This week you will determine the time complexity for a game of your choice. You should select a game that can be played in algorithmic steps and determine the maximum time (in notation) it will take to play the game. Use the guidelines below in your report.
Include the following in your report:
A brief explanation of the computing concepts to be modeled
A brief explanation of how the game functions if you created it
A brief explanation of the original game on which you have based your assignment if the game already exists
A brief explanation of how the game was integrated with the concepts of computing if the game already exists
Three scenarios of game play, including:
The setup of the game
The desired outcome
A sample game for each scenario
Your submission will be evaluated on the following criteria:
The adaptability of the game chosen to the week's topic
The extent to which the game and the computing concepts integrate
The quality of the work submitted by you. Thought I would see if anyone knew how to help me with this if not I will do my best.
what is this? a question or a prompt?
For this assignment, I have chosen the game of Tic Tac Toe as the game to analyze and determine its time complexity. Tic Tac Toe is a two-player game played on a grid of 3x3 squares. The goal of the game is for a player to get three of their symbols (either X or O) in a row, column, or diagonal, or to fill all the squares without achieving this goal, resulting in a draw.
Computing concepts modeled in Tic Tac Toe:
1. Data Structures: The game board can be represented as a 2-dimensional array or grid, where each cell represents a square on the board.
2. Algorithms: The game involves several algorithms to check for winning conditions, update the game state, and determine the best possible move to make.
Functioning of the game:
- The game starts with an empty 3x3 grid.
- Player X and Player O take turns alternately, with Player X going first.
- Each player chooses an empty cell on their turn and marks it with their symbol (X or O).
- The game continues until either a player wins or all cells are filled.
- If a player gets three of their symbols in a row, column, or diagonal, they win.
- If all cells are filled and no player has won, the game is a draw.
Original game integration with computing concepts:
Tic Tac Toe is a classic game played by people traditionally using pen and paper. However, the game can be easily integrated with computing concepts such as data structures and algorithms to create computer-based versions. Computer programs can store the game state, perform the necessary checks, and even provide AI opponents for players.
Scenarios of game play:
Scenario 1:
Setup: The game starts with an empty 3x3 grid.
Desired outcome: Player X wins by getting three X's in a row.
Sample game:
1 2 3
- - -
X - - (Player X chooses the top-left cell)
- O X (Player O chooses the middle-bottom cell)
- - X (Player X chooses the bottom-right cell)
Player X wins!
Scenario 2:
Setup: The game starts with an empty 3x3 grid.
Desired outcome: The game ends in a draw.
Sample game:
1 2 3
O X X (Player O chooses the top-middle cell)
X X O (Player X chooses the middle-left cell)
O O X (Player O chooses the bottom-left cell)
X O X (Player X chooses the top-right cell)
X O O (Player O chooses the middle-right cell)
O X X (Player X chooses the bottom-middle cell)
No one wins, and the game ends in a draw!
Scenario 3:
Setup: The game starts with an empty 3x3 grid.
Desired outcome: Player O wins by getting three O's in a diagonal.
Sample game:
1 2 3
- - X (Player X chooses the bottom-right cell)
- O - (Player O chooses the middle-middle cell)
O X - (Player X chooses the top-left cell)
- O X (Player O chooses the middle-left cell)
O X X (Player X chooses the top-right cell)
Player O wins!
In terms of time complexity, the maximum time it can take to play Tic Tac Toe is 9 moves, as it is played on a 3x3 grid with a maximum of 9 squares. Regardless of the outcome (win, draw, or loss), the number of moves made will always be 9 or less. Therefore, the time complexity of Tic Tac Toe is O(1).
For this assignment, let's select the card game "Blackjack" as our game of choice to determine its time complexity.
Brief Explanation of the Computing Concepts to be Modeled:
In this game of Blackjack, we will model and analyze the time complexity of the algorithmic steps involved in simulating the gameplay. The computing concepts to be modeled include decision-making, probability calculations, and iterative processes.
Brief Explanation of How the Game Functions:
In Blackjack, players aim to achieve a hand total higher than the dealer's without exceeding 21. Players are dealt two cards initially, and they can choose to "hit" (receive additional cards) or "stand" (end their turn) until they decide to stop or exceed 21 (called a "bust"). The dealer also follows specific rules for drawing cards. The game continues until all players have finished or have busted, and then the dealer reveals their hand to determine the winners.
Brief Explanation of the Original Game on Which We Have Based the Assignment:
Blackjack is a popular casino card game played worldwide. It involves elements of decision-making, probability, and strategy. The original game of Blackjack exists as a physical card game, but various computerized versions and simulations have been developed, integrating the game rules with computing concepts.
Brief Explanation of How the Game Was Integrated with the Concepts of Computing:
To integrate the game of Blackjack with computing concepts, we will design an algorithm that simulates the gameplay. Our algorithm will include decision-making processes, calculating probabilities for drawing cards, and iterative steps to handle multiple players and the dealer.
Three Scenarios of Game Play:
Scenario 1: Single Player vs. Dealer
Setup: One player is playing against the dealer.
Desired Outcome: The player aims to achieve a higher hand total than the dealer without exceeding 21.
Sample Game:
1. Player receives cards: 5 of Hearts, 9 of Diamonds (total: 14).
2. Player decides to hit and receives a 7 of Clubs (total: 21).
3. Dealer reveals their cards: 4 of Spades, Queen of Hearts (total: 14).
4. Dealer decides to hit and receives a 5 of Clubs (total: 19).
5. Player wins as their total is higher than the dealer without exceeding 21.
Scenario 2: Multiple Players vs. Dealer
Setup: Multiple players are playing against the dealer.
Desired Outcome: Each player aims to achieve a higher hand total than the dealer without exceeding 21.
Sample Game:
1. Player 1 receives cards: Ace of Spades, 10 of Hearts (total: 21).
2. Player 2 receives cards: 9 of Clubs, 5 of Diamonds (total: 14).
3. Dealer reveals their cards: 6 of Spades, 7 of Hearts (total: 13).
4. Player 1 wins as their total is higher than the dealer without exceeding 21.
Scenario 3: Player vs. Dealer with Decision Strategies
Setup: One player follows a specific decision strategy while playing against the dealer.
Desired Outcome: The player aims to optimize their chances of winning based on the decision strategy.
Sample Game:
1. Player receives cards: 8 of Diamonds, 6 of Clubs (total: 14).
2. Player uses the decision strategy to hit and receives a 5 of Hearts (total: 19).
3. Dealer reveals their cards: 7 of Spades, King of Diamonds (total: 17).
4. Dealer stands with a total of 17.
5. Player wins as their total is higher than the dealer without exceeding 21.
By analyzing the algorithmic steps involved in playing Blackjack and considering various scenarios, we can determine the maximum time complexity of the game, which depends on factors like the number of players and decision strategies employed.