Leetcode Basic Calculator Ii

An expert tool to compute and understand string-based mathematical expressions.

LeetCode Basic Calculator II

Operator Precedence in Basic Calculator II

Operator	Precedence Level	Execution Order	Example
* (Multiplication)	High	Evaluated before + and -	In 3+2*2, 2*2 is calculated first.
/ (Division)	High	Evaluated before + and -	In 10-8/2, 8/2 is calculated first.
+ (Addition)	Low	Evaluated after * and /	In 3*5+2, addition happens last.
- (Subtraction)	Low	Evaluated after * and /	In 10-2*3, subtraction happens last.

What is leetcode basic calculator ii?

The leetcode basic calculator ii problem is a classic computer science challenge found on the LeetCode platform. It asks a developer to write a program that can evaluate a simple mathematical expression given as a string. This string contains non-negative integers and the four basic arithmetic operators: addition (+), subtraction (-), multiplication (*), and division (/), along with spaces. The key challenge lies in correctly implementing the standard order of operations, often remembered by the acronym PEMDAS/BODMAS, where multiplication and division have higher precedence than addition and subtraction. For more information, you might want to look into efficient stack usage. The integer division must truncate toward zero.

leetcode basic calculator ii Formula and Explanation

There isn’t a single “formula” for the leetcode basic calculator ii problem, but rather an algorithm. The most common and efficient approach uses a stack data structure to handle operator precedence correctly. The algorithm iterates through the expression string, parsing numbers and operators.

The core logic is as follows:

1. Scan the string from left to right.
2. If a number is encountered, parse the full number.
3. If an operator is found (or at the end of the string), process the previously parsed number based on the last operator.
   • If the last operator was +, push the number onto the stack.
   • If the last operator was -, push the negative of the number onto the stack.
   • If the last operator was *, pop the top value from the stack, multiply it by the current number, and push the result back.
   • If the last operator was /, pop the top value, divide it by the current number (with truncation), and push the result back.
4. After iterating through the entire string, the final result is the sum of all numbers remaining in the stack.

Algorithm Variables

Variable	Meaning	Unit	Typical Range
expression	The input string to be evaluated.	String	e.g., “3+5/2”
currentNumber	The integer being parsed from the string.	Unitless Integer	Non-negative integers.
lastOperator	The operator encountered before the currentNumber.	Character	+, -, *, /
stack	A data structure to store intermediate results.	List of Integers	Contains values after high-precedence operations.

Practical Examples

Example 1: Expression with Multiplication

• Input: "3+2*2"
• Units: Not applicable (unitless integers)
• Process:
  1. Parse ‘3’, last operator is `+`. Stack: `[3]`
  2. Parse ‘2’, last operator is `*`. Stack: `[3, 2]`
  3. End of expression with number ‘2’. Last operator is `*`. Pop 2, multiply by 2 (4), push back. Stack: `[3, 4]`
• Result: Sum of stack (3 + 4) = 7.

Example 2: Expression with Division

• Input: " 3+5 / 2 "
• Units: Not applicable (unitless integers)
• Process:
  1. Parse ‘3’, last operator is `+`. Stack: `[3]`
  2. Parse ‘5’, last operator is `/`. Stack: `[3, 5]`
  3. End of expression with number ‘2’. Last operator is `/`. Pop 5, divide by 2 (integer division is 2), push back. Stack: `[3, 2]`
• Result: Sum of stack (3 + 2) = 5.

For a deeper dive, consider reviewing materials on string parsing algorithms.

How to Use This leetcode basic calculator ii Calculator

Using this calculator is straightforward and designed to help you both get answers and understand the process.

1. Enter Expression: Type your mathematical expression into the input field. Ensure it contains only non-negative integers, operators (+, -, *, /), and spaces.
2. Calculate: Click the “Calculate” button to evaluate the expression.
3. Interpret Results: The main result will appear in large text. Below it, you can see intermediate values that give insight into the calculation process.
4. Analyze the Chart: The “Stack Visualization” chart shows the contents of the stack just before the final summation. This is crucial for seeing how multiplication and division are resolved before addition and subtraction. A look at data structures visualization can be beneficial.

Key Factors That Affect leetcode basic calculator ii

Several factors are critical to solving the leetcode basic calculator ii problem correctly.

• Operator Precedence: The most important factor. Multiplication and division must be performed before addition and subtraction.
• Integer Division: The problem specifies that division should truncate toward zero. For example, 5 / 2 results in 2, not 2.5.
• No Parentheses: This version of the calculator problem simplifies things by not including parentheses, which would require a more complex recursive or stack-based approach.
• Handling Spaces: The input string can have leading, trailing, or multiple spaces between numbers and operators. Your parsing logic must ignore them.
• Order of Operations: For operators of the same precedence (e.g., a mix of `*` and `/`), they should be evaluated from left to right.
• Parsing Numbers: The code must correctly parse multi-digit numbers (e.g., ‘123’ should be treated as one hundred twenty-three, not three separate digits). A solid understanding of recursion and backtracking can help with complex parsing.

Frequently Asked Questions (FAQ)

1. Why does “3+5/2” result in 5, not 5.5?

The problem specifies two rules: operator precedence (division before addition) and integer division (truncating decimals). Therefore, 5 / 2 is calculated first to equal 2, and then 3 + 2 equals 5.

2. How are spaces handled?

The parsing algorithm should simply skip over any space characters it encounters while looking for the next number or operator.

3. What is the role of the stack?

The stack is used to manage operator precedence. By pushing numbers to the stack and only performing `*` and `/` operations immediately, we delay all `+` and `-` operations until the very end. This ensures the order of operations is correct.

4. Why not just use the `eval()` function?

The problem explicitly forbids using built-in functions like eval() to encourage a fundamental understanding of parsing and expression evaluation.

5. How does the algorithm handle a string like “10-2*3”?

It would first push 10 to the stack. Then, seeing the `*` operator, it would pop 10, multiply `-2` and `3` (to get -6) and push that result back onto the stack. The final stack would be `[10, -6]`, and the sum is 4.

6. Are negative numbers allowed in the input?

No, the problem statement specifies the string contains only non-negative integers. The subtraction operator is always binary (between two numbers).

7. Does the order matter for “4*5/2”?

Yes. For same-precedence operators, the evaluation is left-to-right. So, it’s `(4 * 5) / 2 = 20 / 2 = 10`.

8. What’s the time complexity of this solution?

The time complexity is O(n), where n is the length of the string, because we iterate through the string a single time. Check out our resources on algorithmic complexity for more details.

Related Tools and Internal Resources

If you found this tool useful, you might also be interested in our other computer science and algorithm resources. Exploring these topics will provide a deeper understanding of the concepts behind the leetcode basic calculator ii solution.

• Algorithmic Complexity Analysis: Understand how to measure the efficiency of algorithms like this one.
• Efficient Stack Usage: A deep dive into the stack data structure, its operations, and common use cases.
• String Parsing Algorithms: Learn advanced techniques for parsing and manipulating strings.
• Recursion and Backtracking: Explore powerful problem-solving techniques often used in more complex parsing problems (like Basic Calculator I & III).
• Data Structures Visualization: Tools to visualize how data structures work.
• Dynamic Programming Patterns: Another powerful technique for solving a wide range of algorithmic problems.