Basic Calculator

1. Clarify the problem:

Before we begin, let's clarify the problem statement. The "Basic Calculator" problem asks us to evaluate a mathematical expression represented as a string. The expression can contain the following elements:

• Non-negative integers.
• The addition operator '+' and subtraction operator '-'.
• Parentheses to indicate the order of operations.

2. Analyze the problem:

Let's analyze the problem to identify the input, output, and constraints.

Input:

• A string representing a valid mathematical expression.

Output:

• The result of evaluating the expression.

Constraints:

• The input expression is guaranteed to be valid.
• The expression contains only non-negative integers, '+', '-', '(', and ')'.
• The integer division should truncate toward zero.

3. Design an algorithm:

To solve this problem, we can use a stack-based approach. Here's the general outline of our algorithm:

1. Initialize an empty stack, stack, to store the intermediate results and operators.
2. Initialize a variable, result, to track the current result.
3. Initialize a variable, sign, to track the sign of the current number. The initial sign is positive.
4. Iterate over each character in the expression:
   • If the character is a digit, update the result by multiplying it by 10 and adding the current digit.
   • If the character is '+' or '-', update the result by adding the sign multiplied by the current result to the stack. Reset the result to 0 and update the sign based on the current operator.
   • If the character is '(', push the current result and sign to the stack, reset the result and sign to 0 and positive, respectively.
   • If the character is ')', update the result by adding the sign multiplied by the current result to the stack. Pop the top element from the stack, which represents the previous sign. Update the result by multiplying it with this previous sign and add it to the value popped from the stack, which represents the previous result.
5. After iterating over all characters, update the result by adding the sign multiplied by the current result to the stack.
6. Return the value on the top of the stack, which represents the final result.

4. Explain your approach:

Our approach involves using a stack to evaluate the expression. We iterate over each character in the expression and perform the necessary operations based on the type of character encountered. By keeping track of the result, sign, and using a stack to handle parentheses, we can evaluate the expression and obtain the final result.

5. Write clean and readable code:

Let's implement the algorithm in Python:

python

def calculate(s):
    stack = []
    result = 0
    sign = 1
    i = 0

    while i < len(s):
        if s[i].isdigit():
            num = 0
            while i < len(s) and s[i].isdigit():
                num = num * 10 + int(s[i])
                i += 1
            result += sign * num
            continue

        if s[i] == '+':
            sign = 1
        elif s[i] == '-':
            sign = -1
        elif s[i] == '(':
            stack.append(result)
            stack.append(sign)
            result = 0
            sign = 1
        elif s[i] == ')':
            result = stack.pop() * result + stack.pop()

        i += 1

    return result

6. Test your code:

Let's test our code with different test cases to ensure its correctness. We'll consider the following cases:

• Case 1:

  python

s = "1 + 2"

python

s = "2 - 1 + 3"

python