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Made some changes to bidirectional. Among them added handling of directed graphs. Added some descriptive comments to dijkstra.

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Bartosz 2022-01-15 18:07:49 +01:00
parent 55f1ecc36c
commit abb169a2f3
2 changed files with 82 additions and 30 deletions
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80
algorithms/bidirectional.py
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@ -2,7 +2,7 @@ def heuristic_cost(start, goal, graph):
return 0 return 0
def bidirectional_algorithm(graph, point_set, start, goal, h=heuristic_cost): def bidirectional_algorithm(graph, start, goal, h=heuristic_cost, is_directed=False):
def return_path_and_weight_front(c_f, c, s): def return_path_and_weight_front(c_f, c, s):
current_node = c_f[c] current_node = c_f[c]
shortest_path = [c, current_node] shortest_path = [c, current_node]
@ -11,10 +11,13 @@ def bidirectional_algorithm(graph, point_set, start, goal, h=heuristic_cost):
shortest_path.append(current_node) shortest_path.append(current_node)
weight = 0 weight = 0
for k in range(len(shortest_path) - 1): for k in range(len(shortest_path) - 1):
if not is_directed:
if shortest_path[k] > shortest_path[k+1]: if shortest_path[k] > shortest_path[k+1]:
weight += graph[(shortest_path[k], shortest_path[k+1])] weight += graph[(shortest_path[k], shortest_path[k+1])]
else: else:
weight += graph[(shortest_path[k + 1], shortest_path[k])] weight += graph[(shortest_path[k + 1], shortest_path[k])]
else:
weight += graph[(shortest_path[k + 1], shortest_path[k])]
return shortest_path, weight return shortest_path, weight
def return_path_and_weight_back(c_f, c, s): def return_path_and_weight_back(c_f, c, s):
@ -26,27 +29,46 @@ def bidirectional_algorithm(graph, point_set, start, goal, h=heuristic_cost):
weight = 0 weight = 0
shortest_path.reverse() shortest_path.reverse()
for k in range(len(shortest_path) - 1): for k in range(len(shortest_path) - 1):
if not is_directed:
if shortest_path[k] > shortest_path[k+1]: if shortest_path[k] > shortest_path[k+1]:
weight += graph[(shortest_path[k], shortest_path[k+1])] weight += graph[(shortest_path[k], shortest_path[k+1])]
else: else:
weight += graph[(shortest_path[k + 1], shortest_path[k])] weight += graph[(shortest_path[k + 1], shortest_path[k])]
else:
weight += graph[(shortest_path[k + 1], shortest_path[k])]
return shortest_path, weight return shortest_path, weight
def return_path_and_weight_front_meet_back(c_f_f, c_f_b, c_f, s, g): def return_path_and_weight_front_meet_back(c_f_f, c_f_b, c_f, s, g):
shortest_path_front, weight_front = return_path_and_weight_back(c_f_f, c_f, s) shortest_path_front, weight_front = return_path_and_weight_front(c_f_f, c_f, s)
shortest_path_back, weight_back = return_path_and_weight_back(c_f_b, c_f, g) shortest_path_back, weight_back = return_path_and_weight_back(c_f_b, c_f, g)
shortest_path_back.reverse() shortest_path_back.reverse()
shortest_path_front.reverse()
return shortest_path_front + shortest_path_back[1:], weight_front + weight_back return shortest_path_front + shortest_path_back[1:], weight_front + weight_back
def return_path_and_weight_back_meet_front(c_f_f, c_f_b, c_b, s, g): def return_path_and_weight_back_meet_front(c_f_f, c_f_b, c_b, s, g):
shortest_path_front, weight_front = return_path_and_weight_back(c_f_f, c_b, s) shortest_path_front, weight_front = return_path_and_weight_front(c_f_f, c_b, s)
shortest_path_back, weight_back = return_path_and_weight_back(c_f_b, c_b, g) shortest_path_back, weight_back = return_path_and_weight_back(c_f_b, c_b, g)
shortest_path_back.reverse() shortest_path_back.reverse()
shortest_path_front.reverse()
return shortest_path_front + shortest_path_back[1:], weight_front + weight_back return shortest_path_front + shortest_path_back[1:], weight_front + weight_back
for edge in graph.keys(): point_set_front = dict()
point_set[edge[0]].append(edge[1]) point_set_back = dict()
point_set[edge[1]].append(edge[0]) for arc in g.keys():
point_set_front[arc[0]] = []
point_set_front[arc[1]] = []
point_set_back[arc[0]] = []
point_set_back[arc[1]] = []
for arc in graph.keys():
point_set_front[arc[0]].append(arc[1])
if not is_directed:
point_set_back[arc[1]].append(arc[0])
point_set_front[arc[1]].append(arc[0])
point_set_back[arc[0]].append(arc[1])
else:
point_set_back[arc[1]].append(arc[0])
open_set_front = set() open_set_front = set()
open_set_front.add(start) open_set_front.add(start)
@ -56,16 +78,16 @@ def bidirectional_algorithm(graph, point_set, start, goal, h=heuristic_cost):
came_from_front = {} came_from_front = {}
came_from_back = {} came_from_back = {}
g_score_front = {k: float('inf') for k in point_set.keys()} g_score_front = {k: float('inf') for k in point_set_front.keys()}
g_score_front[start] = 0 g_score_front[start] = 0
g_score_back = {k: float('inf') for k in point_set.keys()} g_score_back = {k: float('inf') for k in point_set_back.keys()}
g_score_back[goal] = 0 g_score_back[goal] = 0
f_score_front = {k: float('inf') for k in point_set.keys()} f_score_front = {k: float('inf') for k in point_set_front.keys()}
f_score_front[start] = h(start, goal, graph) f_score_front[start] = h(start, goal, graph)
f_score_back = {k: float('inf') for k in point_set.keys()} f_score_back = {k: float('inf') for k in point_set_back.keys()}
f_score_back[goal] = h(goal, start, graph) f_score_back[goal] = h(goal, start, graph)
while len(open_set_front) > 0 and len(open_set_back) > 0: while len(open_set_front) > 0 and len(open_set_back) > 0:
@ -86,6 +108,15 @@ def bidirectional_algorithm(graph, point_set, start, goal, h=heuristic_cost):
if current_back == start: if current_back == start:
return return_path_and_weight_back(came_from_back, current_back, goal) return return_path_and_weight_back(came_from_back, current_back, goal)
if current_front in came_from_back.keys() and current_back in came_from_front.keys():
path1, weight1 = return_path_and_weight_front_meet_back(came_from_front, came_from_back, current_front,
start, goal)
path2, weight2 = return_path_and_weight_back_meet_front(came_from_front, came_from_back, current_back,
start, goal)
if weight1 < weight2:
return path1, weight1
return path2, weight2
if current_front in came_from_back.keys(): if current_front in came_from_back.keys():
return return_path_and_weight_front_meet_back(came_from_front, came_from_back, current_front, start, goal) return return_path_and_weight_front_meet_back(came_from_front, came_from_back, current_front, start, goal)
@ -95,14 +126,16 @@ def bidirectional_algorithm(graph, point_set, start, goal, h=heuristic_cost):
open_set_front.remove(current_front) open_set_front.remove(current_front)
open_set_back.remove(current_back) open_set_back.remove(current_back)
for neighbor in point_set[current_front]: for neighbor in point_set_front[current_front]:
tentative_g_score = g_score_front[current_front] tentative_g_score = g_score_front[current_front]
if not is_directed:
if current_front > neighbor: if current_front > neighbor:
tentative_g_score += graph[(current_front, neighbor)] tentative_g_score += graph[(current_front, neighbor)]
else: else:
tentative_g_score += graph[(neighbor, current_front)] tentative_g_score += graph[(neighbor, current_front)]
else:
tentative_g_score += graph[(current_front, neighbor)]
if tentative_g_score < g_score_front[neighbor]: if tentative_g_score < g_score_front[neighbor]:
came_from_front[neighbor] = current_front came_from_front[neighbor] = current_front
g_score_front[neighbor] = tentative_g_score g_score_front[neighbor] = tentative_g_score
@ -110,14 +143,15 @@ def bidirectional_algorithm(graph, point_set, start, goal, h=heuristic_cost):
if neighbor not in open_set_front: if neighbor not in open_set_front:
open_set_front.add(neighbor) open_set_front.add(neighbor)
for neighbor in point_set[current_back]: for neighbor in point_set_back[current_back]:
tentative_g_score = g_score_back[current_back] tentative_g_score = g_score_back[current_back]
if not is_directed:
if current_back > neighbor: if current_back > neighbor:
tentative_g_score += graph[(current_back, neighbor)] tentative_g_score += graph[(current_back, neighbor)]
else: else:
tentative_g_score += graph[(neighbor, current_back)] tentative_g_score += graph[(neighbor, current_back)]
else:
tentative_g_score += graph[(neighbor, current_back)]
if tentative_g_score < g_score_back[neighbor]: if tentative_g_score < g_score_back[neighbor]:
came_from_back[neighbor] = current_back came_from_back[neighbor] = current_back
g_score_back[neighbor] = tentative_g_score g_score_back[neighbor] = tentative_g_score
@ -143,9 +177,15 @@ if __name__ == "__main__":
(9, 1): 8 (9, 1): 8
} }
v = dict() g2 = {
for i in g.keys(): (4, 1): 6,
v[i[0]] = [] (1, 3): 4,
v[i[1]] = [] (1, 2): 2,
(2, 4): 5,
(3, 4): 1,
(5, 3): 1
}
print(bidirectional_algorithm(g, v, 7, 10, heuristic_cost)) print(bidirectional_algorithm(g, 7, 10, heuristic_cost))
print(bidirectional_algorithm(g2, 1, 4, heuristic_cost, is_directed=True))
print(bidirectional_algorithm(g2, 1, 5, heuristic_cost, is_directed=True))

14
algorithms/dijkstra.py
View File

@ -16,6 +16,7 @@ def dijkstra_algorithm(graph, start, goal, is_directed=False):
# list which is used to keep priority queue with vertexes to be explored by the algorithm # list which is used to keep priority queue with vertexes to be explored by the algorithm
queue = [] queue = []
# dictionary for keeping neighbors of vertexes.
point_set = dict() point_set = dict()
for arc in graph.keys(): for arc in graph.keys():
point_set[arc[0]] = [] point_set[arc[0]] = []
@ -27,19 +28,31 @@ def dijkstra_algorithm(graph, start, goal, is_directed=False):
if not is_directed: if not is_directed:
point_set[arc[1]].append(arc[0]) point_set[arc[1]].append(arc[0])
# initialization of needed lists
for vertex in point_set: for vertex in point_set:
# setting distance of every vertex from the starting vertex to infinity
dist[vertex] = float('inf') dist[vertex] = float('inf')
# setting previous vertex in currently found shortest path for every vertex to None
prev[vertex] = None prev[vertex] = None
# setting flag for every vertex keeping track if it was already visited my the algorithm
visited[vertex] = False visited[vertex] = False
# pushing start vertex to priority queue
heap.heappush(queue, (0, start)) heap.heappush(queue, (0, start))
# setting distance to start for start vertex to 0
dist[start] = 0 dist[start] = 0
# setting start vertex not to be added to priority queue again
visited[start] = True visited[start] = True
# main loop
while len(queue) > 0: while len(queue) > 0:
# getting first vertex from the priority queue and saving it in current variable
current = heap.heappop(queue) current = heap.heappop(queue)
# iterating trough all neighbors of the current vertex
for neighbor in point_set[current[1]]: for neighbor in point_set[current[1]]:
# initializing potential distance to be replaced with the current neighbors
new_dist = 0 new_dist = 0
#
if not is_directed: if not is_directed:
if neighbor > current[1]: if neighbor > current[1]:
new_dist = dist[current[1]] + graph[(neighbor, current[1])] new_dist = dist[current[1]] + graph[(neighbor, current[1])]
@ -93,6 +106,5 @@ if __name__ == "__main__":
(5, 3): 1 (5, 3): 1
} }
print('')
print(dijkstra_algorithm(g, 7, 10)) print(dijkstra_algorithm(g, 7, 10))
print(dijkstra_algorithm(g2, 1, 5, is_directed=True)) print(dijkstra_algorithm(g2, 1, 5, is_directed=True))