def cal_simple_expression(exp):
"""只有+-*/四种运算, 运算数为整数, 运算符前后有空格."""
end = '$' # 表达式结束标志, 最低优先级
priority = {end: 0, '+': 1, '-': 1, '*': 2, '/': 2}
operator_func = {'+': add, '-': sub, '*': mul, '/': truediv}
operand = ArrayStack()
operator = ArrayStack()
exp = exp.split()
exp.append(end) # 添加表达式结束标志以计算最终结果
i = 0
while i < len(exp):
e = exp[i]
if e not in priority.keys():
operand.push(int(e))
i += 1
else:
# 高优先级运算符直接push
if operator.is_empty() or priority[e] > priority[operator.top()]:
operator.push(e)
i += 1
# 低优先级运算符在下一次循环时处理
else:
func = operator_func[operator.pop()]
num1 = operand.pop()
num2 = operand.pop()
operand.push(func(num2, num1))
return operand.pop()
def evaluate_expression(tokens):
stack_number = ArrayStack()
stack_operator = ArrayStack()
stack_pa = ArrayStack()
for token in tokens:
if token.isdigit():
stack_number.push(BinaryTree(token))
else:
if token in '({[':
stack_pa.push(token)
elif token in '+-*/':
stack_operator.push(BinaryTree(token))
else:
if stack_operator.is_empty():
return
stack_pa.pop()
arg_2 = stack_number.pop()
arg_1 = stack_number.pop()
tree = stack_operator.pop()
tree.left_node = arg_1
tree.right_node = arg_2
stack_number.push(tree)
if stack_number.is_empty():
return
value = stack_number.pop()
if not stack_number.is_empty():
return
if not stack_pa.is_empty():
return
if not stack_operator.is_empty():
return
return value
def match_paranthesis(paranthesis):
left = '{[(|'
right = '}])|'
stack = ArrayStack()
for s in paranthesis:
if s in left and s not in right:
stack.push(s)
if s in right:
if s not in left:
if stack.is_empty():
return False
else:
if right.index(s) == left.index(stack.top()):
stack.pop()
else:
return False
else:
if stack.is_empty():
stack.push(s)
else:
if s != stack.top():
stack.push(s)
else:
stack.pop()
return stack.is_empty()
def postFix(e):
'''
I've noticed that this sometimes doesnt work because somehow the '*' and '-' characters
are technically different on some computers than others, so if it doesnt work, just
replace the symbols in my 'if' statements with the versions on your keyboard and then
try your examples
'''
#solves an expression in postfix notation
#makes the array stack to store values from the expression until they are used
s = ArrayStack()
#checks each char in the expression to see if it is a digit. If it is, it puts it in the stack,
#otherwise it performs the proper operation on the last 2 numbers in the stack
for i in e:
if i in ["0", "1", "2", "3", "4", "5", "6", "7", "8", "9"]:
s.push(int(i))
elif i == "+":
s.push(s.pop()+s.pop())
elif i == "-":
a = s.pop()
b = s.pop()
s.push(b-a)
elif i == "*":
s.push(s.pop()*s.pop())
elif i == "/":
a = s.pop()
b = s.pop()
s.push(b/a)
#returns the end value
return s.pop()
def evalueate_expression(tokens):
parentheses = {')': '(', '}': '{', ']': '['}
stack = ArrayStack()
for token in tokens:
try:
token = (int(token))
except ValueError:
pass
if token not in parentheses:
stack.push(token)
else:
try:
arg_2 = stack.pop()
operator = stack.pop()
arg_1 = stack.pop()
opening_group_symbol = stack.pop()
if parentheses[token] != opening_group_symbol:
return
stack.push({
'+': add,
'-': sub,
'*': mul,
'/': truediv
}[operator](arg_1, arg_2))
except EmptyStackError:
return
if stack.is_empty():
return
value = stack.pop()
if not stack.is_empty():
return
return value
def test_array_stack():
array_stack = ArrayStack()
# Assert that we start with an empty stack
assert array_stack.is_empty()
with pytest.raises(Empty):
array_stack.top()
# Push a bunch of elements onto the stack
for i in range(10):
array_stack.push(i)
array_stack, top = array_stack.top()
assert top == i
assert len(array_stack) == i + 1
# Pop all the elements off
for i in range(len(array_stack) - 1, -1, -1):
array_stack, val = array_stack.pop()
assert val == i
assert len(array_stack) == i
# Assert we are back to an empty stack
assert array_stack.is_empty()
with pytest.raises(Empty):
array_stack.pop()
def test_push_two_then_pop(self):
stack = ArrayStack()
stack.push(1)
stack.push(2)
res = stack.pop()
self.assertEqual(res, 2)
self.assertEqual(stack.list(), [1])
def infix_to_postfix(expression):
postfix = []
priority = {'(': 1, '+': 2, '-': 2, '*': 3, '/': 3, '^': 4}
operators = ArrayStack()
for token in expression:
if token in OPERATORS:
# Operators are added to the stack, but first the ones with a
# higher priority are added to the result:
while not operators.is_empty() and priority[token] <= priority[
operators.top()]:
postfix.append(operators.pop())
operators.push(token)
# Left parenthesis are added to the stack:
elif token == '(':
operators.push(token)
# Operators between parenthesis are added from the stack to the result:
elif token == ')':
while operators.top() != '(':
postfix.append(operators.pop())
operators.pop() # Pop the left parentheses from the stack.
# Operands are added to the result:
else:
postfix.append(token)
while not operators.is_empty():
# The remaining operators are added from the stack to the result:
postfix.append(operators.pop())
return postfix
def is_matching(expr):
"""
Return True if delimiters in expr match correctly, False otherwise
Parameters
----------
test_str: str or unicode
expression to evaluate parameters correctness
Returns
-------
Boolean
"""
delimiters_map = {'(': ')', '{': '}', '[': ']'}
stack = ArrayStack()
for c in expr:
if c in delimiters_map:
stack.push(c)
elif c in delimiters_map.itervalues():
if stack.is_empty() or delimiters_map[stack.top()] != c:
return False
else:
stack.pop()
return stack.is_empty()
def parse_expression(tokens):
stack = ArrayStack()
for token in tokens:
stack.push(token)
if token in [')', '}', ']']:
try:
right = stack.pop()
arg_2 = stack.pop()
if type(arg_2) == str:
arg_2 = BinaryTree(int(arg_2))
operate = stack.pop()
arg_1 = stack.pop()
if type(arg_1) == str:
arg_1 = BinaryTree(int(arg_1))
left = stack.pop()
except EmptyStackError:
return
except ValueError:
return
if (left, right) not in [('(', ')'), ('{', '}'), ('[', ']')]:
return
parse_tree = BinaryTree(operate)
parse_tree.left_node = arg_1
parse_tree.right_node = arg_2
stack.push(parse_tree)
if stack.is_empty():
return
parse_tree = stack.pop()
if not stack.is_empty():
return
if type(parse_tree) == str:
parse_tree = BinaryTree(int(parse_tree))
return parse_tree
def parse_expression(tokens):
parentheses = {')': '(', ']': '[', '}': '{'}
stack = ArrayStack()
for token in tokens:
try:
token = BinaryTree(int(token))
except ValueError:
pass
if token not in parentheses:
stack.push(token)
else:
try:
arg_2 = stack.pop()
operator = stack.pop()
arg_1 = stack.pop()
opening_group_symbol = stack.pop()
if parentheses[token] != opening_group_symbol:
return
parse_tree = BinaryTree(operator)
parse_tree.left_node = arg_1
parse_tree.right_node = arg_2
stack.push(parse_tree)
except EmptyStackError:
return
if stack.is_empty():
return
parse_tree = stack.pop()
if not stack.is_empty():
return
return parse_tree
def is_valid_html(raw_html):
"""
Return True if the each opening html tag in the raw_html string has and associated closing html tag.
Parameters
----------
raw_html: str or unicode
The raw html string we need to check for validity
Returns
-------
Boolean
"""
def is_opening_tag(tag):
return not tag.startswith('/')
stack = ArrayStack()
opening_idx = raw_html.find('<')
while opening_idx != -1:
closing_idx = raw_html.find('>', opening_idx + 1)
if closing_idx == -1:
return False
tag = raw_html[opening_idx + 1:closing_idx]
if is_opening_tag(tag):
stack.push(tag)
else:
if stack.is_empty() or stack.top() != tag[1:]:
return False
else:
stack.pop()
opening_idx = raw_html.find('<', closing_idx + 1)
return stack.is_empty()
def reverse_file(file_path):
stack = ArrayStack()
with open(file_path, 'r') as f:
for line in f:
stack.push(line.rstrip('\n'))
with open(file_path, 'w') as f:
while not stack.is_empty():
f.write(''.join([stack.pop(), '\n']))
def match_paranthesis(expression):
"""Checks if the parantheses from the expression match up correctly"""
stack=ArrayStack()
for s in expression:
if s == '(':
stack.push(s)
if s == ')':
if stack.is_empty():
return False
else:
stack.pop()
return stack.is_empty()
class ArrayStack:
"""LIFO Stack implementation using a Python list as underlying storage."""
def __init__(self):
"""Create an empty stack."""
self._data = [] # nonpublic list instance
def __len__(self):
"""Return the number of elements in the stack."""
return len(self._data)
def is_empty(self):
"""Return True if the stack is empty."""
return len(self._data) == 0
def push(self, e):
"""Add element e to the top of the stack."""
self._data.append(e) # new item stored at end of list
def top(self):
"""
Return (but do not remove) the element at the top of the stack.
Raise Empty exception if the stack is empty.
"""
if self.is_empty():
raise Exception('Stack is empty')
return self._data[-1] # the last item in the list
def pop(self):
"""Remove and return the element from the top of the stack (i.e., LIFO).
Raise Empty exception if the stack is empty.
"""
if self.is_empty():
raise Exception('Stack is empty')
return self._data.pop() # remove last item from list
if __name__ == '__main__':
from array_stack import ArrayStack
s = ArrayStack()
# question 3 of take home exam
s.push(3) # bottom
s.push(2) # middle
s.push(1) # top
x = s.pop()
if x < s.top():
x = s.top()
print x
def reverse_file(filename):
"""Overwrite given file with its contents reversed line-by-line"""
S = ArrayStack()
original = open(filename)
for line in original:
S.push(line.rstrip('\n')) #we will re-insert newlines when writing
original.close()
#Now overwrite contents with LIFO order
output = open(filename, 'w')
while not S.is_empty():
output.write(S.pop() + '\n')
output.close()
def is_matched_delimiters(expr):
sym_stack = ArrayStack()
lefty = "[{("
righty = "]})"
for c in expr:
if c in lefty:
sym_stack.push(c)
elif c in righty:
if sym_stack.is_empty():
return False
e = sym_stack.pop()
if lefty.index(e) != righty.index(c):
return False
return sym_stack.is_empty()
def is_matched(expr):
"""Return True if all delimiters are matched; False otherwise"""
openers = '([{'
closers = ')]}'
S = ArrayStack()
for c in expr:
if c in openers:
S.push(c)
elif c in closers:
if S.is_empty(): #nothing to match
return False
elif closers.index(c) != openers.index(S.pop()): #mismatched
return False
return S.is_empty() #Are all opening brackets matched?
def is_matched(expr):
"""Return True if all delimiters are properly match; False otherwise."""
lefty = '({[' # opening delimiters
righty = ')}]' # respective closing delims
S = ArrayStack()
for c in expr:
if c in lefty:
S.push(c) # push left delimiter on stack
elif c in righty:
if S.is_empty():
return False # nothing to match with
if righty.index(c) != lefty.index(S.pop()):
return False # mismatched
return S.is_empty() # were all symbols matched?
def is_matched_html(raw):
"""Return True if all HTML tags are properly match; False otherwise."""
S = ArrayStack()
j = raw.find('<') # find first '<' character (if any)
while j != -1:
k = raw.find('>', j + 1) # find next '>' character
if k == -1:
return False # invalid tag
tag = raw[j + 1:k] # strip away < >
if not tag.startswith('/'): # this is opening tag
S.push(tag)
else: # this is closing tag
if S.is_empty():
return False # nothing to match with
if tag[1:] != S.pop(): # tag[1:] strip away '/'
return False # mismatched delimiter
j = raw.find('<', k + 1) # find next '<' character (if any)
return S.is_empty() # were all opening tags matched?
def delimiter_matched_v2(expr: str) -> bool:
"""
>>> delimiter_matched_v2('[(2+x)*(3+y)]')
True
>>> delimiter_matched_v2('{[{(xbcd))]}')
False
"""
S = ArrayStack()
d = {")": "(", "]": "[", "}": "{"}
for c in expr:
if c in d.values():
S.push(c)
elif c in d:
if S.is_empty() or d[c] != S.pop():
return False
return S.is_empty()
def is_matched_html(raw):
"""Return True if all HTML tags are propery matched; False otherwise"""
S = ArrayStack()
j = raw.find('<') #find first opening tag
while j != -1: #while there are still opening tags left
k = raw.find('>', j + 1) #find next closing tag
if k == -1:
return False
tag = raw[j + 1:k] #strip off brackets... TODO: only select tag name
if not tag.startswith('/'): #this is an opening tag
S.push(tag)
else: #closing tag
if S.is_empty(): #nothing to match with
return False
if tag[1:] != S.pop():
return False #mismatched
j = raw.find('<', k + 1) #find next delimiter
return S.is_empty() #were all opening tags matched?
def evaluate_expression(tokens):
stack = ArrayStack()
for token in tokens:
stack.push(token)
if token in [')', '}', ']']:
try:
right = stack.pop()
arg_2 = stack.pop()
if type(arg_2) == str:
arg_2 = int(arg_2)
operate = stack.pop()
arg_1 = stack.pop()
if type(arg_1) == str:
arg_1 = int(arg_1)
left = stack.pop()
except EmptyStackError:
return
except ValueError:
return
#print((left,right))
if (left, right) not in [('(', ')'), ('{', '}'), ('[', ']')]:
return
A = {
'+': add,
'-': sub,
'*': mul,
'/': truediv
}[operate](arg_1, arg_2)
#print(A)
stack.push({
'+': add,
'-': sub,
'*': mul,
'/': truediv
}[operate](arg_1, arg_2))
if stack.is_empty():
return
value = stack.pop()
if not stack.is_empty():
return
if type(value) == str:
value = int(value)
return value
def delimiter_matched_v1(expr):
"""Return True if all delimiters are properly match; False otherwise.
>>> delimiter_matched_v1('[(2+x)*(3+y)]')
True
>>> delimiter_matched_v1('{[{(xbcd))]}')
False
"""
left, right = '({[', ')}]'
S = ArrayStack()
for c in expr:
if c in left:
S.push(c)
elif c in right:
if S.is_empty() or right.index(c) != left.index(S.pop()):
return False
return S.is_empty()
def is_matched_html(string):
tag_stack = ArrayStack()
open_idx = string.find("<")
while open_idx != -1:
close_idx = string.find(">", open_idx + 1)
if close_idx == -1:
return False
tag = string[open_idx + 1:close_idx]
if tag.startswith("/"): # It is close tag
if tag_stack.is_empty():
return False
if tag_stack.pop() != tag[1:]:
return False
else:
tag_stack.push(tag)
open_idx = string.find("<", close_idx + 1)
return tag_stack.is_empty()
def evaluate(expression):
operands = ArrayStack()
for token in expression:
if token in OPERATORS:
b = operands.pop() # second operand
a = operands.pop() # first operand
if token == '/' and b == 0:
return 'Cannot divide by zero, try again.'
elif token == '^' and b < 1 and a < 0:
return 'Cannot root negative number, try again.'
else:
operands.push(calculate(b, a, token))
else:
operands.push(float(token))
return operands.pop()
def text2notes(text):
'''
Takes text and maps it to notes.
'''
notes = [] # The notes
num_stack = ArrayStack() # Our stack of numbers
for ch in text: # Iterate over every character in the string
note = __get_mapping(ch) # Get the mapping
if ch.isdigit():
# If digit, add to num_stack
num_stack.push(int(ch))
elif ch.lower() == repeat_char and not num_stack.is_empty():
# If the repeat character and numbers on the stack,
# pop the most recent number and call the repeat function
__append_repeat(notes, num_stack.pop())
elif note != None:
# If the note has a mapping, add it to notes
notes.append(note)
return notes
def is_matched_html(raw):
stack = ArrayStack()
j = raw.find('<')
while j != -1:
k = raw.find('>', j + 1) # find next '>'
if k == -1:
return False
tag = raw[j + 1:k] # < > 之间的内容
if not tag.startswith('/'): # it's a opening tag
stack.push(tag)
else:
if stack.is_empty():
return False
if tag[1:] != stack.pop():
return False # mismatched delimiter
j = raw.find('<', k + 1)
return stack.is_empty()
def test_stack(self):
stack = ArrayStack()
assert stack.__repr__() == 'Stack: bottom [] top'
assert stack.is_empty() == True
stack.push(1)
assert stack.is_empty() == False
assert stack.__repr__() == 'Stack: bottom [1] top'
stack.push(2)
assert len(stack) == 2
assert stack.__repr__() == 'Stack: bottom [1,2] top'
assert stack.top() == 2
assert stack.pop() == 2
assert len(stack) == 1
assert stack.__repr__() == 'Stack: bottom [1] top'
assert stack.top() == 1
assert stack.pop() == 1
assert stack.__repr__() == 'Stack: bottom [] top'
with pytest.raises(EmptyError):
stack.top()
with pytest.raises(EmptyError):
stack.pop()
def main():
print("Creating a stack...")
a = ArrayStack()
print("Length of the stack:", len(a))
print("The stack is empty:", a.is_empty())
print()
print("Pushing 10 to the stack...")
a.push(10)
print("The element at the top of the stack is", a.top())
print("Length of the stack:", len(a))
print("The stack is empty:", a.is_empty())
print()
print("Pushing 20 30 40 50 to the stack in this order...")
a.push(20)
a.push(30)
a.push(40)
a.push(50)
print("The element at the top of the stack is", a.top())
print("Length of the stack:", len(a))
print("The stack is empty:", a.is_empty())
print()
print("Popping the stack...")
a.pop()
print("The element at the top of the stack is", a.top())
print("Length of the stack:", len(a))
print("The stack is empty:", a.is_empty())
print()
print("Popping the stack 4 times...")
for i in range(3):
a.pop()
print("The element at the top of the stack is", a.top())
print("Length of the stack:", len(a))
print("The stack is empty:", a.is_empty())
print()