private static int RunStep4(float[,] costs, bool[] rowsCovered, bool[] colsCovered, int w, int h)
{
if (costs == null)
{
throw new ArgumentNullException("Empty");
}
if (rowsCovered == null)
{
throw new ArgumentNullException("Empty");
}
if (colsCovered == null)
{
throw new ArgumentNullException("Empty");
}
var minValue = HungarianAlgorithm.FindMinimum(costs, rowsCovered, colsCovered, w, h);
for (var i = 0; i < h; i++)
{
for (var j = 0; j < w; j++)
{
if (rowsCovered[i])
{
costs[i, j] += minValue;
}
if (!colsCovered[j])
{
costs[i, j] -= minValue;
}
}
}
return(2);
}
private static int RunStep2(float[,] costs, byte[,] masks, bool[] rowsCovered, bool[] colsCovered, int w, int h, ref Location pathStart)
{
if (costs == null)
{
throw new ArgumentNullException("Empty");
}
if (masks == null)
{
throw new ArgumentNullException("Empty");
}
if (rowsCovered == null)
{
throw new ArgumentNullException("Empty");
}
if (colsCovered == null)
{
throw new ArgumentNullException("Empty");
}
while (true)
{
var loc = HungarianAlgorithm.FindZero(costs, rowsCovered, colsCovered, w, h);
if (loc.row == -1)
{
return(4);
}
masks[loc.row, loc.column] = 2;
var starCol = HungarianAlgorithm.FindStarInRow(masks, w, loc.row);
if (starCol != -1)
{
rowsCovered[loc.row] = true;
colsCovered[starCol] = false;
}
else
{
pathStart = loc;
return(3);
}
}
}
private static int RunStep3(byte[,] masks, bool[] rowsCovered, bool[] colsCovered, int w, int h, Location[] path, Location pathStart)
{
if (masks == null)
{
throw new ArgumentNullException("Empty");
}
if (rowsCovered == null)
{
throw new ArgumentNullException("Empty");
}
if (colsCovered == null)
{
throw new ArgumentNullException("Empty");
}
var pathIndex = 0;
path[0] = pathStart;
while (true)
{
var row = HungarianAlgorithm.FindStarInColumn(masks, h, path[pathIndex].column);
if (row == -1)
{
break;
}
pathIndex++;
path[pathIndex] = new Location(row, path[pathIndex - 1].column);
var col = HungarianAlgorithm.FindPrimeInRow(masks, w, path[pathIndex].row);
pathIndex++;
path[pathIndex] = new Location(path[pathIndex - 1].row, col);
}
HungarianAlgorithm.ConvertPath(masks, path, pathIndex + 1);
HungarianAlgorithm.ClearCovers(rowsCovered, colsCovered, w, h);
HungarianAlgorithm.ClearPrimes(masks, w, h);
return(1);
}
/// <summary>
/// Finds the optimal assignments for a given matrix of agents and costed tasks such that the total cost is minimized.
/// </summary>
/// <param name="costs">A cost matrix; the element at row <em>i</em> and column <em>j</em> represents the cost of agent <em>i</em> performing task <em>j</em>.</param>
/// <returns>A matrix of assignments; the value of element <em>i</em> is the column of the task assigned to agent <em>i</em>.</returns>
/// <exception cref="ArgumentNullException"><paramref name="costs"/> is null.</exception>
public static int[] FindAssignments(this float[,] costs)
{
if (costs == null)
{
throw new ArgumentNullException("Empty");
}
var h = costs.GetLength(0);
var w = costs.GetLength(1);
for (var i = 0; i < h; i++)
{
float min = int.MaxValue;
for (var j = 0; j < w; j++)
{
min = Math.Min(min, costs[i, j]);
}
for (var j = 0; j < w; j++)
{
costs[i, j] -= min;
}
}
var masks = new byte[h, w];
var rowsCovered = new bool[h];
var colsCovered = new bool[w];
for (var i = 0; i < h; i++)
{
for (var j = 0; j < w; j++)
{
if (costs[i, j] == 0 && !rowsCovered[i] && !colsCovered[j])
{
masks[i, j] = 1;
rowsCovered[i] = true;
colsCovered[j] = true;
}
}
}
HungarianAlgorithm.ClearCovers(rowsCovered, colsCovered, w, h);
var path = new Location[w * h];
var pathStart = default(Location);
var step = 1;
while (step != -1)
{
switch (step)
{
case 1:
step = HungarianAlgorithm.RunStep1(masks, colsCovered, w, h);
break;
case 2:
step = HungarianAlgorithm.RunStep2(costs, masks, rowsCovered, colsCovered, w, h, ref pathStart);
break;
case 3:
step = HungarianAlgorithm.RunStep3(masks, rowsCovered, colsCovered, w, h, path, pathStart);
break;
case 4:
step = HungarianAlgorithm.RunStep4(costs, rowsCovered, colsCovered, w, h);
break;
}
}
var agentsTasks = new int[h];
for (var i = 0; i < h; i++)
{
for (var j = 0; j < w; j++)
{
if (masks[i, j] == 1)
{
agentsTasks[i] = j;
break;
}
}
}
return(agentsTasks);
}
