LeetCode Basic Calculator II: Solution & Explanation

Basic Calculator II Expression Evaluator

Example Intermediate Calculations

Key Calculation Stages for “3 + 2 * 2 / 4 – 1”

Step	Operation	Current Value	Description
1	2 * 2	4	Multiplication performed before addition/subtraction.
2	4 / 4	1	Division performed before addition/subtraction.
3	3 + 1	4	Addition performed after multiplications/divisions.
4	4 – 1	3	Subtraction performed last.

What is LeetCode Basic Calculator II?

The LeetCode “Basic Calculator II” problem is a common coding challenge that requires you to implement a program capable of evaluating a given arithmetic expression. This expression consists of non-negative integers, the operators `+`, `-`, `*`, `/`, and importantly, it does not involve parentheses. The core of the problem lies in correctly handling the order of operations (PEMDAS/BODMAS), where multiplication and division must be performed before addition and subtraction.

This problem is fundamental for understanding how to parse and evaluate mathematical expressions, a skill crucial in areas like compiler design, scientific computing, and even financial modeling. Programmers are typically given a string representing the expression and must return the integer result of its evaluation.

Who should use it? This calculator is primarily for developers practicing for technical interviews, students learning about algorithms and data structures, or anyone interested in how expression evaluation works programmatically. It helps in visualizing the process and testing different inputs.

Common misconceptions: A frequent mistake is evaluating the expression strictly from left to right, ignoring the precedence of multiplication and division. Another is mishandling integer division (where the fractional part is discarded). Some might also overlook edge cases like division by zero or malformed input strings.

Basic Calculator II: Formula and Mathematical Explanation

The “Basic Calculator II” problem doesn’t rely on a single, fixed formula in the traditional sense. Instead, it involves an algorithm that parses an expression and applies arithmetic rules. The underlying mathematical principle is the order of operations (PEMDAS/BODMAS).

Algorithm Overview: A common and efficient approach uses a stack data structure. The algorithm iterates through the expression, maintaining the current number being parsed and the last operator encountered. When an operator is found or the expression ends, the current number is processed based on the last operator.

Step-by-step Derivation (Conceptual):

1. Initialize an empty stack to store intermediate results.
2. Initialize `currentNumber = 0` and `lastOperator = ‘+’`.
3. Iterate through each character of the expression string.
4. If the character is a digit, update `currentNumber = currentNumber * 10 + digitValue`.
5. If the character is an operator (`+`, `-`, `*`, `/`) or the end of the string is reached:
   • Based on `lastOperator`:
     • If `+`: Push `currentNumber` onto the stack.
     • If `-`: Push `-currentNumber` onto the stack.
     • If `*`: Pop the top element from the stack, multiply it by `currentNumber`, and push the result back.
     • If `/`: Pop the top element from the stack, perform integer division by `currentNumber`, and push the result back.
   • Update `lastOperator` to the current operator.
   • Reset `currentNumber = 0`.
6. After iterating through the entire string, the final result is the sum of all numbers in the stack.

Variable Explanations:

Variables Used in the Algorithm

Variable	Meaning	Unit	Typical Range
`expression`	Input string containing the arithmetic expression.	String	Varies, typically up to a few hundred characters.
`currentNumber`	The integer value currently being parsed from digits.	Integer	0 to the maximum integer value representable.
`lastOperator`	The most recently encountered operator (`+`, `-`, `*`, `/`) that determines how `currentNumber` is applied.	Character/String	‘+’, ‘-‘, ‘*’, ‘/’
`stack`	A data structure (typically LIFO) holding intermediate results or numbers ready for final summation.	List/Array of Integers	Contains integers based on parsed operations.
`result`	The final computed integer value of the expression.	Integer	Integer range, potentially large positive or negative.

Practical Examples (Real-World Use Cases)

While LeetCode problems are often abstract, the logic behind Basic Calculator II has practical applications. Imagine a simple calculator app where users input expressions without parentheses, or a system that needs to process basic data transformations.

Example 1: Simple Calculation

Input Expression: "10 + 2 * 6"

• Parsing: The calculator encounters ’10’, then ‘+’, then ‘2’.
• Operator Encountered (‘+’): `lastOperator` is ‘+’, `currentNumber` is 10. Push 10 onto the stack. Reset `currentNumber`. Update `lastOperator` to ‘+’.
• Parsing: The calculator encounters ‘2’. `currentNumber` becomes 2.
• Parsing: The calculator encounters ‘*’, then ‘6’.
• Operator Encountered (‘*’): `lastOperator` is ‘+’. The previous operator for ‘2’ was actually ‘+’, so we pushed 2. Now we see ‘*’. The top of the stack is 2. We pop it, calculate `2 * 6 = 12`, and push 12 back. Update `lastOperator` to ‘*’. Reset `currentNumber`.
• End of Expression: The last operator processed was ‘*’, and the `currentNumber` was 12. The stack now contains [10, 12].
• Final Summation: Sum elements in the stack: 10 + 12 = 22.

Result: 22. This respects that multiplication (2 * 6) is done before addition (10 + result).

Example 2: Division and Subtraction

Input Expression: "20 / 2 - 3"

• Parsing: ’20’. `currentNumber` = 20.
• Operator Encountered (‘/’): `lastOperator` is ‘+’. Push 20. `lastOperator` becomes ‘/’. `currentNumber` = 0.
• Parsing: ‘2’. `currentNumber` = 2.
• Operator Encountered (‘-‘): `lastOperator` is ‘/’. Pop 20. Integer divide `20 / 2 = 10`. Push 10. `lastOperator` becomes ‘-‘. `currentNumber` = 0.
• Parsing: ‘3’. `currentNumber` = 3.
• End of Expression: `lastOperator` is ‘-‘. Push `-currentNumber` (-3) onto the stack. Stack is [10, -3].
• Final Summation: Sum elements: 10 + (-3) = 7.

Result: 7. Division (20 / 2) is performed first, then subtraction (result – 3).

How to Use This Basic Calculator II Calculator

Using this interactive calculator is straightforward and designed to help you understand the evaluation process.

1. Enter Expression: In the “Arithmetic Expression” input field, type the mathematical expression you want to evaluate. Ensure it contains only non-negative integers, the operators `+`, `-`, `*`, `/`, and optionally spaces. For example: "7 + 2 * 3 - 6 / 2".
2. Evaluate: Click the “Evaluate Expression” button.
3. View Results:
   • The primary highlighted result will display the final integer answer.
   • The intermediate values show key numbers derived during the calculation process, illustrating parts of the evaluation.
   • The formula explanation briefly describes the underlying principle (order of operations).
4. Reset: To clear the input and results and start over, click the “Reset” button.
5. Copy Results: Click “Copy Results” to copy the main result, intermediate values, and formula explanation to your clipboard for use elsewhere.

Decision-making guidance: This calculator helps confirm the correct output for a given expression based on standard arithmetic rules. If your manual calculation differs, review the order of operations – ensure multiplications and divisions were handled before additions and subtractions.

Key Factors That Affect Basic Calculator II Results

While the core logic seems simple, several factors influence the outcome of evaluating an expression:

1. Order of Operations (Operator Precedence): This is the most critical factor. Multiplication (`*`) and Division (`/`) have higher precedence than Addition (`+`) and Subtraction (`-`). Calculations are performed in this order, from left to right within the same precedence level.
2. Integer Division: In many programming contexts, including the typical LeetCode constraints, division between integers results in an integer. Any fractional part is truncated (discarded). For example, 7 / 2 evaluates to 3, not 3.5.
3. Left-to-Right Evaluation within Same Precedence: When multiple operators of the same precedence appear consecutively (e.g., 10 / 2 * 3 or 5 + 3 - 1), they are evaluated from left to right. So, 10 / 2 * 3 becomes (10 / 2) * 3 = 5 * 3 = 15.
4. Whitespace Handling: Expressions may contain spaces. The algorithm must correctly ignore spaces and parse numbers and operators accurately. For example, " 3 + 2 * 2 " should be evaluated the same as "3+2*2".
5. Input Validity (Parsing Errors): Malformed expressions (e.g., consecutive operators like "3++2", invalid characters, leading/trailing operators, or division by zero like "5 / 0") can lead to errors or undefined behavior if not handled. The LeetCode problem statement usually guarantees valid inputs, but a robust implementation should consider these.
6. Integer Overflow/Underflow: While the problem often assumes standard integer sizes, very large intermediate or final results could potentially exceed the maximum representable value for an integer type, leading to incorrect results due to overflow. The constraints in a specific problem context are important here.

Frequently Asked Questions (FAQ)

Q1: Does Basic Calculator II handle negative numbers?

A: The standard LeetCode “Basic Calculator II” problem typically specifies non-negative integers. However, the calculation logic itself (especially the stack-based approach) can be adapted to handle negative numbers if they appear as operands or results of operations, often by treating subtraction as adding a negative number.

Q2: What about parentheses?

A: The “Basic Calculator II” problem explicitly excludes parentheses. Problems involving parentheses require a more complex approach, often using recursion or two stacks (one for numbers, one for operators) to manage nested expressions.

Q3: How is integer division handled?

A: Integer division truncates any remainder. For example, in most programming languages, 5 / 2 results in 2. This is a key detail to implement correctly.

Q4: Can the expression be evaluated strictly left-to-right?

A: No, that’s the main challenge. Multiplication and division must take precedence over addition and subtraction. For instance, 3 + 2 * 2 is 7, not 10.

Q5: What if the input expression is empty or invalid?

A: The LeetCode problem usually guarantees a valid expression. For a real-world application, you’d need error handling for empty strings, strings with only operators, or strings containing invalid characters.

Q6: How does the stack help in solving this?

A: The stack helps manage the operands that are ready for addition. Multiplication and division are handled immediately as they are encountered, modifying the top of the stack. This ensures precedence. Finally, summing the stack gives the result.

Q7: What is the time complexity of a typical solution?

A: A well-implemented stack-based solution typically has a time complexity of O(N), where N is the length of the expression string, because each character is processed a constant number of times.

Q8: What is the space complexity?

A: The space complexity is generally O(N) in the worst case for the stack, as it might need to store all numbers if the expression consists only of additions.

Related Tools and Internal Resources

• LeetCode Algorithm Solutions Explore solutions for other popular LeetCode challenges.
• Expression Parser Tutorial Learn more about the theory behind parsing and evaluating expressions.
• Data Structures Guide Understand stacks, queues, and other essential data structures.
• Operator Precedence Explained A deep dive into the rules of mathematical operator priority.
• JavaScript Math Functions Discover built-in math capabilities in JavaScript.
• Algorithmic Problem Solving Tips and strategies for tackling complex coding problems.