/*
* Algorithm Source: https://www.geeksforgeeks.org/combinatorial-game-theory-set-2-game-nim/
*
* Based on the number of stones - calculate the nim sum (aka binary sum ignoring the carries)
*
* If the Nim Sum does not equal zero - find a way to make it zero:
* Check the XOR between each value and the nim sum
* If this value is less than the value in the pile - reduce the pile to this number
*
* Example: piles = {3, 4, 5}
* nim sum = 3 ^ 4 ^ 5 = 2
*
* 3 ^ 2 = 1 <---- Since 1 < 3, we want to reduce this pile to 1 (remove 2 stones from pile 1)
* 4 ^ 2 = 6
* 5 ^ 2 = 7
*
* Why? Because 1 ^ 4 ^ 5 = 0 and ending your turn with a nim sum of 0 is a winning position
*
* However, if the nim sum starts at zero - its been mathematically proven that you will lose.
* Therefore, make a random move and hope your opponent makes a mistake
*/
public static void MakeOptimalMove()
{
int nimSum = CalculateNimSum();
int[] remainingStones = { Heaps.Heap1, Heaps.Heap2, Heaps.Heap3 };
if (nimSum != 0)
{
for (int i = 0; i < remainingStones.Length; i++)
{
if ((remainingStones[i] ^ nimSum) < remainingStones[i])
{
int amountToRemove = remainingStones[i] - (remainingStones[i] ^ nimSum);
Render.ClearLine();
Console.WriteLine($"Computer removed {amountToRemove} stones from pile {i + 1}");
Heaps.UpdateNumberOfStones(amountToRemove, i);
break;
}
}
}
else
{
MakeRandomMove();
}
}
public static void MakeRandomMove()
{
int randomAmountToRemove = -1; //Start at invalid amount & heap
int heapToRemoveFrom = -1;
bool isValidMove = false;
while (!isValidMove) //Make sure move is valid before updating board
{
randomAmountToRemove = rnd.Next(1, Game.MAX_STONES);
heapToRemoveFrom = rnd.Next(0, 3);
isValidMove = Game.CheckIfValidMove(randomAmountToRemove, heapToRemoveFrom);
}
Render.ClearLine();
Console.WriteLine($"Computer removed {randomAmountToRemove} stones from pile {heapToRemoveFrom + 1}");
Heaps.UpdateNumberOfStones(randomAmountToRemove, heapToRemoveFrom);
}
public static int CURSOR_LEFT = 6; //user input the cursor will move & write the message without disrupting the game
public static void Turn()
{
bool validMove = false;
bool validNumber = false;
int amountToRemove = 0;
while (!validNumber || !validMove) //User must enter an integer that is a valid move
{
SelectedHeap = GetSelectedHeap();
AskForUserInput();
validNumber = int.TryParse(Console.ReadLine(), out amountToRemove); //Check if user gave an integer value
validMove = Game.CheckIfValidMove(amountToRemove, SelectedHeap); //Check if that integer value is a valid move
if (!validNumber)
{
amountToRemove = AskForValidNumber();
} //Lines22-23: error messages for invalid input
else if (!validMove)
{
amountToRemove = AskForValidMove(amountToRemove);
}
}
Heaps.UpdateNumberOfStones(amountToRemove, SelectedHeap);
}