In the function AStar, we start by creating a new matrixNode, with the parameters fromX and fromY. A matrixNode has properties, "fr" which is the distance of any given matrixNode from the starting node, a "to" property which is the distance of a given matrixNode from the destination matrixNode (would be 'E' at coordinates (3,3) in the unitTest's example), and a property "sum" which is the sum of "to" and "fr". The property parent, is a reference to the matrixNode that the given node was moved to in the path for reaching from the start node to the end node. The dictionaries greens and reds, are the openSet and closedSet respectively as described in the A* search algorithm page on Wikipedia. The general idea with these sets, is that we are trying to find the matrixNode in the green/open set which has the lowest "sum" value, as "sum" was the sum of the distances of the node from the start node at (fromX,fromY) and the end node at (toX, toY)
public static void unitTest_AStar()
{
char[][] matrix = new char[][] { new char[] {'-', 'S', '-', '-', 'X'},
new char[] {'-', 'X', 'X', '-', '-'},
new char[] {'-', '-', '-', 'X', '-'},
new char[] {'X', '-', 'X', 'E', '-'},
new char[] {'-', '-', '-', '-', 'X'}};
//looking for shortest path from 'S' at (0,1) to 'E' at (3,3)
//obstacles marked by 'X'
int fromX = 0, fromY = 1, toX = 3, toY = 3;
matrixNode endNode = AStar(matrix, fromX, fromY, toX, toY);
//looping through the Parent nodes until we get to the start node
Stack<matrixNode> path = new Stack<matrixNode>();
while (endNode.x != fromX || endNode.y != fromY)
{
path.Push(endNode);
endNode = endNode.parent;
}
path.Push(endNode);
Console.WriteLine("The shortest path from " +
"(" + fromX + "," + fromY + ") to " +
"(" + toX + "," + toY + ") is: \n");
while (path.Count > 0)
{
matrixNode node = path.Pop();
Console.WriteLine("(" + node.x + "," + node.y + ")");
}
}
public class matrixNode
{
public int fr = 0, to = 0, sum = 0;
public int x, y;
public matrixNode parent;
}
public static matrixNode AStar(char[][] matrix, int fromX, int fromY, int toX, int toY)
{
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
// in this version an element in a matrix can move left/up/right/down in one step, two steps for a diagonal move.
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
//the keys for greens and reds are x.ToString() + y.ToString() of the matrixNode
Dictionary<string, matrixNode> greens = new Dictionary<string, matrixNode>(); //open
Dictionary<string, matrixNode> reds = new Dictionary<string, matrixNode>(); //closed
matrixNode startNode = new matrixNode { x = fromX, y = fromY };
string key = startNode.x.ToString() + startNode.x.ToString();
greens.Add(key, startNode);
Func<KeyValuePair<string, matrixNode>> smallestGreen = () =>
{
KeyValuePair<string, matrixNode> smallest = greens.ElementAt(0);
foreach (KeyValuePair<string, matrixNode> item in greens)
{
if (item.Value.sum < smallest.Value.sum)
smallest = item;
else if (item.Value.sum == smallest.Value.sum
&& item.Value.to < smallest.Value.to)
smallest = item;
}
return smallest;
};
//add these values to current node's x and y values to get the left/up/right/bottom neighbors
List<KeyValuePair<int, int>> fourNeighbors = new List<KeyValuePair<int, int>>()
{ new KeyValuePair<int, int>(-1,0),
new KeyValuePair<int, int>(0,1),
new KeyValuePair<int, int>(1, 0),
new KeyValuePair<int, int>(0,-1) };
int maxX = matrix.GetLength(0);
if (maxX == 0)
return null;
int maxY = matrix[0].Length;
while (true)
{
if (greens.Count == 0)
return null;
KeyValuePair<string, matrixNode> current = smallestGreen();
if (current.Value.x == toX && current.Value.y == toY)
return current.Value;
greens.Remove(current.Key);
reds.Add(current.Key, current.Value);
foreach (KeyValuePair<int, int> plusXY in fourNeighbors)
{
int nbrX = current.Value.x + plusXY.Key;
int nbrY = current.Value.y + plusXY.Value;
string nbrKey = nbrX.ToString() + nbrY.ToString();
if (nbrX < 0 || nbrY < 0 || nbrX >= maxX || nbrY >= maxY
|| matrix[nbrX][nbrY] == 'X' //obstacles marked by 'X'
|| reds.ContainsKey(nbrKey))
continue;
if (greens.ContainsKey(nbrKey))
{
matrixNode curNbr = greens[nbrKey];
int from = Math.Abs(nbrX - fromX) + Math.Abs(nbrY - fromY);
if (from < curNbr.fr)
{
curNbr.fr = from;
curNbr.sum = curNbr.fr + curNbr.to;
curNbr.parent = current.Value;
}
}
else
{
matrixNode curNbr = new matrixNode { x = nbrX, y = nbrY };
curNbr.fr = Math.Abs(nbrX - fromX) + Math.Abs(nbrY - fromY);
curNbr.to = Math.Abs(nbrX - toX) + Math.Abs(nbrY - toY);
curNbr.sum = curNbr.fr + curNbr.to;
curNbr.parent = current.Value;
greens.Add(nbrKey, curNbr);
}
}
}
}
