Next we’re going to create a search tree from which the algorithm can chose the best move. This is done by using the Minimax algorithm. In this algorithm, the recursive tree of all possible moves is explored to a given depth, and the position is evaluated at the ending “leaves” of the tree. A console chess program that features normal chess rules including Castling, En Passant and promotion by choice. Detects draw if only kings are left, no moves possible and not in check or 50 consecutive moves without movement of a Pawn or a capture. Detects check/mate (obviously). Would be glad if.
# Create six vertices numbered 0 through 5. # Display the vertex dictionary g = Graph for i in range( 6): g.addVertex(i) print(g.vertList) # Add the edges that connect the vertices together g.addEdge( 0, 1, 5) g.addEdge( 0, 5, 2) g.addEdge( 1, 2, 4) g.addEdge( 2, 3, 9) g.addEdge( 3, 4, 7) g.addEdge( 3, 5, 3) g.addEdge( 4, 0, 1) g.addEdge( 5, 4, 8) g.addEdge( 5, 2, 1) # Nested loop verifies that each edge in the graph is properly stored. For v in g: for w in v.getConnections: print( '(%s,%s ) '% (v.getId, w.getId)) Graph Implementation – Solving Word Ladder Problem using Breadth First Search (BFS) let’s consider the following puzzle called a word ladder.
Transform the word “FOOL” into the word “SAGE”. In a word ladder puzzle you must make the change occur gradually by changing one letter at a time.
At each step you must transform one word into another word, you are not allowed to transform a word into a non-word. The following sequence of words shows one possible solution to the problem posed above. FOOL. POOL. POLL. POLE.
PALE. SALE. SAGE This is implemented using dictionary. # The Graph class, contains a dictionary that maps vertex names to vertex objects. # Graph creates a new, empty graph.
Graph buildGraph #BFS begins at the starting vertex s and colors start gray to show that #it is currently being explored. Two other values, the distance and the #predecessor, are initialized to 0 and None respectively for the starting #vertex. Finally, start is placed on a Queue. The next step is to begin #to systematically explore vertices at the front of the queue. We explore #each new node at the front of the queue by iterating over its adjacency #list. As each node on the adjacency list is examined its color is #checked. If it is white, the vertex is unexplored, and four things happen: #.
The new, unexplored vertex nbr, is colored gray. #. The predecessor of nbr is set to the current node currentVert #The distance to nbr is set to the distance to currentVert + 1 #nbr is added to the end of a queue. Adding nbr to the end of the queue #effectively schedules this node for further exploration, but not until all the #other vertices on the adjacency list of currentVert have been explored. Bfs Graph Implementation – Solving Knight tour problem using Depth First Search (DFS) The knight’s tour puzzle is played on a chess board with a single chess piece, the knight. The object of the puzzle is to find a sequence of moves that allow the knight to visit every square on the board exactly once.
One such sequence is called a “tour.” we will solve the problem using two main steps: Represent the legal moves of a knight on a chessboard as a graph. Use a graph algorithm to find a path of length rows×columns−1rows×columns−1 where every vertex on the graph is visited exactly once. To represent the knight’s tour problem as a graph we will use the following two ideas: Each square on the chessboard can be represented as a node in the graph.
Each legal move by the knight can be represented as an edge in the graph. # The Graph class, contains a dictionary that maps vertex names to vertex objects. # Graph creates a new, empty graph. Graph # To represent the knight’s tour problem as a graph we will use the # following two ideas: Each square on the chessboard can be represented # as a node in the graph. Each legal move by the knight can be represented # as an edge in the graph. KnightGraph # The genLegalMoves function takes the position of the knight on the # board and generates each of the eight possible moves. The legalCoord # helper function makes sure that a particular move that is generated is # still on the board.
GenLegalMoves # DFS implementation # we will look at two algorithms that implement a depth first search. # The first algorithm we will look at directly solves the knight’s tour # problem by explicitly forbidding a node to be visited more than once. # The second implementation is more general, but allows nodes to be visited # more than once as the tree is constructed.
The second version is used in # subsequent sections to develop additional graph algorithms. # The depth first exploration of the graph is exactly what we need in # order to find a path that has exactly 63 edges. We will see that when # the depth first search algorithm finds a dead end (a place in the graph # where there are no more moves possible) it backs up the tree to the next # deepest vertex that allows it to make a legal move.
# The knightTour function takes four parameters: n, the current depth in # the search tree; path, a list of vertices visited up to this point; u, # the vertex in the graph we wish to explore; and limit the number of nodes # in the path. The knightTour function is recursive.
When the knightTour # function is called, it first checks the base case condition. If we have # a path that contains 64 vertices, we return from knightTour with a status # of True, indicating that we have found a successful tour. If the path is not # long enough we continue to explore one level deeper by choosing a new vertex # to explore and calling knightTour recursively for that vertex.
# DFS also uses colors to keep track of which vertices in the graph have been visited. # Unvisited vertices are colored white, and visited vertices are colored gray. # If all neighbors of a particular vertex have been explored and we have not yet reached # our goal length of 64 vertices, we have reached a dead end. When we reach a dead end we # must backtrack.
Backtracking happens when we return from knightTour with a status of False. # In the breadth first search we used a queue to keep track of which vertex to visit next. # Since depth first search is recursive, we are implicitly using a stack to help us with # our backtracking. When we return from a call to knightTour with a status of False, in line 11, # we remain inside the while loop and look at the next vertex in nbrList. KnightTour Please check for the full working code. I will keep adding more problems/solutions. Ref: The inspiration of implementing DS in Python is from course.