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import sys
STATE_ANY, STATE_OPERATOR, STATE_NUMBER, *_ = range(100)
(
LEFT_PARENTHESIS, RIGHT_PARENTHESIS, NUMBER,
MULTIPLY, PLUS, MINUS, POW,
*_
) = range(100)
OPERATORS = [MULTIPLY, PLUS, MINUS, POW]
PRECEDENCE = {
PLUS: 10,
MINUS: 10,
MULTIPLY: 20,
POW: 30,
}
class Node:
def __init__(self, node_type, value):
self.type = node_type
self.value = value
self.parent = None
self.right = None
self.left = None
def __eq__(self, other):
return self.type == other.type and self.value == other.value
def __repr__(self):
if self.type == LEFT_PARENTHESIS:
return "Node(LEFT_PARENTHESIS)"
if self.type == RIGHT_PARENTHESIS:
return "Node(RIGHT_PARENTHESIS)"
if self.type == NUMBER:
return f"Node({self.value})"
if self.type == MULTIPLY:
return "Node(MULTIPLY)"
if self.type == PLUS:
return "Node(PLUS)"
if self.type == MINUS:
return "Node(MINUS)"
if self.type == POW:
return "Node(POW)"
__str__ = __repr__
class Token:
def __init__(self, node_type, value):
self.type = node_type
self.value = value
def __eq__(self, other):
return self.type == other.type and self.value == other.value
def __repr__(self):
if self.type == LEFT_PARENTHESIS:
return "Token(LEFT_PARENTHESIS)"
if self.type == RIGHT_PARENTHESIS:
return "Token(RIGHT_PARENTHESIS)"
if self.type == NUMBER:
return f"Token({self.value})"
if self.type == MULTIPLY:
return "Token(MULTIPLY)"
if self.type == PLUS:
return "Token(PLUS)"
if self.type == MINUS:
return "Token(MINUS)"
if self.type == POW:
return "Token(POW)"
__str__ = __repr__
def parse_number(line, start):
number = ""
if line[start] in "+-":
number += line[start]
start += 1
i = start
while i < len(line) and line[i] in "0123456789":
number += line[i]
i += 1
return int(number), i - 1
def tokenize(line):
state = STATE_NUMBER
tokens = []
i = 0
while i < len(line):
char = line[i]
if char == "(":
tokens.append(Token(LEFT_PARENTHESIS, None))
state = STATE_NUMBER
elif char == ")":
tokens.append(Token(RIGHT_PARENTHESIS, None))
state = STATE_OPERATOR
elif char == "+" and state == STATE_OPERATOR:
tokens.append(Token(PLUS, None))
state = STATE_NUMBER
elif char == "-" and state == STATE_OPERATOR:
tokens.append(Token(MINUS, None))
state = STATE_NUMBER
elif char == "*":
if state == STATE_OPERATOR:
tokens.append(Token(MULTIPLY, None))
state = STATE_NUMBER
else:
raise ValueError("Line is not a valid expression")
elif char == "^":
if state == STATE_OPERATOR:
tokens.append(Token(POW, None))
state = STATE_NUMBER
else:
raise ValueError("Line is not a valid expression")
elif char in "-+0123456789":
val, i = parse_number(line, i)
tokens.append(Token(NUMBER, val))
state = STATE_OPERATOR
elif char != " ":
raise ValueError("Line is not a valid expression")
i += 1
return tokens
def parse_parenthesis(tokens, start):
end = start
depth = 0
while True:
token = tokens[end]
if token.type == RIGHT_PARENTHESIS:
depth -= 1
if token.type == LEFT_PARENTHESIS:
depth += 1
if depth == 0 and token.type == RIGHT_PARENTHESIS:
break
end += 1
node = build_tree(tokens[start + 1: end])
return node, end
def build_tree(tokens):
i = 0
current_node = None
while i < len(tokens):
token = tokens[i]
if token.type in [LEFT_PARENTHESIS, NUMBER]:
if token.type == LEFT_PARENTHESIS:
node, i = parse_parenthesis(tokens, i)
elif token.type == NUMBER:
node = Node(NUMBER, token.value)
if current_node is None:
current_node = node
elif current_node.type == NUMBER:
raise ValueError("Not a valid expression")
elif current_node.type in OPERATORS:
if current_node.left is None:
current_node.left = node
node.parent = current_node
elif current_node.right is None:
current_node.right = node
node.parent = current_node
current_node = node
else:
raise ValueError("Not a valid expression")
elif token.type in OPERATORS:
node = Node(token.type, None)
if current_node is None:
raise ValueError("Not a valid expression")
elif current_node.type in [NUMBER] + OPERATORS:
while current_node.parent is not None:
if PRECEDENCE[current_node.parent.type] < PRECEDENCE[node.type]:
node.parent = current_node.parent
if node.parent is not None:
node.parent.right = node
break
current_node = current_node.parent
current_node.parent = node
node.left = current_node
current_node = node
else:
raise ValueError("Not a valid expression")
i += 1
while current_node.parent is not None:
current_node = current_node.parent
return current_node
def expr_eval(node):
if node.type == NUMBER:
return node.value
elif node.type == MULTIPLY:
return expr_eval(node.left) * expr_eval(node.right)
elif node.type == PLUS:
return expr_eval(node.left) + expr_eval(node.right)
elif node.type == MINUS:
return expr_eval(node.left) - expr_eval(node.right)
elif node.type == POW:
return expr_eval(node.left) ** expr_eval(node.right)
def main(*argv):
data = argv[0]
tokens = tokenize(data)
node1 = build_tree(tokens)
print(expr_eval(node1))
if __name__ == "__main__":
main(*sys.argv[1:])
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