Depth-First Search Algorithm in Python

I am going to implement depth-first search (DFS) for a grid and a graph in this tutorial. Depth-first search is an uninformed search algorithm as it does not use any heuristics to guide the search. DFS is used to find a path from a starting point to a goal point, the length of the path can also be calculated.

Depth-first search starts from a root node and expands neighbor nodes in the depth until it reaches a goal node, this is implemented by using a LIFO-queue (Last In First Out). Depth-first search can loop forever if the search space is infinite and the goal node not is in the depth of the current search path. A DFS algorithm can ignore a lot of nodes if it reaches the end in a depth of a tree and it is therefore more memory efficient than breadth-first search in some cases.

Depth-first search is not guaranteed to find the optimal solution and it is very time consuming in the worst case. The time complexity is O(n) in a grid and O(b^d) in a graph with a branching factor (b) and a depth (d). The branching factor is the average number of neighbor nodes that can be expanded from each node and the depth is the average number of levels in a graph/tree. DFS and variants of the algorithm is used in AI-searches because it is memory efficient compared to other search algorithms.

Grid problem (maze)

I have created a simple maze (download it) with a starting point, a goal point and walls. DFS is used to find a path to the goal, the algorithm uses a Node class. The DFS algorithm has an array for open nodes and an array for closed nodes, it will loop until it finds a goal node or until the list of open nodes is empty. The code and the output from running the algorithm is shown below.

# This class represent a node
class Node:

    # Initialize the class
    def __init__(self, position:(), parent:()):
        self.position = position
        self.parent = parent
        self.g = 0 # Distance to start node
        self.h = 0 # Distance to goal node
        self.f = 0 # Total cost

    # Compare nodes
    def __eq__(self, other):
        return self.position == other.position

    # Sort nodes
    def __lt__(self, other):
         return self.f < other.f

    # Print node
    def __repr__(self):
        return ('({0},{1})'.format(self.position, self.f))

# Draw a grid
def draw_grid(map, width, height, spacing=2, **kwargs):
    for y in range(height):
        for x in range(width):
            print('%%-%ds' % spacing % draw_tile(map, (x, y), kwargs), end='')
        print()

# Draw a tile
def draw_tile(map, position, kwargs):
    
    # Get the map value
    value = map.get(position)

    # Check if we should print the path
    if 'path' in kwargs and position in kwargs['path']: value = '+'

    # Check if we should print start point
    if 'start' in kwargs and position == kwargs['start']: value = '@'

    # Check if we should print the goal point
    if 'goal' in kwargs and position == kwargs['goal']: value = '$'

    # Return a tile value
    return value 

# Depth-first search (DFS)
def depth_first_search(map, start, end):
    
    # Create lists for open nodes and closed nodes
    open = []
    closed = []

    # Create a start node and an goal node
    start_node = Node(start, None)
    goal_node = Node(end, None)

    # Add the start node
    open.append(start_node)
    
    # Loop until the open list is empty
    while len(open) > 0:

        # Get the last node (LIFO)
        current_node = open.pop(-1)

        # Add the current node to the closed list
        closed.append(current_node)
        
        # Check if we have reached the goal, return the path
        if current_node == goal_node:
            path = []
            while current_node != start_node:
                path.append(current_node.position)
                current_node = current_node.parent
            #path.append(start) 
            # Return reversed path
            return path[::-1]

        # Unzip the current node position
        (x, y) = current_node.position

        # Get neighbors
        neighbors = [(x-1, y), (x+1, y), (x, y-1), (x, y+1)]

        # Loop neighbors
        for next in neighbors:

            # Get value from map
            map_value = map.get(next)

            # Check if the node is a wall
            if(map_value == '#'):
                continue

            # Create a neighbor node
            neighbor = Node(next, current_node)

            # Check if the neighbor is in the closed list
            if(neighbor in closed):
                continue

            # Everything is green, add the node if it not is in open
            if (neighbor not in open):
                open.append(neighbor)

    # Return None, no path is found
    return None

# The main entry point for this module
def main():

    # Get a map (grid)
    map = {}
    chars = ['c']
    start = None
    end = None
    width = 0
    height = 0

    # Open a file
    fp = open('annytab\\ai_search_algorithms\\data\\maze.in', 'r')
    
    # Loop until there is no more lines
    while len(chars) > 0:

        # Get chars in a line
        chars = [str(i) for i in fp.readline().strip()]

        # Calculate the width
        width = len(chars) if width == 0 else width

        # Add chars to map
        for x in range(len(chars)):
            map[(x, height)] = chars[x]
            if(chars[x] == '@'):
                start = (x, height)
            elif(chars[x] == '$'):
                end = (x, height)
        
        # Increase the height of the map
        if(len(chars) > 0):
            height += 1

    # Close the file pointer
    fp.close()

    # Find the closest path from start(@) to end($)
    path = depth_first_search(map, start, end)
    print()
    print(path)
    print()
    draw_grid(map, width, height, spacing=1, path=path, start=start, goal=end)
    print()
    print('Steps to goal: {0}'.format(len(path)))
    print()

# Tell python to run main method
if __name__ == "__main__": main()
#################################################################################
#.#...#....$....#...................#...#.........#.......#.............#.......#
#.#.#.#.###+###.#########.#########.#.#####.#####.#####.#.#.#######.###.#.#####.#
#...#.....#+++#.#.........#.#.....#.#...#...#...#.......#.#.#.......#.#.#.#...#.#
#############+#.#.#########.#.###.#.###.#.###.#.#.#######.###.#######.#.#.#.#.#.#
#+++++++++++#+#...#.#.....#...#...#...#.#.#.#.#...#...#.......#.......#.#.#.#.#.#
#+#########+#+#####.#.#.#.#.###.#####.#.#.#.#.#####.#.#########.###.###.###.#.#.#
#+#........+#+++#...#.#.#.#...#.....#.#.#.#...#.#...#.......#.....#.#...#...#...#
#+#########+#.#+###.#.#.#####.###.#.#.#.#.#.###.#.#########.#####.#.#.###.#####.#
#+#+++++++#+#.#+++#...#.#.....#.#.#.#...#.#.....#.#.....#.#...#...#.......#...#.#
#+#+#####+#+#.###+#####.#.#####.#.#.###.#.#######.###.#.#.###.#.###########.#.#.#
#+++#+++#+#+#...#+++++#.#.......#.#.#...#.....#...#...#.....#.#.#...#...#...#...#
#####+#+#+#+#########+#.#######.#.###.#######.#.###.#########.###.#.#.#.#.#######
#+++++#+++#+#+++++++++#.......#.#...#.#.#.....#.#.....#.......#...#.#.#.#.#.....#
#+#########+#+#########.###.###.###.#.#.#.###.#.#.###.#.#######.###.#.###.#.###.#
#+++#.#+++++#+++#.....#.#.#...#.#.#.....#...#.#.#...#.#...#...#...#.#.#...#...#.#
###+#.#+#####.#+#.#.###.#.###.#.#.#####.###.###.#####.###.#.#.#.###.#.#.#####.#.#
#+++#+++#.....#+#.#.#...#...#.....#...#.#...#...........#.#.#...#...#.......#.#.#
#+###+#########+#.#.#.###.#.#####.#.#.###.###.###########.#.#####.#########.###.#
#+#..+++++++++++#.#.......#.#...#.#.#...#.#...#.#.......#.......#.#...#.....#...#
#+#.#############.#########.#.#.###.###.#.#.###.#.#####.#.#######.#.#.#.#####.#.#
#+#.#+++++++++++#.#.#.#.....#.#.....#...#.#.....#...#.#.#.#.#...#.#.#.#.#.....#.#
#+###+#########+#.#.#.#######.#######.###.#####.###.#.#.#.#.###.#.#.#.#.#####.#.#
#+++++#+++#+++++#...#.........#.....#...#.....#...#...#.#.....#.#...#.#.#.....#.#
#.#####+#+#+#######.###########.#######.#.#######.###.#.###.###.#####.#.#.#####.#
#.....#+#+#+++#...#.#+++++++#.........#.#...#.......#.#.#...#...#.....#.#.#...#.#
#######+#+###+#.###.#+#####+#.#####.###.#.#.#.#######.#.#####.###.#####.#.###.#.#
#+++++++#+#+++#.....#+#...#+#...#.#.....#.#.#.#.#.....#...#...#...#.....#...#.#.#
#+#######+#+#.#####.#+###.#+###.#.#######.#.#.#.#.#######.#.###.#.###.#####.#.#.#
#+#.#+++++#+#.#+++#.#+++#.#+++#...#.#...#.#...#.#.....#.#...#...#...#.......#...#
#+#.#+#####+#.#+#+#####+#.###+###.#.#.#.#.#####.#####.#.#####.#####.#########.###
#+#..+#..+++#.#+#+#+++#+++#.#+#...#...#.#.#...#.....#...#.#...#...#.....#...#.#.#
#+###+###+#.###+#+#+#+###+#.#+#.#######.#.#.#.#####.###.#.#.###.#.#####.###.#.#.#
#+++#+++#+#.#+++#+#+#+++#+#.#+#.#.......#...#.........#.#...#...#.#...#...#.#...#
#.#+###+#+#.#+###+#+###+#+#.#+#.###.###.###########.###.#.###.###.###.###.#.###.#
#.#+++#+#+#.#+++#+++#+++#+#.#+#.....#...#...#.....#.#...#.....#.....#.#...#...#.#
#.###+#+#+#####+#####+#.#+#.#+#######.###.#.#####.#.#.#############.#.#.###.#.#.#
#...#+#+++#+++#+++++#+#.#+#.#+#+++#...#.#.#.......#.#.#...#...#...#...#.#.#.#...#
###.#+#####+#+#####+#+###+#.#+#+#+#.###.#.#########.#.#.#.#.#.#.#.#####.#.#.#####
#...#+++++++#+++++++#+++++..#+++#+++++++@...........#...#...#...#.......#.......#
#################################################################################

Steps to goal: 339

Graph problem

This graph problem is about finding the shortest path from one city to another city, a map has been used to create connections between cities. The DFS algorithm uses a Graph class and a Node class, it has a list of open nodes and a list of closed nodes. The DFS algorithm will find a path to a destination, but it is not the shortest path. The code and the output is shown below.

# This class represent a graph
class Graph:

    # Initialize the class
    def __init__(self, graph_dict=None, directed=True):
        self.graph_dict = graph_dict or {}
        self.directed = directed
        if not directed:
            self.make_undirected()

    # Create an undirected graph by adding symmetric edges
    def make_undirected(self):
        for a in list(self.graph_dict.keys()):
            for (b, dist) in self.graph_dict[a].items():
                self.graph_dict.setdefault(b, {})[a] = dist

    # Add a link from A and B of given distance, and also add the inverse link if the graph is undirected
    def connect(self, A, B, distance=1):
        self.graph_dict.setdefault(A, {})[B] = distance
        if not self.directed:
            self.graph_dict.setdefault(B, {})[A] = distance

    # Get neighbors or a neighbor
    def get(self, a, b=None):
        links = self.graph_dict.setdefault(a, {})
        if b is None:
            return links
        else:
            return links.get(b)

    # Return a list of nodes in the graph
    def nodes(self):
        s1 = set([k for k in self.graph_dict.keys()])
        s2 = set([k2 for v in self.graph_dict.values() for k2, v2 in v.items()])
        nodes = s1.union(s2)
        return list(nodes)

# This class represent a node
class Node:

    # Initialize the class
    def __init__(self, name:str, parent:str):
        self.name = name
        self.parent = parent
        self.g = 0 # Distance to start node
        self.h = 0 # Distance to goal node
        self.f = 0 # Total cost

    # Compare nodes
    def __eq__(self, other):
        return self.name == other.name

    # Sort nodes
    def __lt__(self, other):
         return self.f < other.f

    # Print node
    def __repr__(self):
        return ('({0},{1})'.format(self.position, self.f))

# Depth-first search (DFS)
def depth_first_search(graph, start, end):
    
    # Create lists for open nodes and closed nodes
    open = []
    closed = []

    # Create a start node and an goal node
    start_node = Node(start, None)
    goal_node = Node(end, None)

    # Add the start node
    open.append(start_node)
    
    # Loop until the open list is empty
    while len(open) > 0:

        # Get the last node (LIFO)
        current_node = open.pop(-1)

        # Add the current node to the closed list
        closed.append(current_node)
        
        # Check if we have reached the goal, return the path
        if current_node == goal_node:
            path = []
            while current_node != start_node:
                path.append(current_node.name + ': ' + str(current_node.g))
                current_node = current_node.parent
            path.append(start_node.name + ': ' + str(start_node.g))
            # Return reversed path
            return path[::-1]

        # Get neighbours
        neighbors = graph.get(current_node.name)

        # Loop neighbors
        for key, value in neighbors.items():

            # Create a neighbor node
            neighbor = Node(key, current_node)

            # Check if the neighbor is in the closed list
            if(neighbor in closed):
                continue

            # Check if neighbor is in open list and if it has a lower f value
            if(neighbor in open):
                continue

            # Calculate cost so far
            neighbor.g = current_node.g + graph.get(current_node.name, neighbor.name)

            # Everything is green, add neighbor to open list
            open.append(neighbor)

    # Return None, no path is found
    return None

# The main entry point for this module
def main():

    # Create a graph
    graph = Graph()

    # Create graph connections (Actual distance)
    graph.connect('Frankfurt', 'Wurzburg', 111)
    graph.connect('Frankfurt', 'Mannheim', 85)
    graph.connect('Wurzburg', 'Nurnberg', 104)
    graph.connect('Wurzburg', 'Stuttgart', 140)
    graph.connect('Wurzburg', 'Ulm', 183)
    graph.connect('Mannheim', 'Nurnberg', 230)
    graph.connect('Mannheim', 'Karlsruhe', 67)
    graph.connect('Karlsruhe', 'Basel', 191)
    graph.connect('Karlsruhe', 'Stuttgart', 64)
    graph.connect('Nurnberg', 'Ulm', 171)
    graph.connect('Nurnberg', 'Munchen', 170)
    graph.connect('Nurnberg', 'Passau', 220)
    graph.connect('Stuttgart', 'Ulm', 107)
    graph.connect('Basel', 'Bern', 91)
    graph.connect('Basel', 'Zurich', 85)
    graph.connect('Bern', 'Zurich', 120)
    graph.connect('Zurich', 'Memmingen', 184)
    graph.connect('Memmingen', 'Ulm', 55)
    graph.connect('Memmingen', 'Munchen', 115)
    graph.connect('Munchen', 'Ulm', 123)
    graph.connect('Munchen', 'Passau', 189)
    graph.connect('Munchen', 'Rosenheim', 59)
    graph.connect('Rosenheim', 'Salzburg', 81)
    graph.connect('Passau', 'Linz', 102)
    graph.connect('Salzburg', 'Linz', 126)

    # Make graph undirected, create symmetric connections
    graph.make_undirected()

    # Run search algorithm
    path = depth_first_search(graph, 'Frankfurt', 'Ulm')
    print(path)
    print()

# Tell python to run main method
if __name__ == "__main__": main()
['Frankfurt: 0', 'Mannheim: 85', 'Karlsruhe: 152', 'Stuttgart: 216', 'Ulm: 323']

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