result = parse_multiplication(parser)
while parser.match("+"):
op = parser.prev()
rhs = parse_multiplication(parser)
result = ["+", result, rhs]
return result
def parse_multiplication(parser):
result = parse_terminal(parser)
while parser.match("*"):
op = parser.prev()
rhs = parse_terminal(parser)
result = ["*", result, rhs]
return result
def parse_terminal(parser):
# If we reach here, the current token *must* be a number.
return parser.consume()
def evaluate_ast(ast):
if type(ast) == int:
return ast
else:
op, lhs, rhs = ast[0], ast[1], ast[2]
return apply_operator(op, evaluate_ast(lhs), evaluate_ast(rhs))
def evaluate_recursive_descent(expr):
tokens = tokenize(expr)
print("Tokens: {}".format(tokens))
ast = parse_expression(tokens)
print("AST: {}".format(ast))
result = evaluate_ast(ast)
return result
methods = {
'Polish Notation': evaluate_with_polish_notation,
'Evaluate Tokens': evaluate_tokens,
'Ad Hoc Tree': evaluate_ad_hoc_tree,
'Recursive Descent': evaluate_recursive_descent,
}
for name, fn in methods.items():
expr = "13 + 2 * 4 + 7 + 3 * 8"
print("Evaluating \"{}\" using the \"{}\" method...".format(expr, name))
assert fn(expr) == eval(expr)
print("Success!")
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