Number Guessing Game Process

Here’s a breakdown of the typical flow for a number guessing game:

1. Initialization:
   • The game selects a secret number within a defined range.
   • The player is informed about the range.
   • The player is usually given a limited number of attempts.
2. Player Input:
   • The player enters their guess.
3. Comparison:
   • The player’s guess is compared to the secret number.
4. Feedback:
   • The game provides feedback to the player:
     • “Too high!” if the guess is greater than the secret number.
     • “Too low!” if the guess is less than the secret number.
     • “Correct!” if the guess matches the secret number.
5. Game End Conditions:
   • Success: The player guesses the correct number.
   • Failure: The player runs out of attempts without guessing correctly.
6. Outcome:
   • If the player wins, a congratulatory message is displayed.
   • If the player loses, the secret number is revealed.
   • The player might be asked if they want to play again.

Workflow Diagram for Number Guessing Game

Here’s how you can visualize the number guessing game as a workflow diagram:

1. Start: The process begins.
2. Set Range: The game defines the lower and upper bounds for the number to be guessed.
3. Generate Secret Number: The game randomly selects a secret number within the defined range.
4. Input Guess: The player enters their guess.
5. Compare Guess:
   • Is guess correct? (Decision Point)
     • Yes: Go to “Display Win”
     • No: Go to the next step.
6. Is guess too high? (Decision Point)
   • Yes: Display “Too High!” and go back to “Input Guess.”
   • No: Display “Too Low!” and go back to “Input Guess.”
7. Display Win: Show a congratulatory message, revealing the number of attempts.
8. Display Lose: (Reached if the player runs out of attempts) Reveal the secret number.
9. End: The game finishes.

Complete Python Method

import random

def number_guessing_game(lower_bound, upper_bound, max_attempts):
    """Plays a number guessing game with the user.

    Args:
        lower_bound (int): The lower limit of the guessing range (inclusive).
        upper_bound (int): The upper limit of the guessing range (inclusive).
        max_attempts (int): The maximum number of guesses allowed.

    Returns:
        bool: True if the player guesses correctly, False otherwise.
    """
    secret_number = random.randint(lower_bound, upper_bound)
    attempts = 0
    print(f"Welcome to the Number Guessing Game!")
    print(f"I'm thinking of a number between {lower_bound} and {upper_bound}.")

    while attempts < max_attempts:
        try:
            guess = int(input(f"Attempt {attempts + 1}/{max_attempts}: Enter your guess: "))
            attempts += 1

            if guess < secret_number:
                print("Too low!")
            elif guess > secret_number:
                print("Too high!")
            else:
                print(f"Congratulations! You guessed the number {secret_number} in {attempts} attempts!")
                return True
        except ValueError:
            print("Invalid input. Please enter a whole number.")

    print(f"You ran out of attempts! The secret number was {secret_number}.")
    return False

if __name__ == "__main__":
    number_guessing_game(1, 100, 10)

Mathematical Process Used

The primary mathematical concept at play here is comparison. The game relies on comparing the player’s integer guess with the randomly generated secret integer. The feedback (“Too high,” “Too low,” “Correct”) is a direct result of these inequality ($\<, \>$) or equality (=) comparisons.

While not explicitly a complex mathematical process, the underlying principle of binary search becomes relevant when considering optimal guessing strategies. A player employing a binary search-like approach would repeatedly halve the search interval based on the feedback, significantly reducing the number of guesses needed on average.

Code Analysis for Different Game Options

Let’s analyze how the provided code can be adapted for simple, intermediate, and complex game options by adjusting the input parameters.

1. Simple Game:

• Characteristics: Small range, generous number of attempts.
• Code Adaptation: Call the number_guessing_game function with a small range and a high number of max_attempts.

if __name__ == "__main__":
    print("\n--- Simple Game ---")
    number_guessing_game(1, 10, 5) # Range 1-10, 5 attempts

• Code Analysis:
  • Range (1-10): The small range makes it easier for players to guess the number through trial and error.
  • Attempts (5): With 5 attempts for a range of 10, players have a good chance of guessing correctly even without a strategic approach.
  • Complexity: Low cognitive load, suitable for beginners or younger players.

2. Intermediate Game:

• Characteristics: Moderate range, moderate number of attempts.
• Code Adaptation: Increase the range and adjust the max_attempts to make it more challenging.

if __name__ == "__main__":
    print("\n--- Intermediate Game ---")
    number_guessing_game(1, 100, 7) # Range 1-100, 7 attempts

• Code Analysis:
  • Range (1-100): A larger range requires more strategic guessing. Random guessing becomes less efficient.
  • Attempts (7): The number of attempts is reduced, putting more pressure on the player to make informed guesses.
  • Complexity: Requires a bit more thought and potentially the application of a rudimentary binary search strategy to narrow down the possibilities.

3. Complex Game:

• Characteristics: Large range, limited number of attempts, potentially with added constraints or features.
• Code Adaptation: Significantly increase the range and decrease the max_attempts. We could also introduce features like hints or different difficulty levels affecting the feedback.

import random

def complex_number_guessing_game(lower_bound, upper_bound, max_attempts):
    """A more complex number guessing game with hints."""
    secret_number = random.randint(lower_bound, upper_bound)
    attempts = 0
    print(f"Welcome to the Complex Number Guessing Game!")
    print(f"I'm thinking of a number between {lower_bound} and {upper_bound}.")

    while attempts < max_attempts:
        try:
            guess = int(input(f"Attempt {attempts + 1}/{max_attempts}: Enter your guess: "))
            attempts += 1

            if guess < secret_number:
                print("Too low!")
                if attempts % 2 == 0: # Provide a hint every other attempt
                    print("Hint: The number is greater than", guess + (secret_number - guess) // 2)
            elif guess > secret_number:
                print("Too high!")
                if attempts % 2 == 0:
                    print("Hint: The number is less than", guess - (guess - secret_number) // 2)
            else:
                print(f"Congratulations! You guessed the number {secret_number} in {attempts} attempts!")
                return True
        except ValueError:
            print("Invalid input. Please enter a whole number.")

    print(f"You ran out of attempts! The secret number was {secret_number}.")
    return False

if __name__ == "__main__":
    print("\n--- Complex Game ---")
    complex_number_guessing_game(1, 1000, 5) # Range 1-1000, 5 attempts, with hints

• Code Analysis (Complex):
  • Range (1-1000): A very large range makes random guessing highly improbable within the limited attempts.
  • Attempts (5): The significantly reduced number of attempts demands a strategic approach.
  • Complexity: High cognitive load. Players need to employ a more refined binary search strategy or utilize the provided hints effectively. The introduction of hints adds another layer of information processing.
  • Added Features: The complex_number_guessing_game function includes a hint mechanism every other turn, providing additional information to guide the player. This increases the complexity and requires the player to interpret and use the hints effectively.

By adjusting the lower_bound, upper_bound, and max_attempts parameters, you can easily control the difficulty and complexity of the number guessing game. Adding features like hints, difficulty levels with different feedback mechanisms, or limiting the type of guesses allowed (e.g., only even numbers) can further increase the complexity.

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