class Solution:
def calculate(self, s: str) -> int:
"""
Evaluate a basic mathematical expression containing integers, '+', '-', parentheses, and spaces.
Parameters:
s (str): A valid string expression to be evaluated.
Returns:
int: The result of the evaluated expression.
"""
stack = [] # Stack to keep track of previous results and signs.
result = 0 # Holds the cumulative result of the expression.
number = 0 # Holds the current number being constructed from digits.
sign = 1 # Current sign multiplier; 1 for positive, -1 for negative.
for char in s:
if char.isdigit():
# Construct the number from consecutive digits.
number = number * 10 + int(char)
elif char in ['+', '-']:
# Update result with the current number and sign.
result += sign * number
# Set sign for the next number.
sign = 1 if char == '+' else -1
# Reset current number.
number = 0
elif char == '(':
# Push the current result and sign onto the stack.
stack.append(result)
stack.append(sign)
# Reset result and sign for the new sub-expression.
result = 0
sign = 1
elif char == ')':
# Finish the current number before closing parenthesis.
result += sign * number
number = 0 # Reset number after processing.
# Pop sign and previous result from the stack.
prev_sign = stack.pop()
prev_result = stack.pop()
# Combine the sub-expression result with the previous context.
result = prev_result + prev_sign * result
# Ignore any whitespace characters.
# Add any number left after the loop.
result += sign * number
return result
Summary of Techniques and Approaches:
Stack Utilization for Nested Expressions: A stack is used to store the previous result and sign when a parenthesis is encountered. This method allows handling nested or recursive expressions by preserving the context before diving into the inner expression.
Single-Pass Iteration: The solution processes the input string in a single pass, ensuring linear time complexity. It accumulates digits to form numbers, applies the current sign, and resets variables appropriately.
In-Place Sign and Number Accumulation: By maintaining a current number and sign that are updated as the string is traversed, we efficiently handle arithmetic operations and seamlessly integrate them into the result without extra passes.
General Applicability: These techniques can be applied to various problems involving expression evaluation, nested structures, and in-place modifications of data. Identifying opportunities to use a stack for tracking previous states is key when dealing with nested or recursive data patterns.