public IEnumerator SolveGame(Game game)
{
yield return(null);
LogsManager.ins.AddLog(string.Format("{0} ma dokładnie dwie strategie.", game.gameData.playerB));
LogsManager.ins.AddLog("Wyszukiwanie strategii dającej największą przegraną dla gracza");
yield return(LogsManager.Wait());
id = IDTheLargestVal(game.gameData);
yield return(CrossOverMax(id, game.gameData));
subGame[1, 0] = game.gameData.matrix[point.strategyA_ID, 0];
subGame[1, 1] = game.gameData.matrix[point.strategyA_ID, 1];
subGame[0, 0] = game.gameData.matrix[point.strategyB_ID, 0];
subGame[0, 1] = game.gameData.matrix[point.strategyB_ID, 1];
char[] useingStrategies = new char[2] {
game.gameData.rowStrategies[point.strategyA_ID],
game.gameData.rowStrategies[point.strategyB_ID]
};
game.gameData.rowStrategies = useingStrategies.ToList();
game.gameData.matrix = subGame;
}
public IEnumerator SolveGame(Game game)
{
sbyte minInRow, maxInCol;
byte cellID = 0;
LogsManager.ins.AddLog("Zaznaczanie punktów siodłowych.");
yield return(MinMaxPanel.ins.SetUp(true));
yield return(LogsManager.Wait());
TableManager.ins.SelectCell(0, EColors.Default, true);
for (byte i = 0; i < game.gameData.matrix.GetLength(0); i++)
{
for (byte j = 0; j < game.gameData.matrix.GetLength(1); j++)
{
if (game.gameData.matrix[i, j] == (sbyte)valueOfGame)
{
minInRow = game.GetRow(i).Min();
maxInCol = game.GetColumn(j).Max();
if (minInRow == maxInCol)
{
LogsManager.ins.AddLog("Zaznaczono punkt siodłowy.");
yield return(LogsManager.Wait());
TableManager.ins.SelectCell(cellID, EColors.Green);
}
}
cellID++;
}
}
}
private IEnumerator WriteLines(int[] strA, int[] strB)
{
LogsManager.ins.AddLog("Trwa wypisywanie strategii drugiego gracza w postaci prostych.");
yield return(LogsManager.Wait());
Rect rect = valuesList.GetComponent <RectTransform>().rect;
int valA, valB;
float height = rect.height / leftValues.childCount;
float width = rect.width;
float halfOnce = height / 2;
for (int i = 0; i < strA.Length; i++)
{
valA = strA[i];
valB = strB[i];
UILineRenderer lR = Instantiate(linePrefab, valuesList).GetComponent <UILineRenderer>();
lR.Points[0] = new Vector2(0, rect.height - (GetChildID(valA) * height) - halfOnce);
lR.Points[1] = new Vector2(width, rect.height - (GetChildID(valB) * height) - halfOnce);
lines.Add(lR);
LogsManager.ins.AddLog("Wypisano strategię.");
yield return(LogsManager.Wait());
}
}
public IEnumerator SetUp(int[,] matrix)
{
//cG.alpha = 1;
this.matrix = matrix;
yield return(null);
int[] strategyA = (matrix.GetLength(0) == 2) ? GetRow(0) : GetColumn(0);
int[] strategyB = (matrix.GetLength(0) == 2) ? GetRow(1) : GetColumn(1);
#region Wyszukiwanie najmniejszej i największej wartości
int min, max;
int minA = strategyA.Min();
int minB = strategyB.Min();
int maxA = strategyA.Max();
int maxB = strategyB.Max();
min = (minA < minB) ? minA : minB;
max = (maxA > maxB) ? maxA : maxB;
#endregion
LogsManager.ins.AddLog("Trwa wypisywanie wartości dla gracza, który posiada dokładnie dwie strategie.");
yield return(LogsManager.Wait());
WriteValues(min, max);
yield return(WriteLines(strategyA, strategyB));
}
private IEnumerator RowsDomination()
{
sbyte[] rowA, rowB;
yield return(LogsManager.Wait());
for (byte i = 0; i < gameData.matrix.GetLength(0) - 1; i++)
{
rowA = GetRow(i);
for (byte j = (byte)(i + 1); j < gameData.matrix.GetLength(0); j++)
{
LogsManager.ins.AddLog(string.Format("Porównuję strategię gracza: {2} - {0} z {1}", gameData.rowStrategies[i].ToString(), gameData.rowStrategies[j].ToString(), gameData.playerA));
rowB = GetRow(j);
TableManager.ins.SelectRow((byte)gameData.matrix.GetLength(0), i, EColors.Green, true);
yield return(LogsManager.Wait());
TableManager.ins.SelectRow((byte)gameData.matrix.GetLength(0), j, EColors.Blue);
yield return(LogsManager.Wait());
// -1 = rowA dominuje rowB; 1 = rowB dominuje rowA; 0 = brak dominacji
sbyte domination = Compare(rowA, rowB);
if (domination == -1)
{
LogsManager.ins.AddLog(string.Format("Strategia {0} jest dominowana przez {1}", gameData.rowStrategies[j].ToString(), gameData.rowStrategies[i].ToString()));
TableManager.ins.SelectRow((byte)gameData.matrix.GetLength(0), j, EColors.Red, true);
yield return(LogsManager.Wait());
gameData.matrix = RemoveRowFromMatrix(j--);
TableManager.ins.DisplayTable(gameData);
yield return(LogsManager.Wait());
}
else if (domination == 1)
{
LogsManager.ins.AddLog(string.Format("Strategia {0} dominuje strategię {1}", gameData.rowStrategies[j].ToString(), gameData.rowStrategies[i].ToString()));
TableManager.ins.SelectRow((byte)gameData.matrix.GetLength(0), i, EColors.Red, true);
yield return(LogsManager.Wait());
gameData.matrix = RemoveRowFromMatrix(i--);
TableManager.ins.DisplayTable(gameData);
yield return(LogsManager.Wait());
break;
}
else
{
LogsManager.ins.AddLog("Brak dominacji pomiędzy strategiami.");
TableManager.ins.SelectCell(0, EColors.Default, true);
yield return(LogsManager.Wait());
}
}
}
yield return(null);
}
private IEnumerator ColumnsDomination()
{
sbyte[] colA, colB;
yield return(LogsManager.Wait());
for (byte i = 0; i < gameData.matrix.GetLength(1) - 1; i++)
{
colA = GetColumn(i);
for (byte j = (byte)(i + 1); j < gameData.matrix.GetLength(1); j++)
{
colB = GetColumn(j);
LogsManager.ins.AddLog(string.Format("Porównuję strategię gracza: {2} - {0} z {1}", gameData.colStrategies[i].ToString(), gameData.colStrategies[j].ToString(), gameData.playerB));
TableManager.ins.SelectColumn((byte)gameData.matrix.GetLength(1), i, EColors.Green, true);
yield return(LogsManager.Wait());
TableManager.ins.SelectColumn((byte)gameData.matrix.GetLength(1), j, EColors.Blue);
yield return(LogsManager.Wait());
// 1 = colA dominuje colB; 1 = colB dominuje colA; 0 = brak dominacji
sbyte domination = Compare(colA, colB);
if (domination == 1)
{
LogsManager.ins.AddLog(string.Format("Strategia {0} jest dominowana przez {1}", gameData.colStrategies[j].ToString(), gameData.colStrategies[i].ToString()));
TableManager.ins.SelectColumn((byte)gameData.matrix.GetLength(1), j, EColors.Red, true);
yield return(LogsManager.Wait());
gameData.matrix = RemoveColumnFromMatrix(j--);
TableManager.ins.DisplayTable(gameData);
yield return(LogsManager.Wait());
}
else if (domination == -1)
{
LogsManager.ins.AddLog(string.Format("Strategia {0} dominuje strategię {1}", gameData.colStrategies[j].ToString(), gameData.colStrategies[i]).ToString());
TableManager.ins.SelectColumn((byte)gameData.matrix.GetLength(1), i, EColors.Red, true);
yield return(LogsManager.Wait());
gameData.matrix = RemoveColumnFromMatrix(i--);
TableManager.ins.DisplayTable(gameData);
yield return(LogsManager.Wait());
break;
}
else
{
TableManager.ins.SelectCell(0, EColors.Default, true);
LogsManager.ins.AddLog("Brak dominacji pomiędzy strategiami");
yield return(LogsManager.Wait());
}
}
}
yield return(null);
}
public IEnumerator SetUp(bool succes)
{
CanvasGroup panel = (succes) ? successPanel : failedPanel;
panel.alpha = 1;
blurImage.enabled = true;
yield return(LogsManager.Wait(3));
blurImage.enabled = false;
panel.alpha = 0;
}
public IEnumerator CheckDominations()
{
if (stateSolver.GetType() == typeof(StateNoSaddlePoint))
{
LogsManager.ins.AddLog("Sprawdzanie strategii zdominowanych.");
yield return(RemoveDominatedStrategies());
}
else
{
yield return(LogsManager.Wait());
}
}
private IEnumerator RemoveDominatedStrategies()
{
yield return(LogsManager.Wait());
byte oldCols; // ile wierszy i kolumn posiada macierz przed dominacją
do
{
oldCols = (byte)gameData.matrix.GetLength(1);
yield return(RowsDomination());
yield return(ColumnsDomination());
} while (oldCols != gameData.matrix.GetLength(1));
}
private IEnumerator FindMinMax()
{
yield return(LogsManager.Wait());
sbyte max = sbyte.MinValue;
sbyte minInRow;
sbyte[] row;
for (byte i = 0; i < gameData.matrix.GetLength(0); i++)
{
row = GetRow(i);
TableManager.ins.SelectRow((byte)gameData.matrix.GetLength(0), i, EColors.Green, true);
minInRow = row.Min();
MiniMaksManager.ins.ChangeMinVal(i, minInRow);
LogsManager.ins.AddLog(string.Format("Znaleziono najmniejszą wartość w strategii {0} gracza: {1}", gameData.rowStrategies[i].ToString(), gameData.playerA));
yield return(LogsManager.Wait());
if (minInRow > max)
{
max = minInRow;
LogsManager.ins.AddLog("Znaleziony min wiersza jest największy.");
MiniMaksManager.ins.SelectMin(i, EColors.Red, true);
yield return(LogsManager.Wait());
}
else if (minInRow == max)
{
LogsManager.ins.AddLog("Znaleziono kolejny min wiersza");
MiniMaksManager.ins.SelectMin(i, EColors.Red);
yield return(LogsManager.Wait());
}
else
{
LogsManager.ins.AddLog("Znaleziona strategia nie jest największa spośród minimów");
yield return(LogsManager.Wait());
}
}
minMax = max;
}
private IEnumerator FindMaxMin()
{
yield return(LogsManager.Wait());
sbyte min = sbyte.MaxValue;
sbyte maxInColumn;
sbyte[] column;
for (byte i = 0; i < gameData.matrix.GetLength(1); i++)
{
column = GetColumn(i);
TableManager.ins.SelectColumn((byte)gameData.matrix.GetLength(1), i, EColors.Green, true);
maxInColumn = column.Max();
MiniMaksManager.ins.ChangeMaxVal(i, maxInColumn);
LogsManager.ins.AddLog(string.Format("Znaleziono największą wartość w strategii {0} gracza: {1}", gameData.colStrategies[i].ToString(), gameData.playerB));
yield return(LogsManager.Wait());
if (maxInColumn < min)
{
min = maxInColumn;
LogsManager.ins.AddLog("Znaleziony maks kolumny jest najmniejszy.");
MiniMaksManager.ins.SelectMaks(i, EColors.Red, true);
yield return(LogsManager.Wait());
}
else if (maxInColumn == min)
{
LogsManager.ins.AddLog("Znaleziono kolejny maks kolumny");
MiniMaksManager.ins.SelectMaks(i, EColors.Red);
yield return(LogsManager.Wait());
}
else
{
LogsManager.ins.AddLog("Znaleziona strategia nie jest najmniejsza spośród maksimów");
yield return(LogsManager.Wait());
}
}
maxMin = min;
}
public IEnumerator CheckSaddlePoint()
{
LogsManager.ins.AddLog("Sprawdzanie punktów siodłowych.");
MiniMaksManager.ins.SetUp(gameData);
yield return(LogsManager.Wait());
yield return(FindMinMax());
yield return(FindMaxMin());
if (minMax == maxMin)
{
LogsManager.ins.AddLog("Znaleziono punkt siodłowy.", EColors.Green);
stateSolver = new StateSaddlePoint(minMax);
yield return(LogsManager.Wait());
}
else
{
LogsManager.ins.AddLog("Brak punktów siodłowych.", EColors.Red);
stateSolver = new StateNoSaddlePoint();
yield return(LogsManager.Wait());
}
}
public IEnumerator SolveGame(Game game)
{
yield return(null);
LogsManager.ins.AddLog(string.Format("{0} ma dokładnie dwie strategie.", game.gameData.playerA));
yield return(LogsManager.Wait());
id = IdTheSmalestVal(game.gameData);
yield return(CrossOverMin(id, game.gameData));
subGame[0, 1] = game.gameData.matrix[0, point.strategyA_ID];
subGame[1, 1] = game.gameData.matrix[1, point.strategyA_ID];
subGame[0, 0] = game.gameData.matrix[0, point.strategyB_ID];
subGame[1, 0] = game.gameData.matrix[1, point.strategyB_ID];
char[] useingStrategies = new char[2] {
game.gameData.colStrategies[point.strategyA_ID],
game.gameData.colStrategies[point.strategyB_ID]
};
game.gameData.colStrategies = useingStrategies.ToList();
game.gameData.matrix = subGame;
}
private IEnumerator CrossOverMax(byte idLargest, GameData gameData, double max = double.MaxValue)
{
LogsManager.ins.AddLog("Strategia znaleziona: " + gameData.rowStrategies[idLargest]);
GraphicalManager.ins.SelectLine(idLargest, EColors.Red, true);
yield return(LogsManager.Wait());
byte newID = 0;
Vector strategyA_start = new Vector(gameData.matrix[idLargest, 0], 0);
Vector strategyA_end = new Vector(gameData.matrix[idLargest, 1], 1);
if (GraphicalManager.ins.highLine.Points.Length == 0)
{
GraphicalManager.ins.SetHighLinePoint(new Vector2((float)strategyA_start.X, (float)strategyA_start.Y));
}
Vector strategyB_start, strategyB_end;
Vector maxIntersaction = new Vector(double.MinValue, 0);
Vector intersection;
for (byte i = 0; i < gameData.matrix.GetLength(0); i++)
{
if (strategyA_start.X < strategyA_end.X)
{
break;
}
strategyB_start = new Vector(gameData.matrix[i, 0], 0);
strategyB_end = new Vector(gameData.matrix[i, 1], 1);
if (strategyA_start.Equals(strategyB_start) && strategyA_end.Equals(strategyB_end))
{
continue;
}
bool actual = Vector.Intersect(strategyA_start, strategyA_end, strategyB_start, strategyB_end, out intersection);
if (actual && intersection.X > maxIntersaction.X && Math.Round(intersection.X, 2) < Math.Round(max, 2))
{
maxIntersaction = intersection;
newID = i;
}
}
if (maxIntersaction.X > double.MinValue)
{
Cross2x2 c = new Cross2x2(idLargest, newID, maxIntersaction);
if (point == null || c.point.X < point.point.X)
{
point = c;
}
GraphicalManager.ins.SetHighLinePoint(new Vector2((float)point.point.X, (float)point.point.Y));
yield return(CrossOverMax(newID, gameData, maxIntersaction.X));
}
else
{
GraphicalManager.ins.SetHighLinePoint(new Vector2((float)strategyA_end.X, (float)strategyA_end.Y));
GraphicalManager.ins.SelectLine(0, EColors.Default, true);
}
}
public override IEnumerator SolveGame(Game game)
{
LogsManager.ins.AddLog("Rozwiazywanie gry w strategiach mieszanych 2x2");
FrequencyManager.ins.SetUp(game.gameData);
yield return(LogsManager.Wait());
game.gameData.rowFreq = new int[2];
game.gameData.colFreq = new int[2];
sbyte[] row;
for (byte i = 0; i < 2; i++)
{
row = game.GetRow(i);
TableManager.ins.SelectRow(2, i, EColors.Green, true);
LogsManager.ins.AddLog("Wybieram wiersz " + game.gameData.rowStrategies[i].ToString(), EColors.Blue);
yield return(LogsManager.Wait());
LogsManager.ins.AddLog(string.Format("Wykonując obliczenia: |{0}-{1}|=|{2}|={3}. Zapisuje w {4} wierszu dla częstotliwości.",
row[0], row[1], row[0] - row[1], Math.Abs(row[0] - row[1]), 1 - i), EColors.Default);
yield return(LogsManager.Wait());
game.gameData.rowFreq[1 - i] = Math.Abs(row[0] - row[1]);
FrequencyManager.ins.ChangeRowFreq((sbyte)(1 - i), game.gameData.rowFreq[1 - i]);
yield return(LogsManager.Wait());
}
LogsManager.ins.AddLog("Optymalne skracanie wyników.", EColors.Blue);
yield return(LogsManager.Wait());
game.gameData.rowFreq = Game.DivisorRelativeRequences(game.gameData.rowFreq);
for (sbyte i = 0; i < game.gameData.rowFreq.Length; i++)
{
FrequencyManager.ins.ChangeRowFreq(i, game.gameData.rowFreq[i]);
yield return(LogsManager.Wait());
}
sbyte[] column;
for (byte i = 0; i < 2; i++)
{
column = game.GetColumn(i);
TableManager.ins.SelectColumn(2, i, EColors.Green, true);
LogsManager.ins.AddLog("Wybieram kolumnę " + game.gameData.colStrategies[i].ToString(), EColors.Blue);
yield return(LogsManager.Wait());
LogsManager.ins.AddLog(string.Format("Wykonując obliczenia: |{0}-{1}|=|{2}|={3}. Zapisuje w {4} kolumnie dla częstotliwości.",
column[0], column[1], column[0] - column[1], Math.Abs(column[0] - column[1]), 1 - i), EColors.Default);
yield return(LogsManager.Wait());
game.gameData.colFreq[1 - i] = Math.Abs(column[0] - column[1]);
FrequencyManager.ins.ChangeColFreq((sbyte)(1 - i), game.gameData.colFreq[1 - i]);
yield return(LogsManager.Wait());
}
TableManager.ins.SelectCell(0, EColors.Default, true);
LogsManager.ins.AddLog("Optymalne skracanie wyników.", EColors.Blue);
yield return(LogsManager.Wait());
game.gameData.colFreq = Game.DivisorRelativeRequences(game.gameData.colFreq);
for (sbyte i = 0; i < game.gameData.colFreq.Length; i++)
{
FrequencyManager.ins.ChangeColFreq(i, game.gameData.colFreq[i]);
yield return(LogsManager.Wait());
}
}
private IEnumerator CrossOverMin(byte idSmallest, GameData gameData, double min = double.MinValue)
{
LogsManager.ins.AddLog("Strategia znaleziona: " + gameData.colStrategies[idSmallest].ToString());
GraphicalManager.ins.SelectLine(idSmallest, EColors.Red, true);
yield return(LogsManager.Wait());
byte newID = 0;
Vector strategyA_start = new Vector(0, gameData.matrix[0, idSmallest]);
Vector strategyA_end = new Vector(1, gameData.matrix[1, idSmallest]);
if (GraphicalManager.ins.highLine.Points.Length == 0)
{
GraphicalManager.ins.SetHighLinePoint(new Vector2((float)strategyA_start.Y, (float)strategyA_start.X));
}
Vector strategyB_start, strategyB_end;
Vector minIntersaction = new Vector(0, double.MaxValue);
Vector intersaction;
for (byte i = 0; i < gameData.matrix.GetLength(1); i++)
{
if (strategyA_start.Y > strategyA_end.Y)
{
break;
}
strategyB_start = new Vector(0, gameData.matrix[0, i]);
strategyB_end = new Vector(1, gameData.matrix[1, i]);
if (strategyA_start.Equals(strategyB_start) && strategyA_end.Equals(strategyB_end))
{
continue;
}
bool actual = Vector.Intersect(strategyA_start, strategyA_end, strategyB_start, strategyB_end, out intersaction);
if (actual && intersaction.Y < minIntersaction.Y && Math.Round(intersaction.Y, 2) > Math.Round(min, 2))
{
minIntersaction = intersaction;
newID = i;
}
}
if (minIntersaction.Y < double.MaxValue)
{
Cross2x2 c = new Cross2x2(idSmallest, newID, minIntersaction);
if (point == null || c.point.Y > point.point.Y)
{
point = c;
}
GraphicalManager.ins.SetHighLinePoint(new Vector2((float)point.point.Y, (float)point.point.X));
yield return(CrossOverMin(newID, gameData, minIntersaction.Y));
}
else
{
GraphicalManager.ins.SetHighLinePoint(new Vector2((float)strategyA_end.Y, (float)strategyA_end.X));
GraphicalManager.ins.SelectLine(0, EColors.Default, true);
}
}
public override IEnumerator SolveGame(Game game)
{
LogsManager.ins.AddLog("Rozwiązywanie gry metodą przybliżoną.", EColors.Blue);
GameData gameData = game.gameData;
FrequencyManager.ins.SetUp(gameData);
SumManager.ins.SetUp(gameData);
yield return(LogsManager.Wait());
int repeatCount = 0;
byte id = 0;
sbyte[] data;
int minVal = 0;
int maxVal = 0;
gameData.rowFreq = new int[gameData.matrix.GetLength(0)];
gameData.colFreq = new int[gameData.matrix.GetLength(1)];
int[] lastRow = new int[gameData.matrix.GetLength(1)];
int[] lastCol = new int[gameData.matrix.GetLength(0)];
int stopCount = gameData.matrix.GetLength(0) * gameData.matrix.GetLength(1);
LogsManager.ins.AddLog(string.Format("Liczba powtórzeń liczona na podstawie ilocznu liczby strategii {0} oraz {1} i wynosi: {2}",
gameData.playerA, gameData.playerB, stopCount), EColors.Default);
yield return(LogsManager.Wait());
while (repeatCount < stopCount)
{
data = game.GetRow(id);
lastRow = AddToLast(lastRow, data);
gameData.rowFreq[id]++;
LogsManager.ins.AddLog(string.Format("Pobieram strategię {0} gracza {1} i dodaję do dodatkowej tablicy", gameData.rowStrategies[id].ToString(), gameData.playerA));
SumManager.ins.ChangeColSum(lastRow);
TableManager.ins.SelectRow((byte)gameData.matrix.GetLength(0), id, EColors.Green, true);
yield return(LogsManager.Wait());
LogsManager.ins.AddLog("Dla wybranej strategii zwiększam częstotliwość o 1");
FrequencyManager.ins.ChangeRowFreq((sbyte)id, gameData.rowFreq[id]);
yield return(LogsManager.Wait());
minVal = lastRow.Min();
id = GetElementID(lastRow, minVal);
LogsManager.ins.AddLog("Znajduję najmniejszą wartość w wybranym wierszu.");
SumManager.ins.SelectRow(id);
yield return(LogsManager.Wait());
data = game.GetColumn(id);
lastCol = AddToLast(lastCol, data);
gameData.colFreq[id]++;
LogsManager.ins.AddLog(string.Format("Pobieram strategię {0} gracza {1} i dodaję do dodatkowej tablicy", gameData.colStrategies[id].ToString(), gameData.playerB));
SumManager.ins.ChangeRowSm(lastCol);
TableManager.ins.SelectColumn((byte)gameData.matrix.GetLength(1), id, EColors.Green, true);
yield return(LogsManager.Wait());
LogsManager.ins.AddLog("Dla wybranej strategii zwiększam częstotliwość o 1");
FrequencyManager.ins.ChangeColFreq((sbyte)id, gameData.colFreq[id]);
yield return(LogsManager.Wait());
maxVal = lastCol.Max();
id = GetElementID(lastCol, maxVal);
LogsManager.ins.AddLog("Znajduję najmniejszą wartość w wybranej kolumnie.");
SumManager.ins.SelectColumn(id);
yield return(LogsManager.Wait());
repeatCount++;
LogsManager.ins.AddLog(string.Format("Powtórzenie: {0}/{1}.", repeatCount, stopCount), EColors.Yellow);
}
SumManager.ins.UnselectAll();
TableManager.ins.SelectCell(0, EColors.Default, true);
LogsManager.ins.AddLog("Optymalne skracanie wyników.", EColors.Blue);
gameData.rowFreq = Game.DivisorRelativeRequences(gameData.rowFreq);
gameData.colFreq = Game.DivisorRelativeRequences(gameData.colFreq);
for (sbyte i = 0; i < gameData.rowFreq.Length; i++)
{
FrequencyManager.ins.ChangeRowFreq(i, gameData.rowFreq[i]);
}
for (sbyte i = 0; i < gameData.colFreq.Length; i++)
{
FrequencyManager.ins.ChangeColFreq(i, gameData.colFreq[i]);
}
}
