Tree with ast
You could use ast
to get a tree of the expression :
import ast
source="((81 * 6) /42+ (3-1))"
node = ast.parse(source)
def show_children(node, level=0):
if isinstance(node, ast.Num):
print(' ' * level + str(node.n))
else:
print(' ' * level + str(node))
for child in ast.iter_child_nodes(node):
show_children(child, level+1)
show_children(node)
It outputs :
<_ast.Module object at 0x7f56abbc5490>
<_ast.Expr object at 0x7f56abbc5350>
<_ast.BinOp object at 0x7f56abbc5450>
<_ast.BinOp object at 0x7f56abbc5390>
<_ast.BinOp object at 0x7f56abb57cd0>
81
<_ast.Mult object at 0x7f56abbd0dd0>
6
<_ast.Div object at 0x7f56abbd0e50>
42
<_ast.Add object at 0x7f56abbd0cd0>
<_ast.BinOp object at 0x7f56abb57dd0>
3
<_ast.Sub object at 0x7f56abbd0d50>
1
As @user2357112 wrote in the comments : ast.parse
interprets Python syntax, not mathematical expressions. (1+2)(3+4)
would be parsed as a function call and list comprehensions would be accepted even though they probably shouldn’t be considered a valid mathematical expression.
List with a regex
If you want a flat structure, a regex could work :
import re
number_or_symbol = re.compile('(\d+|[^ 0-9])')
print(re.findall(number_or_symbol, source))
# ['(', '(', '81', '*', '6', ')', "https://stackoverflow.com/", '42', '+', '(', '3', '-', '1', ')', ')']
It looks for either :
- multiple digits
- or any character which isn’t a digit or a space
Once you have a list of elements, you could check if the syntax is correct, for example with a stack
to check if parentheses are matching, or if every element is a known one.