Basic Calculator III

class Solution {
    private int calculateValue(char op, int operand1, int operand2) {
        if (op == '+') {
            return operand1;
        } else if (op == '-') {
            return -operand1;
        } else if (op == '*') {
            return operand1 * operand2;
        }

        return operand1 / operand2;
    }

    private int processExpression(String expression, int[] index) {
        Stack<Integer> numbers = new Stack<>();
        int currentNumber = 0;
        char lastOperator = '+';

        while (index[0] < expression.length()) {
            char character = expression.charAt(index[0]);
            if (character == '(') {
                index[0]++;
                currentNumber = processExpression(expression, index);
            } else if (Character.isDigit(character)) {
                currentNumber = currentNumber * 10 + Character.getNumericValue(character);
            } else {
                if (lastOperator == '*' || lastOperator == '/') {
                    numbers.push(calculateValue(lastOperator, numbers.pop(), currentNumber));
                } else {
                    numbers.push(calculateValue(lastOperator, currentNumber, 0));
                }

                if (character == ')') {
                    break;
                }

                currentNumber = 0;
                lastOperator = character;
            }

            index[0]++;
        }

        int result = 0;
        for (int value : numbers) {
            result += value;
        }

        return result;
    }

    public int calculate(String s) {
        s += "@";
        int[] idx = new int[1];
        return processExpression(s, idx);
    }
}

This Java solution implements a calculator that can handle basic mathematical operations including addition, subtraction, multiplication, and division, as well as properly dealing with nested expressions enclosed in parentheses. The primary method calculate prepares the input string and initiates the parsing of the expression by calling processExpression, which recursively evaluates the string.

• Start by using a stack to manage numbers as they are processed.
• As characters are consumed from the expression:
  • Detect and handle nested expressions recursively when encountering an opening parenthesis '('.
  • Accumulate numeric values when a digit is found.
  • Calculate intermediate results using basic arithmetic operations, depending on the last encountered operator which is stored and updated. Operators are properly managed with respect to their precedence and associativity.
  • Handle closing parenthesis ')' to properly exit sub-expressions and continue evaluating the parent expression.
• The solution utilizes helper function calculateValue to perform the arithmetic operations depending on the last operator encountered.
• After processing the entire expression, sum all values contained in the stack to produce the final result.

The solution ensures that operations are processed in the correct order, particularly handling the precedence of multiplication and division over addition and subtraction. This implementation effectively addresses the requirement of parsing and evaluating complex string-based arithmetic expressions with nested operations.

class Solver:
    def compute(self, expr: str) -> int:
        def calc(num1, num2, op):
            if op == "+":
                return num1
            if op == "-":
                return -num1
            if op == "*":
                return num1 * num2
            return int(num1 / num2)
        
        def process(index):
            numbers = []
            current_num = 0
            last_op = "+"
            
            while index[0] < len(expr):
                char = expr[index[0]]
                if char == "(":
                    index[0] += 1
                    current_num = process(index)
                elif char.isdigit():
                    current_num = current_num * 10 + int(char)
                else:
                    if last_op in "*/":
                        numbers.append(calc(numbers.pop(), current_num, last_op))
                    else:
                        numbers.append(calc(current_num, 0, last_op))
                     
                    if char == ")":
                        break
                     
                    current_num = 0
                    last_op = char
                    
                index[0] += 1
            
            return sum(numbers)

        expr += "@"
        return process([0])

The provided Python code implements a class Solver with a method compute() to evaluate a mathematical expression passed as a string. This function can handle integers and the operators "+", "-", "*", and "/", including handling of parentheses for prioritizing operations.

You calculate expressions using the following approach:

1. Define a nested function calc() that takes two numbers and an operator, performing the basic arithmetic operation based on the given operator.

2. Define another nested function process() which uses recursion for evaluating expressions, particularly for handling nested expressions within parentheses. The function iterates over the characters of the expression, evaluating sub-expressions recursively whenever opening parentheses are encountered.

3. Within process(), manage a list numbers to store intermediate results, and use current_num to construct numbers digit by digit as parsed from the string.

4. Use last_op to remember the last operator encountered, applying it to current_num and the previous results in numbers, depending on whether the operator is a multiplication/division or addition/subtraction.

5. The loop within process() deals with the characters one by one, updating the list numbers based on the operators. If a closing parenthesis or the end of the string is reached, break the loop and sum up all values in numbers which holds the final result of the current (sub-)expression.

6. Append a non-numeric character (e.g., "@") to the end of the expression to ensure the last number or operation is processed.

7. The main function call starts the processing with process([0]) where 0 is the initial index of the string.

With this implementation, ensure correct formation and ordering of operations, especially for expressions involving multiple types of operators and nested expressions. This solution will handle the parsing and computation of the input string as an arithmetic expression, returning the correct integer result.