```
"""
The nested brackets problem is a problem that determines if a sequence of
brackets are properly nested. A sequence of brackets s is considered properly nested
if any of the following conditions are true:
- s is empty
- s has the form (U) or [U] or {U} where U is a properly nested string
- s has the form VW where V and W are properly nested strings
For example, the string "()()[()]" is properly nested but "[(()]" is not.
The function called is_balanced takes as input a string S which is a sequence of
brackets and returns true if S is nested and false otherwise.
"""
def is_balanced(S):
stack = []
open_brackets = set({"(", "[", "{"})
closed_brackets = set({")", "]", "}"})
open_to_closed = dict({"{": "}", "[": "]", "(": ")"})
for i in range(len(S)):
if S[i] in open_brackets:
stack.append(S[i])
elif S[i] in closed_brackets:
if len(stack) == 0 or (
len(stack) > 0 and open_to_closed[stack.pop()] != S[i]
):
return False
return len(stack) == 0
def main():
s = input("Enter sequence of brackets: ")
if is_balanced(s):
print(s, "is balanced")
else:
print(s, "is not balanced")
if __name__ == "__main__":
main()
```