The Check for Redundant Brackets problem involves checking if an expression contains any redundant brackets. Redundant brackets are those which enclose a subexpression that doesn't need to be enclosed. This can be efficiently solved using a stack to track operators and brackets.

Consider an expression containing brackets and operators:

```
"((a+b))"
```

To check for redundant brackets using a stack, follow these steps:

**Initialize an Empty Stack**: Use a stack to keep track of characters.**Traverse the Expression**: Iterate through each character in the expression.**Push Non-Closing Brackets and Operators**: Push opening brackets, operators, and operands onto the stack.**Check for Redundant Brackets**: When a closing bracket is encountered, pop from the stack until an opening bracket is found. If no operators were found between the brackets, the brackets are redundant.

After performing these steps, determine if the expression contains redundant brackets:

```
Input: "((a+b))"
Output: True (The brackets are redundant)
```

Consider the input expression "((a+b))". We want to check if it contains redundant brackets.

**Initialize an Empty Stack**: Stack = []**Traverse the Expression**:- Current Character: '(', Stack = ['(']
- Current Character: '(', Stack = ['(', '(']
- Current Character: 'a', Stack = ['(', '(', 'a']
- Current Character: '+', Stack = ['(', '(', 'a', '+']
- Current Character: 'b', Stack = ['(', '(', 'a', '+', 'b']
- Current Character: ')', Stack = ['(', '('] (Pop until '(', no operator found, redundant bracket)
- Current Character: ')', Stack = [] (Pop until '(', no operator found, redundant bracket)
**Final Result**: The expression contains redundant brackets.

```
Function check_redundant_brackets(expression):
# Initialize an empty stack
stack = []
# Traverse the expression
For char in expression:
If char == ')':
top = stack.pop()
elements_inside = 0
While top != '(': # Check characters inside the brackets
elements_inside += 1
top = stack.pop()
If elements_inside <= 1: # If no operators or single operand inside
Return True
Else:
stack.append(char)
Return False
```

```
def check_redundant_brackets(expression):
# Initialize an empty stack
stack = []
# Traverse the expression
for char in expression:
if char == ')':
top = stack.pop()
elements_inside = 0
while top != '(': # Check characters inside the brackets
elements_inside += 1
top = stack.pop()
if elements_inside <= 1: # If no operators or single operand inside
return True
else:
stack.append(char)
return False
# Example usage:
input_expression = "((a+b))"
print(f"Input expression: {input_expression}") # Output: Input expression: ((a+b))
has_redundant_brackets = check_redundant_brackets(input_expression)
print(f"Contains redundant brackets: {has_redundant_brackets}") # Output: Contains redundant brackets: True
```

This Python program defines a function `check_redundant_brackets`

that uses a stack to check if an expression contains redundant brackets. The function iterates through the expression, uses the stack to track characters, and identifies redundant brackets by checking the number of elements between matching brackets.