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| LEFT_BRACKET = '('
RIGHT_BRACKET = ')'
def bracket_validate(input_str):
"""
function for part1
checks whether any brackets occurring in the string appear as correctly matched pairs of one opening bracket
:param input_str:
:return: bracket is matched or not
"""
stack = []
for char in input_str:
if char == LEFT_BRACKET:
stack.append(char)
elif char == RIGHT_BRACKET:
if len(stack) != 0 and stack[-1] == LEFT_BRACKET:
stack.pop()
else:
return False
else:
pass
return len(stack) == 0
def test_bracket_validate():
assert bracket_validate("()") is True
assert bracket_validate("a") is True
assert bracket_validate("(b())") is True
assert bracket_validate("(") is False
assert bracket_validate("()a)") is False
assert bracket_validate("|)") is False
assert bracket_validate("(]") is False
assert bracket_validate("([)") is True
assert bracket_validate("[[") is True
assert bracket_validate("(a(bb)ccc)dddd") is True
assert bracket_validate("(a)bb()ccc") is True
def get_content_of_first_bracket(input_str):
"""
function for part2a
returns the contents of the first matched pair of brackets
:param input_str:
:return: content of first brackets
"""
if bracket_validate(input_str):
stack = []
start_idx, end_idx = None, None
for idx in range(len(input_str)):
char = input_str[idx]
if char == LEFT_BRACKET:
if start_idx is None:
start_idx = idx
stack.append(char)
elif char == RIGHT_BRACKET:
if len(stack) != 0 and stack[-1] == LEFT_BRACKET:
stack.pop()
if end_idx is None and len(stack) == 0:
end_idx = idx
else:
pass
if start_idx is not None:
result = input_str[(start_idx + 1): end_idx]
return result
else:
return ""
else:
print("error, input string contains mismatched brackets!")
return None
def test_get_content_of_first_bracket():
assert get_content_of_first_bracket("(a)") == "a"
assert get_content_of_first_bracket("()") == ""
assert get_content_of_first_bracket("abcd") == ""
assert get_content_of_first_bracket("a (b) c (d)") == "b"
assert get_content_of_first_bracket("((a) b (c) d)") == "(a) b (c) d"
assert get_content_of_first_bracket("(a(bb)ccc)dddd") == "a(bb)ccc"
assert get_content_of_first_bracket("()a)") is None
def get_content_without_nested_bracket_in_first_bracket(input_str):
"""
function for part2b
returns the contents of the first pair of brackets, except not including anything contained within any further nested brackets
:param input_str:
:return: content of first pair of brackets without content in nested brackets
"""
content_of_first_bracket = get_content_of_first_bracket(input_str)
if content_of_first_bracket is None:
return None
stack = []
result = ''
for char in content_of_first_bracket:
if char == LEFT_BRACKET:
stack.append(char)
elif char == RIGHT_BRACKET:
stack.pop()
else:
if len(stack) == 0:
result += char
else:
pass
return result
def test_get_content_without_nested_bracket_in_first_bracket():
assert get_content_without_nested_bracket_in_first_bracket("(a)") == "a"
assert get_content_without_nested_bracket_in_first_bracket("((a))") == ""
assert get_content_without_nested_bracket_in_first_bracket("((a)b)") == "b"
assert get_content_without_nested_bracket_in_first_bracket("a (b (c) d) e") == "b d"
assert get_content_without_nested_bracket_in_first_bracket("(a(bb)ccc)dddd") == "accc"
assert get_content_without_nested_bracket_in_first_bracket("((a) b (c) d)") == " b d"
assert get_content_without_nested_bracket_in_first_bracket("((a)b") is None
OPERATORS = ['+', '-', '*', '/', '^']
def parse_mathematical_expressions(expression):
"""
function for part3
analyze a math expression and spilt them into list formatted as [operator, left-hand tree, right-hand tree]
:param expression:
:return: list of math expression
"""
if len(expression) == 1 and expression.isalpha():
return expression
if expression.isdigit():
return expression
stack = []
item_temp = ''
for char in expression:
if char == LEFT_BRACKET:
stack.append(char)
elif char == RIGHT_BRACKET:
if len(item_temp):
stack.append(item_temp)
item_temp = ''
right = stack.pop()
op = stack.pop()
left = stack.pop()
left_bracket = stack.pop()
stack.append([op, left, right])
elif char in OPERATORS:
if len(item_temp):
stack.append(item_temp)
stack.append(char)
item_temp = ''
else:
item_temp += char
return stack.pop()
def test_parse_mathematical_expressions():
assert parse_mathematical_expressions("52837") == '52837'
assert parse_mathematical_expressions("x") == 'x'
assert parse_mathematical_expressions("(a+b)") == ['+', "a", "b"]
assert parse_mathematical_expressions("((a+b)^2)") == ['^', ['+', "a", "b"], "2"]
assert parse_mathematical_expressions("((a+b)/(374-c))") == ['/', ['+', "a", "b"], ['-', "374", "c"]]
assert parse_mathematical_expressions("(((x^2)*(x/(y^3)))+1)") == ['+', ['*', ['^', "x", "2"],
['/', "x", ['^', "y", "3"]]], "1"]
FUNCTIONS = ['exp', 'log', 'sin', 'cos']
def parse_mathematical_expressions_with_function(expression):
"""
function for part4
analyze math expression with math function such as sin and cos eg.
:param expression: math expression
:return:list of math expression
"""
stack = []
item_temp = ''
for char in expression:
if char == LEFT_BRACKET:
if len(item_temp):
stack.append(item_temp)
item_temp = ''
stack.append(char)
elif char == RIGHT_BRACKET:
if len(item_temp):
stack.append(item_temp)
item_temp = ''
temp_arr = []
item = stack.pop()
while item != LEFT_BRACKET:
temp_arr.insert(0, item)
item = stack.pop()
if len(stack) != 0 and stack[-1] in FUNCTIONS:
stack.append([stack.pop(), temp_arr[0]])
elif len(temp_arr) == 3:
stack.append([temp_arr[1], temp_arr[0], temp_arr[2]])
else:
stack.append(temp_arr[0])
elif char in OPERATORS:
if len(item_temp):
stack.append(item_temp)
stack.append(char)
item_temp = ''
else:
item_temp += char
if item_temp != '':
stack.append(item_temp)
return stack.pop()
def test_parse_mathematical_expressions_with_function():
assert parse_mathematical_expressions_with_function("exp(1)") == ["exp", "1"]
assert parse_mathematical_expressions_with_function("(a+sin(x))") == ['+', "a", ["sin", "x"]]
assert parse_mathematical_expressions_with_function("(log(r)^3)") == ['^', ["log", "r"], "3"]
assert parse_mathematical_expressions_with_function("log(log(((2*n)+1)))") == ["log", ["log",
['+', ['*', "2", "n"],
"1"]]]
def simple_diff(fx):
"""
function for part5
get diff of f(x)
:param fx: f(x)
:return: diff of f(x)
"""
if fx == 'x':
return 1
if fx.isdigit() or fx.isalpha():
return 0
if fx.startswith('exp'):
return f"exp({get_content_of_first_bracket(fx)})"
if fx.startswith('log'):
return f"1/{get_content_of_first_bracket(fx)}"
if fx.startswith('sin'):
return f"cos({get_content_of_first_bracket(fx)})"
if fx.startswith('cos'):
return f"-sin({get_content_of_first_bracket(fx)})"
if '^' in fx:
power_items = fx.split('^')
power_value = int(power_items[1])
if power_value >= 1:
return f"{power_value}*({power_items[0]}^{power_value - 1})"
else:
return 0
FUNCTION_OPERATORS = ['+', '-', '*', '/']
def is_simple_diff(item_list):
"""
function for part5
judge that input can apply simple_diff function or not
:param item_list:
:return:
"""
for item in item_list:
if isinstance(item, list):
return False
return True
def get_source_item(item_list):
"""
get source expression from split list
:param item_list:
:return:
"""
if not isinstance(item_list, list):
return item_list
if is_simple_diff(item_list):
if len(item_list) == 3:
return f"{item_list[1]}{item_list[0]}{item_list[2]}"
elif len(item_list) == 2:
return f"{item_list[0]}({item_list[1]})"
else:
if len(item_list) == 3:
return f"{get_source_item(item_list[1])}{get_source_item(item_list[0])}{get_source_item(item_list[2])}"
elif len(item_list) == 2:
return f"{get_source_item(item_list[0])}({get_source_item(item_list[1])})"
def recursion_diff(item_list):
"""
get diff of complex expression by recursion
:param item_list:
:return:
"""
len_of_item_list = len(item_list)
if is_simple_diff(item_list):
if len_of_item_list == 3:
operator = item_list[0]
left_hand = item_list[1]
right_hand = item_list[2]
if operator == '^':
return simple_diff(f"{left_hand}^{right_hand}")
elif operator == '-':
return f"{simple_diff(left_hand)}-{simple_diff(right_hand)}"
elif operator == '+':
return f"{simple_diff(left_hand)}+{simple_diff(right_hand)}"
elif operator == '*':
pass
else:
pass
elif len_of_item_list == 2:
func = item_list[0]
func_parameter = item_list[1]
return simple_diff(f"{func}({func_parameter})")
else:
if len_of_item_list == 3:
operator = item_list[0]
left_hand = item_list[1]
right_hand = item_list[2]
if operator == '^':
return None
elif operator == '-':
return f"{recursion_diff(left_hand)}-{recursion_diff(right_hand)}"
elif operator == '+':
return f"{recursion_diff(left_hand)}+{recursion_diff(right_hand)}"
elif operator == '*':
return f"{recursion_diff(left_hand)}*{get_source_item(right_hand)}" \
f"+{recursion_diff(right_hand)}*{get_source_item(left_hand)}"
elif operator == '/':
a = f"{recursion_diff(left_hand)}*{get_source_item(right_hand)}-{recursion_diff(right_hand)}*{get_source_item(left_hand)}"
b = f"({get_source_item(right_hand)})^2"
return f"({a}/{b})"
else:
pass
elif len_of_item_list == 2:
func = item_list[0]
func_parameter = item_list[1]
a = simple_diff(f"{func}({get_source_item(func_parameter)})")
b = recursion_diff(func_parameter)
return f"{a}*{b}"
def symbolic_differentiation(expression):
"""
function for part5
get diff of expression
:param expression:
:return:
"""
mathematical_expressions_with_function_parse_result = parse_mathematical_expressions_with_function(expression)
if not isinstance(mathematical_expressions_with_function_parse_result, list):
return simple_diff(mathematical_expressions_with_function_parse_result)
else:
return recursion_diff(mathematical_expressions_with_function_parse_result)
def test_symbolic_differentiation():
print(symbolic_differentiation("32"))
print(symbolic_differentiation("a"))
print(symbolic_differentiation("x"))
print(symbolic_differentiation("(1+x)"))
print(symbolic_differentiation("(x^5)"))
print(symbolic_differentiation("((x^3)-(x^2))"))
print(symbolic_differentiation("exp(1)"))
print(symbolic_differentiation("exp(x)"))
print(symbolic_differentiation("exp((x^2))"))
print(symbolic_differentiation("((x^2)*exp(x))"))
print(symbolic_differentiation("log(sin(x))"))
print(symbolic_differentiation("log(sin((x^2)))"))
if __name__ == '__main__':
test_bracket_validate()
test_get_content_of_first_bracket()
test_get_content_without_nested_bracket_in_first_bracket()
test_parse_mathematical_expressions()
test_parse_mathematical_expressions_with_function()
test_symbolic_differentiation()
|
