//calculates the modular sum of each bool[] in nums which represents a number in binary
public static bool[] CalcSum(bool[][] nums)
{
if (nums.Length == 1)
{
return(nums[0]);
}
bool[] total = nums[0];
for (int i = 1; i < nums.Length; i++)
{
total = PathCutthroat.ModAdd(total, nums[i]);
}
return(total);
}
//calculates the modular sum of each bool[] in nums except for nums[notIndex]
public static bool[] CalcSumOthers(bool[][] nums, int notIndex)
{
if (nums.Length == 1 && notIndex == 0)
{
return(new bool[1]);
}
bool[] total = (notIndex != 0) ? nums[0] : nums[1];
for (int i = ((notIndex != 0) ? 1 : 2); i < nums.Length; i++)
{
if (i != notIndex)
{
total = PathCutthroat.ModAdd(total, nums[i]);
}
}
return(total);
}
//calculate a winning move if one exists, otherwise just choose the first vertex of the first piece in pieces
public static int CalcMove()
{
//piles represents the grundy numbers of the sizes of each Path in pieces, in binary
bool[][] piles = new bool[pieces.Count][];
for (int i = 0; i < pieces.Count; i++)
{
piles[i] = PathCutthroat.ToBinArray(grunds[pieces[i].Size()]);
}
//totalSum is the sum of all numbers in piles without carry-over
bool[] totalSum = CalcSum(piles);
//endAt is the largest index in totalSum to hold a 1 (true)
int endAt;
for (endAt = totalSum.Length - 1; endAt >= 0; endAt--)
{
if (totalSum[endAt] == true)
{
break;
}
}
//endAt == -1 only if there is no winning move (i.e. totalSum == 0) and so return the first vertex of the first piece in pieces
if (endAt == -1)
{
return(pieces[0].Front());
}
//coorPiles stores the binary numbers in piles truncated at the index endAt
bool[][] coorPiles = new bool[pieces.Count][];
for (int i = 0; i < pieces.Count; i++)
{
bool[] p = piles[i];
coorPiles[i] = new bool[Math.Min(endAt + 1, p.Length)];
for (int j = 0; j < p.Length && j <= endAt; j++)
{
coorPiles[i][j] = p[j];
}
}
//the optimal move is to remove from the Path that corresponds to the max number in coorPiles
int targetIndex = FindMax(coorPiles);
//the optimal move is to make the targetIndex Path have the grundy number of the sum of all the other Paths (without carry-over)
//first calculate what this sum is for the truncated numbers (coorPiles) since it is already equal to the sum for all places above since they were zero
int lowerTargetVal = PathCutthroat.FromBinArray(CalcSumOthers(coorPiles, targetIndex));
//diff stores the change that needs to happen to pieces[targetIndex] in terms of grundy numbers
int diff = PathCutthroat.FromBinArray(coorPiles[targetIndex]) - lowerTargetVal;
//targetVal then stores the grundy number that pieces[targetVal] must have (as an optimal move)
int targetVal = PathCutthroat.FromBinArray(piles[targetIndex]) - diff;
//Need to split pieces[targetIndex] so that the two paths sum to targetVal in grundy value
//splitter will store the index of what needs to be removed in pieces[targetValue] where 0 is the front
int splitter = 0;
int n = pieces[targetIndex].Size();
for (int i = 0; i < n / 2 + 1; i++)
{
//when i is found such that it splits pieces[targetIndex] into two piles equivalent to a nim pile of targetVal, set splitter to i and break
if (PathCutthroat.ModAdd(grunds[i], grunds[n - i - 1]) == targetVal)
{
splitter = i;
break;
}
}
//splitter stores how far into pieces[targetIndex] the vertex to be removed is
return(pieces[targetIndex].Front() + splitter);
}