Update
Thanks to the comments of some community members, I realize that there are some similar problems, but they may a bit different, please allow me to explain it further.
I actually hope to use the same method in a real problem, So briefly:
Reuse of edges in differernt path is completely allowed
a unique(or a new) path from A to B is defined as a collection of vertices that have any different vertices.
Let me use a quiz from Python data structure and algorithm analysis by Bradley .N Miller and David L. Ranum to expain my qusetion.
Quesion:
Consider the task of converting the word FOOL to SAGE, also called word ladder problem. In solving
In the word ladder problem, only one letter must be replaced at a time, and the result of each step must be a word, not non-existent.
Input:
FOUL
FOOL
FOIL
FAIL
COOL
FALL
POOL
PALL
POLL
POLE
PALE
PAGE
SALE
POPE
POPE
SAGE
We can easily find the path from FOOL to SAGE, as Bradley showed:
enter image description here
and I used Breadth First Search (BFS) to solve probem:
class Vertex:
def __init__(self, key, value = None):
self.id = key
self.connectedTo = {}
self.color = 'white'
self.dist = sys.maxsize
self.pred = []
self.disc = 0
self.fin = 0
self.value = value,
#self.GraphBulided = False
self.traverseIndex = 0
self.predNum = 0
def addNeighbor(self, nbr, weight=0):
self.connectedTo[nbr] = weight
def __str__(self):
return '{} connectedTo: {}'.format(self.id, \
str([x.id for x in self.connectedTo]))
def setColor(self, color):
self.color = color
def setDistance(self, d):
self.dist = d
#I want store all Pred for next traverse so I use a list to do it
def setPred(self, p, list = False):
if not list:
self.pred = p
else:
self.pred.append(p)
self.predNum += 1
def setDiscovery(self,dtime):
self.disc = dtime
def setFinish(self,ftime):
self.fin = ftime
#def setGraphBulided(self, tag = True):
# self.GraphBulided = tag
def getFinish(self):
return self.fin
def getDiscovery(self):
return self.disc
def getPred(self):
if isinstance(self.pred, list):
if self.traverseIndex < self.predNum:
return self.pred[self.traverseIndex]
else:
return self.pred[-1]
else:
return self.pred
def __hash__(self):
return hash(self.id)
def getPredById(self):
if self.traverseIndex < self.predNum and isinstance(self.pred, list):
pred = self.pred[self.traverseIndex]
self.traverseIndex += 1
print("vertix {}: {} of {} preds".format(self.id, self.traverseIndex, self.predNum))
return [pred, self.traverseIndex]
else:
pred = None
return [pred, None]
def getCurrPredStaus(self):
#if not self.pred:
# return None
return self.predNum - self.traverseIndex
def getDistance(self):
return self.dist
def getColor(self):
return self.color
def getConnections(self):
return self.connectedTo.keys()
def getId(self):
return self.id
def getWeight(self, nbr):
return self.connectedTo[nbr]
def getValue(self):
return self.value
def findPath(self, dest):
pass
class Graph:
def __init__(self):
self.vertList = {}
self.numVertics = 0
self.verticsInSerach = set()
self.GraphBulided = False
def addVertex(self, key, value = None):
self.numVertics = self.numVertics + 1
newVertex = Vertex(key, value=value)
self.vertList[key] = newVertex
return newVertex
def getVertex(self, n):
if n in self.vertList:
return self.vertList[n]
else:
return None
def __contains__(self, n):
return n in self.vertList
def addEdge(self, f, t, cost = 0, fvalue = None, tvalue = None):
if f not in self.vertList:
nv = self.addVertex(f, fvalue)
if t not in self.vertList:
nv = self.addVertex(t, tvalue)
self.vertList[f].addNeighbor(self.vertList[t], cost)
def setGraphBulided(self, tag = True):
self.GraphBulided = tag
def getVertices(self):
return self.vertList.keys()
def setGraphBulided(self, tag = True):
self.GraphBulided = tag
def setSerachedVertixs(self, vertix):
self.verticsInSerach.add(vertix)
def getGraphBulided(self):
return self.GraphBulided
def getSerachedVertixs(self):
return self.verticsInSerach
def __iter__(self):
return iter(self.vertList.values())
def __hash__(self):
hashIds = [x for x in self.getVertices()]
if len(hashIds) > 0 and hashIds[0]:
return hash(', '.join(hashIds))
else:
return None
Here are some additional functions for building graphs
def buildGraph(wordFile, DFSgraph = False):
d = {}
g = Graph()
if DFSgraph:
g = DFSGraph()
wfile = open(wordFile)
for line in wfile:
word = line[:-1]
for i in range(len(word)):
bucket = word[:i] + '_' + word[i+1:]
if bucket in d:
d[bucket].append(word)
else:
d[bucket] = [word]
for bucket in d.keys():
for word1 in d[bucket]:
for word2 in d[bucket]:
if word1 != word2:
g.addEdge(word1, word2)
wfile.close()
return g
class Queue:
def __init__(self):
self.items = []
def isEmpty(self):
return self.items == []
def enqueue(self, item):
self.items.insert(0,item)
def dequeue(self):
return self.items.pop()
def size(self):
return len(self.items)
def bfs(g, start, listpred = False):
start.setDistance(0)
start.setPred(None)
vertQueue = Queue()
vertQueue.enqueue(start)
while (vertQueue.size() > 0):
currentVert = vertQueue.dequeue()
if currentVert.getConnections():
g.setSerachedVertixs(currentVert)
for nbr in currentVert.getConnections():
#print('sreach {}'.format(currentVert.getId()))
if (nbr.getColor() == 'white' or nbr.getColor() == 'gray'):
nbr.setColor('gray')
nbr.setDistance(currentVert.getDistance() + 1)
if nbr.predNum > 0 and currentVert.getId() not in [x.getId() for x in nbr.pred]:
nbr.setPred(currentVert, listpred)
elif nbr.predNum == 0:
nbr.setPred(currentVert, listpred)
vertQueue.enqueue(nbr)
currentVert.setColor('black')
Therefore, we can easily find the shortest path we need (If we only store one pred for one vertix).
wordGraph = buildGraph('fourletterwords1.txt', DFSgraph=False)
bfs(wordGraph, wordGraph.getVertex('FOOL'), listpred=True)
def traverse(y):
x=y
while(x.getPred()):
print(x.getPred())
x = x.getPred()
print(x.getId())
traverse(wordGraph.getVertex('SAGE'))
However, I still don't know how to trace all the paths correctly, can you give me some suggestions?
FIND path from src to dst ( Dijkstra algorithm )
ADD path to list of paths
LOOP P over list of paths
LOOP V over vertices in P
IF V == src OR V == dst
CONTINUE to next V
COPY graph to working graph
REMOVE V from working graph
FIND path from src to dst in working graph( Dijkstra algorithm )
IF path found
IF path not in list of paths
ADD path to list of paths
Related
This is the python code which uses A* algorithm for finding solution for 8 puzzle problems, I got some error messages, how can I fix it?(The error message is under the code)
There are several object-oriented programming concepts for Problems class, Node class that are implemented to express the problem solution search that you need to understand in order to make the Python program complete. The priority queue is to make the nodes to be explored to be sorted according to their f-evaluation function score and return the min one as the first node to be searched next.
There is also a memorize function to memorize the heuristic value of state as a look-up table so that you don’t need to calculate the redundant computing of heuristic estimation value, so you can ignore it at this point if you don’t understand.
The components you need to implement is to make the abstract part of the program realizable for 8 -puzzle with the successor methods attached to a problem class which consists of initial state and goal state. Make sure the program can run correctly to generate the solution sequence that move the empty tile so that the 8-puzzle can move "Up", "Down", "Left", "Right", from initial state to goal state.
import math
infinity = math.inf
from itertools import chain
import numpy as np
import bisect
class memoize:
def __init__(self, f, memo={}):
self.f = f
self.memo = {}
def __call__(self, *args):
if not str(args) in self.memo:
self.memo[str(args)] = self.f(*args)
return self.memo[str(args)]
def coordinate(state):
index_state = {}
index = [[0,0], [0,1], [0,2], [1,0], [1,1], [1,2], [2,0], [2,1], [2,2]]
for i in range(len(state)):
index_state[state[i]] = index[i]
return index_state
def getInvCount(arr):
inv_count = 0
empty_value = -1
for i in range(0, 9):
for j in range(i + 1, 9):
if arr[j] != empty_value and arr[i] != empty_value and arr[i] > arr[j]:
inv_count += 1
return inv_count
def isSolvable(puzzle) :
inv_count = getInvCount([j for sub in puzzle for j in sub])
return (inv_count % 2 == 0)
def linear(state):
return sum([1 if state[i] != goal[i] else 0 for i in range(9)])
#memoize
def manhattan(state):
index_goal = coordinate(goal)
index_state = coordinate(state)
mhd = 0
for i in range(9):
for j in range(2):
mhd = abs(index_goal[i][j] - index_state[i][j]) + mhd
return mhd
#memoize
def sqrt_manhattan(state):
index_goal = coordinate(goal)
index_state = coordinate(state)
mhd = 0
for i in range(9):
for j in range(2):
mhd = (index_goal[i][j] - index_state[i][j])**2 + mhd
return math.sqrt(mhd)
#memoize
def max_heuristic(state):
score1 = manhattan(state)
score2 = linear(state)
return max(score1, score2)
class PriorityQueueElmt:
def __init__(self,val,e):
self.val = val
self.e = e
def __lt__(self,other):
return self.val < other.val
def value(self):
return self.val
def elem(self):
return self.e
class Queue:
def __init__(self):
pass
def extend(self, items):
for item in items: self.append(item)
class PriorityQueue(Queue):
def __init__(self, order=min, f=None):
self.A=[]
self.order=order
self.f=f
def append(self, item):
queueElmt = PriorityQueueElmt(self.f(item),item)
bisect.insort(self.A, queueElmt)
def __len__(self):
return len(self.A)
def pop(self):
if self.order == min:
return self.A.pop(0).elem()
else:
return self.A.pop().elem()
# Heuristics for 8 Puzzle Problem
class Problem:
def __init__(self, initial, goal=None):
self.initial = initial; self.goal = goal
def successor(self, state):
reachable = []
def get_key(val):
for key, value in index_state.items():
if val == value:
return key
return -1
def candidate(state, Position):
state = state.copy()
zero_index = state.index(0)
swap_index = state.index(get_key(Position))
state[zero_index], state[swap_index] = state[swap_index], state[zero_index]
return state
index_state = coordinate(state)
zero_position = index_state[0]
move_pair = {"left":[zero_position[0], zero_position[1] - 1],
"right":[zero_position[0], zero_position[1] + 1],
"up":[zero_position[0] - 1, zero_position[1]],
"down":[zero_position[0] + 1, zero_position[1]]
}
for action, position in move_pair.items():
#print(action, position)
if get_key(position) != -1:
reachable.append((action, candidate(state, position)))
#print(reachable)
return reachable
def goal_test(self, state):
return state == self.goal
def path_cost(self, c, state1, action, state2):
return c + 1
def value(self):
abstract
class Node:
def __init__(self, state, parent=None, action=None, path_cost=0, depth =0):
self.parent = parent
if parent:
self.depth = parent.depth + 1
else:
self.depth = 0
self.path_cost = path_cost
self.state = state
if action:
self.action = action
else: self.action = "init"
def __repr__(self):
return "Node state:\n " + str(np.array(self.state).reshape(3,3)) +"\n -> action: " + self.action + "\n -> depth: " + str(self.depth)
def path(self):
x, result = self, [self]
while x.parent:
result.append(x.parent)
x = x.parent
return result
def expand(self, problem):
for (act,n) in problem.successor(self.state):
if n not in [node.state for node in self.path()]:
yield Node(n, self, act,
problem.path_cost(self.path_cost, self.state, act, n))
def graph_search(problem, fringe):
closed = {}
fringe.append(Node(problem.initial,depth=0))
while fringe:
node = fringe.pop()
if problem.goal_test(node.state):
return node
if str(node.state) not in closed:
closed[str(node.state)] = True
fringe.extend(node.expand(problem))
return None
def best_first_graph_search(problem, f):
return graph_search(problem, PriorityQueue(min, f))
def astar_search(problem, h = None):
h = h or problem.h
def f(n):
return max(getattr(n, 'f', -infinity), n.path_cost + h(n.state))
return best_first_graph_search(problem, f)
def print_path(path, method):
print("*" * 30)
print("\nPath: (%s distance)" % method)
for i in range(len(path)-1, -1, -1):
print("-" * 15)
print(path[i])
goal = [1, 2, 3, 4, 5, 6, 7, 8, 0]
# Solving the puzzle
puzzle = [7, 2, 4, 5, 0, 6, 8, 3, 1]
if(isSolvable(np.array(puzzle).reshape(3,3))): # even true
# checks whether the initialized configuration is solvable or not
print("Solvable!")
problem = Problem(puzzle,goal)
path = astar_search(problem, manhattan).path()
print_path(path, "manhattan")
path = astar_search(problem, linear).path()
print_path(path, "linear")
path = astar_search(problem, sqrt_manhattan).path()
print_path(path, "sqrt_manhattan")
path = astar_search(problem, max_heuristic).path()
print_path(path, "max_heuristic")
else :
print("Not Solvable!") # non-even false
TypeError Traceback (most recent call last)
<ipython-input-124-2a60ddc8c009> in <module>
9 problem = Problem(puzzle,goal)
10
---> 11 path = astar_search(problem, manhattan).path()
12 print_path(path, "manhattan")
13
<ipython-input-123-caa97275712e> in astar_search(problem, h)
18 def f(n):
19 return max(getattr(n, 'f', -infinity), n.path_cost + h(n.state))
---> 20 return best_first_graph_search(problem, f)
21
22 def print_path(path, method):
<ipython-input-123-caa97275712e> in best_first_graph_search(problem, f)
12
13 def best_first_graph_search(problem, f):
---> 14 return graph_search(problem, PriorityQueue(min, f))
15
16 def astar_search(problem, h = None):
<ipython-input-123-caa97275712e> in graph_search(problem, fringe)
8 if str(node.state) not in closed:
9 closed[str(node.state)] = True
---> 10 fringe.extend(node.expand(problem))
11 return None
12
<ipython-input-121-e5a968bd54f0> in extend(self, items)
18
19 def extend(self, items):
---> 20 for item in items: self.append(item)
21
22 class PriorityQueue(Queue):
<ipython-input-122-db21613469b9> in expand(self, problem)
69
70 def expand(self, problem):
---> 71 for (act,n) in problem.successor(self.state):
72 if n not in [node.state for node in self.path()]:
73 yield Node(n, self, act,
TypeError: cannot unpack non-iterable int object
I got some error messages, how can I fix it?
There is one error message, The pieces of codes you get in the error message are the stack trace, which might help you to know how the execution got at the final point where the error occurred. In this case that is not so important. The essence of the error is this:
for (act,n) in problem.successor(self.state)
TypeError: cannot unpack non-iterable int object
So this means that the successor method returned an int instead of a list.
Looking at the code for successor, I notice that it intends to return a list called reachable, but there is a return statement right in the middle of the code, leaving the largest part of that code unexecuted (so-called "dead code"):
return state
This statement makes no sense where it is positioned. It seems to be an indentation problem: that return belongs inside the function just above it, like this:
def candidate(state, Position):
state = state.copy()
zero_index = state.index(0)
swap_index = state.index(get_key(Position))
state[zero_index], state[swap_index] = state[swap_index], state[zero_index]
return state # <-- indentation!
I have a problem with an algorithmic task. There is content of it: "You have ten points on a plane and none three of them are collinear, each pair of different points is connected by line segment, which is green or blue. Calculate how many triangles have sides only in one colour." I tried a solution with n-ary trees but I get repeated triangles with cyclic permutations of integers on the result list.
Patryk, the problem is solvable with n-trees. However, to avoid cyclic permutations you need to skip symmetric line segments. If you create a line segment from 0 -> 1 you do not need to create a segment from 1 -> 0. Below is a complete code which solves the problem with n-trees with the recursive depth-first search. Excuse for Polish names of classes and methods. The interface is in English however. If you analyze the code you will get the point surely.
from random import choice
import copy
class Punkt:
def __init__(self, numer):
self.__numer = numer
self.__odcinki = {}
def dodaj_odcinek_wychodzący(self, punkt_docelowy, kolor):
self.__odcinki[punkt_docelowy] = Odcinek(self.__numer, punkt_docelowy, kolor)
def wez_odcinek_do_punktu_docelowego(self, punkt_docelowy):
return (punkt_docelowy, self.__odcinki[punkt_docelowy].wez_kolor())
def liczba_odcinkow(self):
return len(self.__odcinki)
def wez_kolor_punktu_docelowego(self, punkt_docelowy):
return self.__odcinki[punkt_docelowy].wez_kolor()
def lista_punktow_docelowych(self):
return self.__odcinki.keys()
class Odcinek:
def __init__(self, punkt_zrodlowy, punkt_docelowy, kolor):
self.__punkt_zrodlowy = punkt_zrodlowy
self.__punkt_docelowy = punkt_docelowy
self.__kolor = kolor
def wez_kolor(self):
return self.__kolor
class Structure:
def __init__(self, liczba_punktow=10):
self.__punkty = [Punkt(i)
for i in range(liczba_punktow)]
for i in range(liczba_punktow):
for j in range(i + 1, liczba_punktow):
self.__punkty[i].dodaj_odcinek_wychodzący(j, choice(["green", "blue"]))
# for j in range(liczba_punktow):
# for i in range (j + 1, liczba_punktow):
# self.__punkty[j].dodaj_odcinek_wychodzący(*(self.__punkty[j].wez_odcinek_do_punktu_docelowego(i)))
def wez_punkt(self, numer):
return self.__punkty[numer]
def wez_liczbe_punktow(self):
return len(self.__punkty)
class Search:
def __init__(self, struktura):
self.__s = struktura
def wez_liczbe_punktow(self):
return self.__s.wez_liczbe_punktow()
def wez_punkt(self, numer):
return self.__s.wez_punkt(numer)
def szukaj(self, kolor="green"):
self.__szukany_kolor = kolor
lista_trojkatow = []
liczba_trojkatow = 0
wszystkie_trojkaty = []
for i in range(self.wez_liczbe_punktow()):
lista_odwiedzonych_punktow = [i]
lista_trojkatow = self.szukaj_z_punktu(i,lista_odwiedzonych_punktow,lista_trojkatow)
return len(lista_trojkatow), lista_trojkatow
def wez_szukany_kolor(self):
return self.__szukany_kolor
def szukaj_z_punktu(self, numer, trojkat, lista_trojkatow):
if len(trojkat) == 3: # jeżeli zebraliśmy już trzy punkty to brakuje tylko zamykającego, czwartego
if self.wez_punkt(trojkat[0]).wez_kolor_punktu_docelowego(
trojkat[-1]) == self.wez_szukany_kolor(): # sprawdź czy do punktu zamykającego prowadzi odcinek o szukanym kolorze
trojkat.append(trojkat[0]) # dodaj punkt zamykajacy do trójkąta
lista_trojkatow.append(trojkat) # dodaj trojkąt do listy trójkątów
# return lista_trojkatow # zwróć liste trójkątów obliczonych dotychczas
else:
potomkowie = []
for punkt_docelowy in self.wez_punkt(numer).lista_punktow_docelowych():
if self.wez_punkt(numer).wez_kolor_punktu_docelowego(punkt_docelowy) == self.wez_szukany_kolor():
potomkowie.append(punkt_docelowy)
for potomek in potomkowie:
trojkat_kopia = copy.copy(trojkat)
trojkat_kopia.append(potomek)
lista_trojkatow = self.szukaj_z_punktu(potomek, trojkat_kopia, lista_trojkatow)
return lista_trojkatow
if __name__ == "__main__":
s = Structure()
for source_point in range(s.wez_liczbe_punktow()):
for destination_point in s.wez_punkt(source_point).lista_punktow_docelowych():
print(f"{source_point} -> {destination_point} = {s.wez_punkt(source_point).wez_kolor_punktu_docelowego(destination_point)}")
color = "green"
searching = Search(s)
number_of_triangles, all_triangles = searching.szukaj("green")
print(f"Number of triangles of color {color} = {number_of_triangles}")
print(f"List of all triangles: {all_triangles}")
I am a starter & want to integrate dfs code with Fibonacci series generating code. The Fibonacci code too runs as dfs, with calls made from left to right.
The integration is incomplete still.
I have two issues :
(i) Unable to update 'path' correctly in fib(), as the output is not correctly depicting that.
(ii) Stated in fib() function below, as comment.
P.S.
Have one more issue that is concerned with program's working:
(iii) On modifying line #16 to: stack = root = stack[1:]; get the same output as before.
import sys
count = 0
root_counter = 0
#path=1
inf = -1
node_counter = 0
root =0
def get_depth_first_nodes(root):
nodes = []
stack = [root]
while stack:
cur_node = stack[0]
stack = stack[1:]
nodes.append(cur_node)
for child in cur_node.get_rev_children():
stack.insert(0, child)
return nodes
def node_counter_inc():
global node_counter
node_counter = node_counter + 1
class Node(object):
def __init__(self, id_,path):
self.id = node_counter_inc()
self.children = []
self.val = inf #On instantiation, val = -1, filled bottom up;
#except for leaf nodes
self.path = path
def __repr__(self):
return "Node: [%s]" % self.id
def add_child(self, node):
self.children.append(node)
def get_children(self):
return self.children
def get_rev_children(self):
children = self.children[:]
children.reverse()
return children
def fib(n, level, val, path):
global count, root_counter, root
print('count :', count, 'n:', n, 'dfs-path:', path)
count += 1
if n == 0 or n == 1:
path = path+1
root.add_child(Node(n, path))
return n
if root_counter == 0:
root = Node(n, path)
root_counter = 1
else:
#cur_node.add_child(Node(n, path)) -- discarded for next(new) line
root.add_child(Node(n, path))
tmp = fib(n-1, level + 1,inf, path) + fib(n-2, level + 1,inf,path+1)
#Issue 2: Need update node's val field with tmp.
#So, need suitable functions in Node() class for that.
print('tmp:', tmp, 'level', level)
return tmp
def test_depth_first_nodes():
fib(n,0,-1,1)
node_list = get_depth_first_nodes(root)
for node in node_list:
print(str(node))
if __name__ == "__main__":
n = int(input("Enter value of 'n': "))
test_depth_first_nodes()
Want to add that took idea for code from here.
Answer to the first question:
Path in this particular question is an int. It is a numbering of path from the root to a leaf in a greedy dfs manner.
This can be achieved by letting path be a global variable rather than an input to fib function. We increment the path count whenever we reach a leaf.
I have also modified the fib function to returns a node rather than a number.
import sys
count = 0
root_counter = 0
path=1
inf = -1
node_counter = 0
root = None
def node_counter_inc():
global node_counter
node_counter = node_counter + 1
print("node_counter:", node_counter)
return node_counter
class Node(object):
def __init__(self, id__,path):
print("calling node_counter_inc() for node:", n )
try:
self.id = int(node_counter_inc())
except TypeError:
self.id = 0 # or whatever you want to do
#self.id = int(node_counter_inc())
self.val = inf #On instantiation, val = -1, filled bottom up;
#except for leaf nodes
self.path = path
self.left = None
self.right = None
def __repr__(self):
return "Node" + str(self.id) + ":"+ str(self.val)
def fib(n, level, val):
# make fib returns a node rather than a value
global count, root_counter, root, path
print('count :', count, 'n:', n, 'dfs-path:', path)
count += 1
if n == 0 or n == 1:
path = path+1
new_Node = Node(n, path)
new_Node.val = n
return new_Node
#root.add_child(new_Node)
# return new_node
#if root_counter == 0:
# root = Node(n, path)
# root_counter = 1
#else:
#cur_node.add_child(Node(n, path)) -- discarded for next(new) line
# root.add_child(Node(n, path))
#tmp = fib(n-1, level + 1,inf) + fib(n-2, level + 1,inf)
#Issue 2: Need update node's val field with tmp.
#So, need suitable functions in Node() class for that.
#print('tmp:', tmp, 'level', level)
#return tmp
ans = Node(n, path)
ans.left = fib(n-1, level + 1, inf)
ans.right = fib(n-2, level + 1, inf)
ans.val = ans.left.val + ans.right.val
print("the node is", ans.id, "with left child", ans.left.id, "and right child", ans.right.id)
print("the corresponding values are", ans.val, ans.left.val, ans.right.val)
return ans
def test_depth_first_nodes():
ans = fib(n,0,-1)
print("The answer is", ans.val)
#node_list = get_depth_first_nodes(root)
#for node in node_list:
# print(str(node))
if __name__ == "__main__":
n = int(input("Enter value of 'n': "))
test_depth_first_nodes()
I am trying to have a program that allows the user to click on a vertex to choose the start vertex and hover over a vertex to choose the end_vertex. Then the program uses breadth first search to choose a path. I haven't been able to create the path because whenever I choose both vertices, I get a none type. Please help.
from collections import deque
from load_graph import load_graph
vertex_dict = load_graph("graph.txt")
def bfs(start, goal):
backpointers = {}
path = []
q = deque()
q.append(start)
backpointers[start] = None
while len(q) >= 1:
x = q.popleft()
if x == goal:
path.append(goal)
while backpointers[x] != None:
print(backpointers)
path.append(backpointers[x])
x = backpointers[x]
return path
else:
for vertex in x.get_adjacent():
vertex = vertex_dict[vertex.strip()]
if vertex not in backpointers:
backpointers[vertex] = x
q.append(vertex)
print(len(x.get_adjacent()))
I am positive that the issue it here because It returns a none-type and when I put a bunch of print statements, it got stuck in the else portion.
This is what it looks likes
Vertex Class:
from cs1lib import *
class Vertex:
def __init__(self, name, adjacent, x, y):
self.name = name
self.adjacent = adjacent.split(",")
self.adjacentSTR = adjacent
self.x = int(x)
self.y = int(y)
self.r = 10
self.distance = None
self.is_red = False
def __str__(self):
return self.name+"; "+"Adjencent Vertices: "+self.adjacentSTR+" Location: "+str(self.x)+", "+ str(self.y)
def get_x(self):
return self.x
def set_distance(self, d):
self.distance = d
def get_vertex(self):
return self
def get_y(self):
return self.y
def get_adjacent(self):
return self.adjacent
def link(self, vertex, r, g, b):
set_fill_color(r, g, b)
set_stroke_width(2)
set_stroke_color(r, g, b)
draw_line(self.x, self.y, vertex.get_x(), vertex.get_y())
def draw(self, r, g, b):
set_fill_color(r, g, b)
set_stroke_width(1)
draw_circle(self.x, self.y, self.r)
def mouse_is_nearby(self, mx, my):
if mx <= self.x + self.r and mx >= self.x - self.r and my <= self.y + self.r and my >= self.y - self.r:
# print("close to: " +self.name)
return True
Try this:
from collections import deque
def path(back_links, goal):
path = [goal]
node = goal
while back_links[node] is not None:
node = back_links[node]
path = [node] + path
return path
def bfs(start, goal):
q = deque([start])
visited, back_links = set([]), {start.name: None}
while q:
node = q.popleft()
visited.add(node.name)
if node.name == goal.name:
return path(back_links, goal.name)
for neighbor in node.get_adjacent():
if neighbor.name in visited:
continue
q.append(neighbor)
back_links[neighbor.name] = node.name
return []
I built a disjoint-set data structure for use with Kruskal's MST algorithm. I need to load and then union a graph with 200k interconnected nodes and I think my data structure implementation is a bottleneck.
Do you have an suggestions for how to improve performance? I think my find method might be problematic.
class partition(object):
def __init__(self, element=None):
self.size = 0
if element == None:
self.contents = set()
self.representative = None
else:
self.contents = {element}
self.representative = element
self.size = 1
def find(self, element):
return element in self.contents
def add(self, partition):
self.contents = self.contents.union(partition)
self.size = len(self.contents)
def show(self):
return self.contents
def __repr__(self):
return str(self.contents)
class disjoint_set(object):
def __init__(self):
self.partitions_count = 0
self.forest = {}
def make_set(self, element):
if self.find(element) == False:
new_partition = partition(element)
self.forest[new_partition.representative] = new_partition
self.partitions_count += 1
def union(self, x, y):
if x != y:
if self.forest[x].size < self.forest[y].size:
self.forest[y].add(self.forest[x].show())
self.delete(x)
else:
self.forest[x].add(self.forest[y].show())
self.delete(y)
def find(self, element):
for partition in self.forest.keys():
if self.forest[partition].find(element):
return self.forest[partition].representative
return False
def delete(self, partition):
del self.forest[partition]
self.partitions_count -= 1
if __name__ == '__main__':
t = disjoint_set()
t.make_set(1)
t.make_set(2)
t.make_set(3)
print("Create 3 singleton partitions:")
print(t.partitions_count)
print(t.forest)
print("Union two into a single partition:")
t.union(1,2)
print(t.forest)
print(t.partitions_count)
EDIT:
After reading the comments and doing additional research I realized how poorly designed my original algorithm was. I started over from scratch and put this together. I put all the partitions into a single hash table and used path compression in the find(). How does this look and are there any glaring problems I should address?
class disjoint_set(object):
def __init__(self):
self.partitions_count = 0
self.size = {}
self.parent = {}
def make_set(self, element):
if self.find(element) == False:
self.parent[element] = element
self.size[element] = 1
self.partitions_count += 1
def union(self, x, y):
xParent = self.find(x)
yParent = self.find(y)
if xParent != yParent:
if self.size[xParent] < self.size[yParent]:
self.parent[xParent] = yParent
self.size[yParent] += self.size[xParent]
self.partitions_count -= 1
else:
self.parent[yParent] = xParent
self.size[xParent] += self.size[yParent]
self.partitions_count -= 1
def find(self, element):
if element in self.parent:
if element == self.parent[element]:
return element
root = self.parent[element]
while self.parent[root] != root:
root = self.find(self.parent[root])
self.parent[element] = root
return root
return False
if __name__ == '__main__':
t = disjoint_set()
t.make_set(1)
t.make_set(2)
t.make_set(3)
t.make_set(4)
t.make_set(5)
print("Create 5 singleton partitions")
print(t.partitions_count)
print("Union two singletons into a single partition")
t.union(1,2)
print("Union three singletones into a single partition")
t.union(3,4)
t.union(5,4)
print("Union a single partition")
t.union(2,4)
print("Parent List: %s" % t.parent)
print("Partition Count: %s" % t.partitions_count)
print("Parent of element 2: %s" % t.find(2))
print("Parent List: %s" % t.parent)
I guess your find implementation is not running effienctly, which it supposed to be.
Following changes may help.
class disjoint_set(object):
def __init__(self):
self.partitions_count = 0
self.forest = {}
self.parent = {}
def make_set(self, element):
if not self.find(element):
new_partition = partition(element)
self.parent[element] = element
self.forest[new_partition.representative] = new_partition
self.partitions_count += 1
def union(self, x, y):
if x != y:
if self.forest[x].size < self.forest[y].size:
self.forest[y].add(self.forest[x].show())
#Update parent details
self.parent[self.forest[x].representative] = self.forest[y].representative
self.delete(x)
else:
self.forest[x].add(self.forest[y].show())
#Update parent details
self.parent[self.forest[y].representative] = self.forest[x].representative
self.delete(y)
def find(self, element):
if self.parent[element] == element:
return element
else:
return find(element)
The code can be still optimized with path-compression to have disjoint_set.find to run in O(1). I guess O(log n) still is good for big numbers.
Another bottleneck could be your union function. Especially the add function implementation.
def add(self, partition):
self.contents = self.contents.union(partition)
Try using an update method of set (which is an inplace union). I think is causing lot of memory overhead for huge no.of nodes. Something like
self.contents.update(partition)
There is a nice discussion on set union and update functions here.
Hope it helps!