Python: The Nim game

python (3 Part Series)

1 Pyenv to handle different versions of Python
2 Use the virtual environments with Python
3 Python: The Nim game

Today we are going to look at a small algorithm exercise in python, through the game called the nim game.

The rule

This is a two-player game. We have n matches to start with (for example 10).
In turn, each player will take 1, 2 or 3 matches. The player who takes the last match loses.

The algorithm

This is a fairly deterministic game, in the sense that when you know the trick, you can’t lose (unless you started from a losing position).

Here is a table of the right number of matches to take (x representing a losing position):

We can therefore observe an infinite periodic loop, with a period of 4.

The player has lost (if the other plays well), when we have a modulo 4 = 1 (in other words the remainder of the division is equal to 1).

The winning strategy is therefore to send the other player to a losing position.

1-player version

We will formalize this in the algorithm, using the modulo function, to write the computer’s AI.


<span>n</span> <span>=</span> <span>int</span><span>(</span><span>input</span><span>(</span><span>"</span><span>Enter the initial number of matches: </span><span>"</span><span>))</span>
<span>print</span><span>(</span><span>"</span><span>Number of matches : </span><span>"</span><span>,</span> <span>n</span><span>)</span>
<span>while</span> <span>n</span><span>></span><span>0</span><span>:</span>
    <span>j</span><span>=-</span><span>1</span>
    <span>print</span><span>(</span><span>"</span><span>P1 turn</span><span>"</span><span>)</span>
    <span>while</span> <span>j</span><span><</span><span>1</span> <span>or</span> <span>j</span><span>></span><span>3</span> <span>or</span> <span>j</span><span>></span><span>n</span><span>:</span>
        <span>j</span><span>=</span><span>int</span><span>(</span><span>input</span><span>(</span><span>"</span><span>How much do you take ? (1-3) </span><span>"</span><span>))</span>
    <span>n</span><span>=</span><span>n</span><span>-</span><span>j</span>
    <span>if</span> <span>n</span><span>==</span><span>0</span><span>:</span>
        <span>print</span><span>(</span><span>"</span><span>You lost !</span><span>"</span><span>)</span>
    <span>else</span><span>:</span>
        <span>print</span><span>(</span><span>"</span><span>P2 turn (cpu)</span><span>"</span><span>)</span>
        <span>print</span><span>(</span><span>"</span><span>Remaining </span><span>"</span><span>,</span> <span>n</span><span>)</span>
        <span>if</span> <span>n</span><span>%</span><span>4</span><span>==</span><span>3</span><span>:</span>
            <span>p</span><span>=</span><span>2</span>
        <span>elif</span> <span>n</span><span>%</span><span>4</span><span>==</span><span>2</span><span>:</span>
            <span>p</span><span>=</span><span>1</span>
        <span>elif</span> <span>n</span><span>%</span><span>4</span><span>==</span><span>0</span><span>:</span>
            <span>p</span><span>=</span><span>3</span>
        <span>else</span><span>:</span>
            <span>p</span><span>=</span><span>1</span>
        <span>print</span><span>(</span><span>"</span><span>I take some</span><span>"</span><span>,</span> <span>p</span><span>)</span>
        <span>n</span><span>=</span><span>n</span><span>-</span><span>p</span>
        <span>print</span><span>(</span><span>"</span><span>Remaining </span><span>"</span><span>,</span> <span>n</span><span>)</span>
        <span>if</span> <span>n</span><span>==</span><span>0</span><span>:</span>
            <span>print</span><span>(</span><span>"</span><span>I lost !</span><span>"</span><span>)</span>
<span>n</span> <span>=</span> <span>int</span><span>(</span><span>input</span><span>(</span><span>"</span><span>Enter the initial number of matches: </span><span>"</span><span>))</span>
<span>print</span><span>(</span><span>"</span><span>Number of matches : </span><span>"</span><span>,</span> <span>n</span><span>)</span>
<span>while</span> <span>n</span><span>></span><span>0</span><span>:</span>
    <span>j</span><span>=-</span><span>1</span>
    <span>print</span><span>(</span><span>"</span><span>P1 turn</span><span>"</span><span>)</span>
    <span>while</span> <span>j</span><span><</span><span>1</span> <span>or</span> <span>j</span><span>></span><span>3</span> <span>or</span> <span>j</span><span>></span><span>n</span><span>:</span>
        <span>j</span><span>=</span><span>int</span><span>(</span><span>input</span><span>(</span><span>"</span><span>How much do you take ? (1-3) </span><span>"</span><span>))</span>
    <span>n</span><span>=</span><span>n</span><span>-</span><span>j</span>
    <span>if</span> <span>n</span><span>==</span><span>0</span><span>:</span>
        <span>print</span><span>(</span><span>"</span><span>You lost !</span><span>"</span><span>)</span>
    <span>else</span><span>:</span>
        <span>print</span><span>(</span><span>"</span><span>P2 turn (cpu)</span><span>"</span><span>)</span>
        <span>print</span><span>(</span><span>"</span><span>Remaining </span><span>"</span><span>,</span> <span>n</span><span>)</span>
        <span>if</span> <span>n</span><span>%</span><span>4</span><span>==</span><span>3</span><span>:</span>
            <span>p</span><span>=</span><span>2</span>
        <span>elif</span> <span>n</span><span>%</span><span>4</span><span>==</span><span>2</span><span>:</span>
            <span>p</span><span>=</span><span>1</span>
        <span>elif</span> <span>n</span><span>%</span><span>4</span><span>==</span><span>0</span><span>:</span>
            <span>p</span><span>=</span><span>3</span>
        <span>else</span><span>:</span>
            <span>p</span><span>=</span><span>1</span>
        <span>print</span><span>(</span><span>"</span><span>I take some</span><span>"</span><span>,</span> <span>p</span><span>)</span>
        <span>n</span><span>=</span><span>n</span><span>-</span><span>p</span>
        <span>print</span><span>(</span><span>"</span><span>Remaining </span><span>"</span><span>,</span> <span>n</span><span>)</span>
        <span>if</span> <span>n</span><span>==</span><span>0</span><span>:</span>
            <span>print</span><span>(</span><span>"</span><span>I lost !</span><span>"</span><span>)</span>
n = int(input("Enter the initial number of matches: "))
print("Number of matches : ", n)
while n>0:
    j=-1
    print("P1 turn")
    while j<1 or j>3 or j>n:
        j=int(input("How much do you take ? (1-3) "))
    n=n-j
    if n==0:
        print("You lost !")
    else:
        print("P2 turn (cpu)")
        print("Remaining ", n)
        if n%4==3:
            p=2
        elif n%4==2:
            p=1
        elif n%4==0:
            p=3
        else:
            p=1
        print("I take some", p)
        n=n-p
        print("Remaining ", n)
        if n==0:
            print("I lost !")

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Two-players version

Here is a version if you want experiment with a friend, keeping in mind this strategy :


<span>def</span> <span>nim_game</span><span>():</span>
    <span>print</span><span>(</span><span>"</span><span>Welcome to the Nim Game!</span><span>"</span><span>)</span>
    <span>print</span><span>(</span><span>"</span><span>Rules: Players take turns removing 1 to 3 objects from the pile.</span><span>"</span><span>)</span>
    <span>print</span><span>(</span><span>"</span><span>The player forced to take the last object loses.</span><span>"</span><span>)</span>
    <span># Initialize the pile </span>    <span>pile</span> <span>=</span> <span>int</span><span>(</span><span>input</span><span>(</span><span>"</span><span>Enter the initial number of objects in the pile: </span><span>"</span><span>))</span>
    <span>while</span> <span>pile</span> <span><=</span> <span>0</span><span>:</span>
        <span>print</span><span>(</span><span>"</span><span>The pile must contain at least 1 object.</span><span>"</span><span>)</span>
        <span>pile</span> <span>=</span> <span>int</span><span>(</span><span>input</span><span>(</span><span>"</span><span>Enter the initial number of objects in the pile: </span><span>"</span><span>))</span>
    <span># Player names </span>    <span>player1</span> <span>=</span> <span>input</span><span>(</span><span>"</span><span>Enter Player 1</span><span>'</span><span>s name: </span><span>"</span><span>)</span>
    <span>player2</span> <span>=</span> <span>input</span><span>(</span><span>"</span><span>Enter Player 2</span><span>'</span><span>s name: </span><span>"</span><span>)</span>
    <span># Start the game </span>    <span>current_player</span> <span>=</span> <span>player1</span>
    <span>while</span> <span>pile</span> <span>></span> <span>0</span><span>:</span>
        <span>print</span><span>(</span><span>f</span><span>"</span><span>\n</span><span>There are </span><span>{</span><span>pile</span><span>}</span><span> objects in the pile.</span><span>"</span><span>)</span>
        <span>print</span><span>(</span><span>f</span><span>"</span><span>{</span><span>current_player</span><span>}</span><span>'</span><span>s turn.</span><span>"</span><span>)</span>
        <span># Get the number of objects to remove </span>        <span>try</span><span>:</span>
            <span>remove</span> <span>=</span> <span>int</span><span>(</span><span>input</span><span>(</span><span>"</span><span>How many objects will you take (1-3)? </span><span>"</span><span>))</span>
            <span>if</span> <span>remove</span> <span><</span> <span>1</span> <span>or</span> <span>remove</span> <span>></span> <span>3</span><span>:</span>
                <span>print</span><span>(</span><span>"</span><span>Invalid move. You can only take 1, 2, or 3 objects.</span><span>"</span><span>)</span>
                <span>continue</span>
            <span>if</span> <span>remove</span> <span>></span> <span>pile</span><span>:</span>
                <span>print</span><span>(</span><span>"</span><span>Invalid move. You cannot take more objects than are in the pile.</span><span>"</span><span>)</span>
                <span>continue</span>
        <span>except</span> <span>ValueError</span><span>:</span>
            <span>print</span><span>(</span><span>"</span><span>Invalid input. Please enter a number between 1 and 3.</span><span>"</span><span>)</span>
            <span>continue</span>
        <span># Update the pile </span>        <span>pile</span> <span>-=</span> <span>remove</span>
        <span># Check if the game is over </span>        <span>if</span> <span>pile</span> <span>==</span> <span>0</span><span>:</span>
            <span>print</span><span>(</span><span>f</span><span>"</span><span>\n</span><span>{</span><span>current_player</span><span>}</span><span> is forced to take the last object and loses!</span><span>"</span><span>)</span>
            <span>break</span>
        <span># Switch players </span>        <span>current_player</span> <span>=</span> <span>player2</span> <span>if</span> <span>current_player</span> <span>==</span> <span>player1</span> <span>else</span> <span>player1</span>
    <span>print</span><span>(</span><span>"</span><span>Game over. Thanks for playing!</span><span>"</span><span>)</span>
<span># Run the game </span><span>if</span> <span>__name__</span> <span>==</span> <span>"</span><span>__main__</span><span>"</span><span>:</span>
    <span>nim_game</span><span>()</span>
<span>def</span> <span>nim_game</span><span>():</span>
    <span>print</span><span>(</span><span>"</span><span>Welcome to the Nim Game!</span><span>"</span><span>)</span>
    <span>print</span><span>(</span><span>"</span><span>Rules: Players take turns removing 1 to 3 objects from the pile.</span><span>"</span><span>)</span>
    <span>print</span><span>(</span><span>"</span><span>The player forced to take the last object loses.</span><span>"</span><span>)</span>

    <span># Initialize the pile </span>    <span>pile</span> <span>=</span> <span>int</span><span>(</span><span>input</span><span>(</span><span>"</span><span>Enter the initial number of objects in the pile: </span><span>"</span><span>))</span>
    <span>while</span> <span>pile</span> <span><=</span> <span>0</span><span>:</span>
        <span>print</span><span>(</span><span>"</span><span>The pile must contain at least 1 object.</span><span>"</span><span>)</span>
        <span>pile</span> <span>=</span> <span>int</span><span>(</span><span>input</span><span>(</span><span>"</span><span>Enter the initial number of objects in the pile: </span><span>"</span><span>))</span>

    <span># Player names </span>    <span>player1</span> <span>=</span> <span>input</span><span>(</span><span>"</span><span>Enter Player 1</span><span>'</span><span>s name: </span><span>"</span><span>)</span>
    <span>player2</span> <span>=</span> <span>input</span><span>(</span><span>"</span><span>Enter Player 2</span><span>'</span><span>s name: </span><span>"</span><span>)</span>

    <span># Start the game </span>    <span>current_player</span> <span>=</span> <span>player1</span>

    <span>while</span> <span>pile</span> <span>></span> <span>0</span><span>:</span>
        <span>print</span><span>(</span><span>f</span><span>"</span><span>\n</span><span>There are </span><span>{</span><span>pile</span><span>}</span><span> objects in the pile.</span><span>"</span><span>)</span>
        <span>print</span><span>(</span><span>f</span><span>"</span><span>{</span><span>current_player</span><span>}</span><span>'</span><span>s turn.</span><span>"</span><span>)</span>

        <span># Get the number of objects to remove </span>        <span>try</span><span>:</span>
            <span>remove</span> <span>=</span> <span>int</span><span>(</span><span>input</span><span>(</span><span>"</span><span>How many objects will you take (1-3)? </span><span>"</span><span>))</span>
            <span>if</span> <span>remove</span> <span><</span> <span>1</span> <span>or</span> <span>remove</span> <span>></span> <span>3</span><span>:</span>
                <span>print</span><span>(</span><span>"</span><span>Invalid move. You can only take 1, 2, or 3 objects.</span><span>"</span><span>)</span>
                <span>continue</span>
            <span>if</span> <span>remove</span> <span>></span> <span>pile</span><span>:</span>
                <span>print</span><span>(</span><span>"</span><span>Invalid move. You cannot take more objects than are in the pile.</span><span>"</span><span>)</span>
                <span>continue</span>
        <span>except</span> <span>ValueError</span><span>:</span>
            <span>print</span><span>(</span><span>"</span><span>Invalid input. Please enter a number between 1 and 3.</span><span>"</span><span>)</span>
            <span>continue</span>

        <span># Update the pile </span>        <span>pile</span> <span>-=</span> <span>remove</span>

        <span># Check if the game is over </span>        <span>if</span> <span>pile</span> <span>==</span> <span>0</span><span>:</span>
            <span>print</span><span>(</span><span>f</span><span>"</span><span>\n</span><span>{</span><span>current_player</span><span>}</span><span> is forced to take the last object and loses!</span><span>"</span><span>)</span>
            <span>break</span>

        <span># Switch players </span>        <span>current_player</span> <span>=</span> <span>player2</span> <span>if</span> <span>current_player</span> <span>==</span> <span>player1</span> <span>else</span> <span>player1</span>

    <span>print</span><span>(</span><span>"</span><span>Game over. Thanks for playing!</span><span>"</span><span>)</span>

<span># Run the game </span><span>if</span> <span>__name__</span> <span>==</span> <span>"</span><span>__main__</span><span>"</span><span>:</span>
    <span>nim_game</span><span>()</span>
def nim_game():
    print("Welcome to the Nim Game!")
    print("Rules: Players take turns removing 1 to 3 objects from the pile.")
    print("The player forced to take the last object loses.")

    # Initialize the pile     pile = int(input("Enter the initial number of objects in the pile: "))
    while pile <= 0:
        print("The pile must contain at least 1 object.")
        pile = int(input("Enter the initial number of objects in the pile: "))

    # Player names     player1 = input("Enter Player 1's name: ")
    player2 = input("Enter Player 2's name: ")

    # Start the game     current_player = player1

    while pile > 0:
        print(f"\nThere are {pile} objects in the pile.")
        print(f"{current_player}'s turn.")

        # Get the number of objects to remove         try:
            remove = int(input("How many objects will you take (1-3)? "))
            if remove < 1 or remove > 3:
                print("Invalid move. You can only take 1, 2, or 3 objects.")
                continue
            if remove > pile:
                print("Invalid move. You cannot take more objects than are in the pile.")
                continue
        except ValueError:
            print("Invalid input. Please enter a number between 1 and 3.")
            continue

        # Update the pile         pile -= remove

        # Check if the game is over         if pile == 0:
            print(f"\n{current_player} is forced to take the last object and loses!")
            break

        # Switch players         current_player = player2 if current_player == player1 else player1

    print("Game over. Thanks for playing!")

# Run the game if __name__ == "__main__":
    nim_game()

Enter fullscreen mode Exit fullscreen mode

Here is a little logic exercise, that you can use to practice algorithms in Python.

Also, you know the secret and will not be fooled by this game anymore, have fun!

python (3 Part Series)

1 Pyenv to handle different versions of Python
2 Use the virtual environments with Python
3 Python: The Nim game

原文链接：Python: The Nim game

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