Score of Parentheses 🎯

Welcome to our comprehensive guide on the fascinating topic of Score of Parentheses! Let's embark on this exciting journey together, where we'll learn how to evaluate the correctness and calculate the score of various parenthesis expressions.

What are Parentheses? 📝

Parentheses ( ( and ) ) are special mathematical symbols that help group expressions in mathematics and computer programming. They ensure that operations within them are performed in the correct order.

Parentheses Evaluation 💡

To evaluate a parenthesis expression, we follow these simple rules:

1. First, evaluate all expressions enclosed within parentheses.
2. Perform the operations from left to right, following the usual order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
3. Repeat until no more parentheses are left.

Parentheses Score 💡

In addition to evaluating the expression, we can also calculate the score of parentheses. The score is a measure of the correctness and complexity of the parenthesis expression.

Parentheses Score Calculation 💡

1. Initialize a score variable to zero.
2. For each open parenthesis (, increment the score by 1.
3. For each closed parenthesis ), decrement the score by 1.
4. If the score ever becomes negative, or if the score does not reach zero when all parentheses are closed, the parenthesis expression is incorrect.

Example: Evaluation and Score Calculation 💡

Let's consider an example: ((5 + 3) * 4) - 2

1. Evaluate the expression: ((5 + 3) * 4) - 2 => (8 * 4) - 2 => 32 - 2 => 30
2. Calculate the score:
   • Initialize the score to 0.
   • For each open parenthesis, increment the score by 1: ( + ( => Score: 2
   • For each closed parenthesis, decrement the score by 1: )) - => Score: 1
   • The final score is 1.

The expression ((5 + 3) * 4) - 2 is both correct and has a score of 1.

Challenge: Parenthesis Evaluation and Score Calculation 🎯

Now it's your turn to practice! Solve these exercises and calculate the scores of the parenthesis expressions.

Stay tuned for our next lesson, where we'll dive deeper into parenthesis expressions and explore more complex scenarios! 💡

Happy learning, and remember: practice makes perfect! 🎯