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- #podvizni prepreki
- import sys
- import bisect
- infinity = float('inf') # sistemski definirana vrednost za beskonecnost
- # ______________________________________________________________________________________________
- # Definiranje na pomosni strukturi za cuvanje na listata na generirani, no neprovereni jazli
- class Queue:
- """Queue is an abstract class/interface. There are three types:
- Stack(): A Last In First Out Queue.
- FIFOQueue(): A First In First Out Queue.
- PriorityQueue(order, f): Queue in sorted order (default min-first).
- Each type supports the following methods and functions:
- q.append(item) -- add an item to the queue
- q.extend(items) -- equivalent to: for item in items: q.append(item)
- q.pop() -- return the top item from the queue
- len(q) -- number of items in q (also q.__len())
- item in q -- does q contain item?
- Note that isinstance(Stack(), Queue) is false, because we implement stacks
- as lists. If Python ever gets interfaces, Queue will be an interface."""
- def __init__(self):
- raise NotImplementedError
- def extend(self, items):
- for item in items:
- self.append(item)
- def Stack():
- """A Last-In-First-Out Queue."""
- return []
- class FIFOQueue(Queue):
- """A First-In-First-Out Queue."""
- def __init__(self):
- self.A = []
- self.start = 0
- def append(self, item):
- self.A.append(item)
- def __len__(self):
- return len(self.A) - self.start
- def extend(self, items):
- self.A.extend(items)
- def pop(self):
- e = self.A[self.start]
- self.start += 1
- if self.start > 5 and self.start > len(self.A) / 2:
- self.A = self.A[self.start:]
- self.start = 0
- return e
- def __contains__(self, item):
- return item in self.A[self.start:]
- class PriorityQueue(Queue):
- """A queue in which the minimum (or maximum) element (as determined by f and
- order) is returned first. If order is min, the item with minimum f(x) is
- returned first; if order is max, then it is the item with maximum f(x).
- Also supports dict-like lookup. This structure will be most useful in informed searches"""
- def __init__(self, order=min, f=lambda x: x):
- self.A = []
- self.order = order
- self.f = f
- def append(self, item):
- bisect.insort(self.A, (self.f(item), item))
- def __len__(self):
- return len(self.A)
- def pop(self):
- if self.order == min:
- return self.A.pop(0)[1]
- else:
- return self.A.pop()[1]
- def __contains__(self, item):
- return any(item == pair[1] for pair in self.A)
- def __getitem__(self, key):
- for _, item in self.A:
- if item == key:
- return item
- def __delitem__(self, key):
- for i, (value, item) in enumerate(self.A):
- if item == key:
- self.A.pop(i)
- # ______________________________________________________________________________________________
- # Definiranje na klasa za strukturata na problemot koj ke go resavame so prebaruvanje
- # Klasata Problem e apstraktna klasa od koja pravime nasleduvanje za definiranje na osnovnite karakteristiki
- # na sekoj eden problem sto sakame da go resime
- class Problem:
- """The abstract class for a formal problem. You should subclass this and
- implement the method successor, and possibly __init__, goal_test, and
- path_cost. Then you will create instances of your subclass and solve them
- with the various search functions."""
- def __init__(self, initial, goal=None):
- """The constructor specifies the initial state, and possibly a goal
- state, if there is a unique goal. Your subclass's constructor can add
- other arguments."""
- self.initial = initial
- self.goal = goal
- def successor(self, state):
- """Given a state, return a dictionary of {action : state} pairs reachable
- from this state. If there are many successors, consider an iterator
- that yields the successors one at a time, rather than building them
- all at once. Iterators will work fine within the framework. Yielding is not supported in Python 2.7"""
- raise NotImplementedError
- def actions(self, state):
- """Given a state, return a list of all actions possible from that state"""
- raise NotImplementedError
- def result(self, state, action):
- """Given a state and action, return the resulting state"""
- raise NotImplementedError
- def goal_test(self, state):
- """Return True if the state is a goal. The default method compares the
- state to self.goal, as specified in the constructor. Implement this
- method if checking against a single self.goal is not enough."""
- return state == self.goal
- def path_cost(self, c, state1, action, state2):
- """Return the cost of a solution path that arrives at state2 from
- state1 via action, assuming cost c to get up to state1. If the problem
- is such that the path doesn't matter, this function will only look at
- state2. If the path does matter, it will consider c and maybe state1
- and action. The default method costs 1 for every step in the path."""
- return c + 1
- def value(self):
- """For optimization problems, each state has a value. Hill-climbing
- and related algorithms try to maximize this value."""
- raise NotImplementedError
- # ______________________________________________________________________________
- # Definiranje na klasa za strukturata na jazel od prebaruvanje
- # Klasata Node ne se nasleduva
- class Node:
- """A node in a search tree. Contains a pointer to the parent (the node
- that this is a successor of) and to the actual state for this node. Note
- that if a state is arrived at by two paths, then there are two nodes with
- the same state. Also includes the action that got us to this state, and
- the total path_cost (also known as g) to reach the node. Other functions
- may add an f and h value; see best_first_graph_search and astar_search for
- an explanation of how the f and h values are handled. You will not need to
- subclass this class."""
- def __init__(self, state, parent=None, action=None, path_cost=0):
- "Create a search tree Node, derived from a parent by an action."
- self.state = state
- self.parent = parent
- self.action = action
- self.path_cost = path_cost
- self.depth = 0
- if parent:
- self.depth = parent.depth + 1
- def __repr__(self):
- return "<Node %s>" % (self.state,)
- def __lt__(self, node):
- return self.state < node.state
- def expand(self, problem):
- "List the nodes reachable in one step from this node."
- return [self.child_node(problem, action)
- for action in problem.actions(self.state)]
- def child_node(self, problem, action):
- "Return a child node from this node"
- next = problem.result(self.state, action)
- return Node(next, self, action,
- problem.path_cost(self.path_cost, self.state,
- action, next))
- def solution(self):
- "Return the sequence of actions to go from the root to this node."
- return [node.action for node in self.path()[1:]]
- def solve(self):
- "Return the sequence of states to go from the root to this node."
- return [node.state for node in self.path()[0:]]
- def path(self):
- "Return a list of nodes forming the path from the root to this node."
- x, result = self, []
- while x:
- result.append(x)
- x = x.parent
- return list(reversed(result))
- # We want for a queue of nodes in breadth_first_search or
- # astar_search to have no duplicated states, so we treat nodes
- # with the same state as equal. [Problem: this may not be what you
- # want in other contexts.]
- def __eq__(self, other):
- return isinstance(other, Node) and self.state == other.state
- def __hash__(self):
- return hash(self.state)
- # ________________________________________________________________________________________________________
- # Pomosna funkcija za informirani prebaruvanja
- # So pomos na ovaa funkcija gi keshirame rezultatite od funkcijata na evaluacija
- def memoize(fn, slot=None):
- """Memoize fn: make it remember the computed value for any argument list.
- If slot is specified, store result in that slot of first argument.
- If slot is false, store results in a dictionary."""
- if slot:
- def memoized_fn(obj, *args):
- if hasattr(obj, slot):
- return getattr(obj, slot)
- else:
- val = fn(obj, *args)
- setattr(obj, slot, val)
- return val
- else:
- def memoized_fn(*args):
- if not memoized_fn.cache.has_key(args):
- memoized_fn.cache[args] = fn(*args)
- return memoized_fn.cache[args]
- memoized_fn.cache = {}
- return memoized_fn
- # ________________________________________________________________________________________________________
- # Informirano prebaruvanje vo ramki na graf
- def best_first_graph_search(problem, f):
- """Search the nodes with the lowest f scores first.
- You specify the function f(node) that you want to minimize; for example,
- if f is a heuristic estimate to the goal, then we have greedy best
- first search; if f is node.depth then we have breadth-first search.
- There is a subtlety: the line "f = memoize(f, 'f')" means that the f
- values will be cached on the nodes as they are computed. So after doing
- a best first search you can examine the f values of the path returned."""
- f = memoize(f, 'f')
- node = Node(problem.initial)
- if problem.goal_test(node.state):
- return node
- frontier = PriorityQueue(min, f)
- frontier.append(node)
- explored = set()
- while frontier:
- node = frontier.pop()
- if problem.goal_test(node.state):
- return node
- explored.add(node.state)
- for child in node.expand(problem):
- if child.state not in explored and child not in frontier:
- frontier.append(child)
- elif child in frontier:
- incumbent = frontier[child]
- if f(child) < f(incumbent):
- del frontier[incumbent]
- frontier.append(child)
- return None
- def greedy_best_first_graph_search(problem, h=None):
- "Greedy best-first search is accomplished by specifying f(n) = h(n)"
- h = memoize(h or problem.h, 'h')
- return best_first_graph_search(problem, h)
- def astar_search(problem, h=None):
- "A* search is best-first graph search with f(n) = g(n)+h(n)."
- h = memoize(h or problem.h, 'h')
- return best_first_graph_search(problem, lambda n: n.path_cost + h(n))
- # ________________________________________________________________________________________________________
- # Dopolnitelni prebaruvanja
- # Recursive_best_first_search e implementiran
- # Kako zadaca za studentite da gi implementiraat SMA* i IDA*
- def recursive_best_first_search(problem, h=None):
- h = memoize(h or problem.h, 'h')
- def RBFS(problem, node, flimit):
- if problem.goal_test(node.state):
- return node, 0 # (The second value is immaterial)
- successors = node.expand(problem)
- if len(successors) == 0:
- return None, infinity
- for s in successors:
- s.f = max(s.path_cost + h(s), node.f)
- while True:
- # Order by lowest f value
- successors.sort(key=lambda x: x.f)
- best = successors[0]
- if best.f > flimit:
- return None, best.f
- if len(successors) > 1:
- alternative = successors[1].f
- else:
- alternative = infinity
- result, best.f = RBFS(problem, best, min(flimit, alternative))
- if result is not None:
- return result, best.f
- node = Node(problem.initial)
- node.f = h(node)
- result, bestf = RBFS(problem, node, infinity)
- return result
- # _________________________________________________________________________________________________________
- # PRIMER 2 : PROBLEM NA SLOZUVALKA
- # OPIS: Dadena e slozuvalka 3x3 na koja ima polinja so brojki od 1 do 8 i edno prazno pole
- # Praznoto pole e obelezano so *. Eden primer na slozuvalka e daden vo prodolzenie:
- # -------------
- # | * | 3 | 2 |
- # |---|---|---|
- # | 4 | 1 | 5 |
- # |---|---|---|
- # | 6 | 7 | 8 |
- # -------------
- # Problemot e kako da se stigne do nekoja pocetna raspredelba na polinjata do nekoja posakuvana, na primer do:
- # -------------
- # | * | 1 | 2 |
- # |---|---|---|
- # | 3 | 4 | 5 |
- # |---|---|---|
- # | 6 | 7 | 8 |
- # -------------
- # AKCII: Akciite ke gi gledame kako dvizenje na praznoto pole, pa mozni akcii se : gore, dole, levo i desno.
- # Pri definiranjeto na akciite mora da se vnimava dali akciite voopsto mozat da se prevzemat vo dadenata slozuvalka
- # STATE: Sostojbata ke ja definirame kako string koj ke ima 9 karakteri (po eden za sekoe brojce plus za *)
- # pri sto stringot ke se popolnuva so izminuvanje na slozuvalkata od prviot kon tretiot red, od levo kon desno.
- # Na primer sostojbata za pocetnata slozuvalka e: '*32415678'
- # Sostojbata za finalnata slozuvalka e: '*12345678'
- # ________________________________________________________________________________________________________
- #
- default_goal = '*12345678' # predefinirana cel
- # Ke definirame 3 klasi za problemot
- # Prvata klasa nema implementirano nikakva hevristika
- class P8(Problem):
- name = 'No Heuristic'
- def __init__(self, goal=default_goal, initial=None, N=20):
- self.goal = goal
- self.initial = initial
- def successor(self, state):
- return successor8(state)
- def actions(self, state):
- return self.successor(state).keys()
- def h(self, node):
- """Heuristic for 8 puzzle: returns 0"""
- return 0
- def result(self, state, action):
- possible = self.successor(state)
- return possible[action]
- # Slednite klasi ke nasleduvaat od prethodnata bez hevristika so toa sto ovde ke ja definirame i hevristikata
- class P8_h1(P8):
- """ Slozuvalka so hevristika
- HEVRISTIKA: Brojot na polinja koi ne se na vistinskoto mesto"""
- name = 'Out of Place Heuristic'
- def h(self, node):
- """Funkcija koja ja presmetuva hevristikata,
- t.e. razlikata pomegu nekoj tekoven jazel od prebaruvanjeto i celniot jazel"""
- matches = 0
- for (t1, t2) in zip(node.state, self.goal):
- # zip funkcijata od dve listi na vlez pravi edna lista od parovi (torki)
- # primer: zip(['a','b','c'],[1,2,3]) == [('a',1),('b',2),('c',3)]
- # zip('abc','123') == [('a','1'),('b','2'),('c','3')]
- if t1 != t2:
- matches = + 1
- return matches
- class P8_h2(P8):
- """ Slozuvalka so hevristika
- HEVRISTIKA: Menheten rastojanie do celna sostojba"""
- name = 'Manhattan Distance Heuristic (MHD)'
- def h(self, node):
- """Funkcija koja ja presmetuva hevristikata,
- t.e. Menheten rastojanieto pomegu nekoj tekoven jazel od prebaruvanjeto i celniot jazel, pri sto
- Menheten rastojanieto megu jazlite e zbir od Menheten rastojanijata pomegu istite broevi vo dvata jazli"""
- sum = 0
- for c in '12345678':
- sum = + mhd(node.state.index(c), self.goal.index(c)) # pomosna funkcija definirana vo prodolzenie
- return sum
- # Za da mozeme da go definirame rastojanieto treba da definirame koordinaten sistem
- # Pozetokot na koordinatniot sistem e postaven vo gorniot lev agol na slozuvalkata
- # Definirame recnik za koordinatite na sekoe pole od slozuvalkata
- coordinates = {0: (0, 0), 1: (1, 0), 2: (2, 0),
- 3: (0, 1), 4: (1, 1), 5: (2, 1),
- 6: (0, 2), 7: (1, 2), 8: (2, 2)}
- # Funkcija koja presmetuva Menheten rastojanie za slozuvalkata
- # Na vlez dobiva dva celi broja koi odgovaraat na dve polinja na koi se naogaat broevite za koi treba da presmetame rastojanie
- def mhd(n, m):
- x1, y1 = coordinates[n]
- x2, y2 = coordinates[m]
- return abs(x1 - x2) + abs(y1 - y2)
- def successor8(S):
- """Pomosna funkcija koja generira recnik za sledbenicite na daden jazel"""
- blank = S.index('*') # kade se naoga praznoto pole
- succs = {}
- # GORE: Ako praznoto pole ne e vo prviot red, togas vo sostojbata napravi swap
- # na praznoto pole so brojceto koe se naoga na poleto nad nego
- if blank > 2:
- swap = blank - 3
- succs['GORE'] = S[0:swap] + '*' + S[swap + 1:blank] + S[swap] + S[blank + 1:]
- # DOLE: Ako praznoto pole ne e vo posledniot red, togas vo sostojbata napravi swap
- # na praznoto pole so brojceto koe se naoga na poleto pod nego
- if blank < 6:
- swap = blank + 3
- succs['DOLE'] = S[0:blank] + S[swap] + S[blank + 1:swap] + '*' + S[swap + 1:]
- # LEVO: Ako praznoto pole ne e vo prvata kolona, togas vo sostojbata napravi swap
- # na praznoto pole so brojceto koe se naoga na poleto levo od nego
- if blank % 3 > 0:
- swap = blank - 1
- succs['LEVO'] = S[0:swap] + '*' + S[swap] + S[blank + 1:]
- # DESNO: Ako praznoto pole ne e vo poslednata kolona, togas vo sostojbata napravi swap
- # na praznoto pole so brojceto koe se naoga na poleto desno od nego
- if blank % 3 < 2:
- swap = blank + 1
- succs['DESNO'] = S[0:blank] + S[swap] + '*' + S[swap + 1:]
- return succs
- # So vaka definiraniot problem mozeme da gi koristime site informirani, no i neinformirani prebaruvanja
- # Vo prodolzenie se dadeni mozni povici (vnimavajte za da moze da napravite povik mora da definirate problem)
- #
- # s='*32415678'
- # p1=P8(initial=s)
- # p2=P8_h1(initial=s)
- # p3=P8_h2(initial=s)
- #
- # answer1 = greedy_best_first_graph_search(p1)
- # print answer1.solve()
- #
- # answer2 = greedy_best_first_graph_search(p2)
- # print answer2.solve()
- #
- # answer3 = greedy_best_first_graph_search(p3)
- # print answer3.solve()
- #
- # answer4 = astar_search(p1)
- # print answer4.solve()
- #
- # answer5 = astar_search(p2)
- # print answer5.solve()
- #
- # answer6 = astar_search(p3)
- # print answer6.solve()
- #
- # answer7 = recursive_best_first_search(p1)
- # print answer7.solve()
- #
- # answer8 = recursive_best_first_search(p2)
- # print answer8.solve()
- #
- # answer9 = recursive_best_first_search(p3)
- # print answer9.solve()
- def updateP1(P1):
- x = P1[0]
- y = P1[1]
- n = P1[2]
- if (y == 4 and n == 1):
- n = n * (-1)
- if (y == 0 and n == -1):
- n = n * (-1)
- ynew = y + n
- return (x, ynew, n)
- def updateP2(P2):
- x = P2[0]
- y = P2[1]
- n = P2[2]
- if (x == 5 and y == 4 and n == 1):
- n = n * (-1)
- if (y == 0 and x == 9 and n == -1):
- n = n * (-1)
- xnew = x - n
- ynew = y + n
- return (xnew, ynew, n)
- def updateP3(P3):
- x = P3[0]
- y = P3[1]
- n = P3[2]
- if (x == 5 and n == -1):
- n = n * (-1)
- if (x == 9 and n == 1):
- n = n * (-1)
- xnew = x + n
- return (xnew, y, n)
- def isValid(x, y, P1, P2, P3):
- t = 1
- if (x == P1[0] and y == P1[1]) or (x == P1[0] and y == P1[1] + 1):
- t = 0
- if (x == P2[0] and y == P2[1]) or (x == P2[0] and y == P2[1] + 1) or (x == P2[0] + 1 and y == P2[1]) or (
- x == P2[0] + 1 and y == P2[1] + 1):
- t = 0
- if (x == P3[0] and y == P3[1]) or (x == P3[0] + 1 and y == P3[1]):
- t = 0
- return t
- class Istrazuvac(Problem):
- def __init__(self, initial, goal):
- self.initial = initial
- self.goal = goal
- def successor(self, state):
- successors = dict()
- X = state[0]
- Y = state[1]
- P1 = state[2]
- P2 = state[3]
- P3 = state[4]
- P1new = updateP1(P1)
- P2new = updateP2(P2)
- P3new = updateP3(P3)
- # Levo
- if Y - 1 >= 0:
- Ynew = Y - 1
- Xnew = X
- if (isValid(Xnew, Ynew, P1new, P2new, P3new)):
- successors['Levo'] = (Xnew, Ynew, P1new, P2new, P3new)
- # Desno
- if X < 5 and Y < 5:
- Ynew = Y + 1
- Xnew = X
- if (isValid(Xnew, Ynew, P1new, P2new, P3new)):
- successors['Desno'] = (Xnew, Ynew, P1new, P2new, P3new)
- elif X >= 5 and Y < 10:
- Xnew = X
- Ynew = Y + 1
- if (isValid(Xnew, Ynew, P1new, P2new, P3new)):
- successors['Desno'] = (Xnew, Ynew, P1new, P2new, P3new)
- # Dolu
- if X < 10:
- Xnew = X + 1
- Ynew = Y
- if (isValid(Xnew, Ynew, P1new, P2new, P3new)):
- successors['Dolu'] = (Xnew, Ynew, P1new, P2new, P3new)
- # Gore
- if Y >= 6 and X > 5:
- Xnew = X - 1
- Ynew = Y
- if (isValid(Xnew, Ynew, P1new, P2new, P3new)):
- successors['Gore'] = (Xnew, Ynew, P1new, P2new, P3new)
- elif Y < 6 and X > 0:
- Xnew = X - 1
- Ynew = Y
- if (isValid(Xnew, Ynew, P1new, P2new, P3new)):
- successors['Gore'] = (Xnew, Ynew, P1new, P2new, P3new)
- return successors
- def actions(self, state):
- return self.successor(state).keys()
- def result(self, state, action):
- possible = self.successor(state)
- return possible[action]
- def goal_test(self, state):
- g = self.goal
- return (state[0] == g[0] and state[1] == g[1])
- def h(self, node):
- rez = abs(node.state[0] - self.goal[0]) + abs(node.state[1] - self.goal[1])
- return rez
- # Vcituvanje na vleznite argumenti za test primerite
- CoveceRedica = input()
- CoveceKolona = input()
- KukaRedica = input()
- KukaKolona = input()
- # Vasiot kod pisuvajte go pod ovoj komentar
- # prepreka 1 ima lev kvadrat na 2,2 odi levo (-1) na pocetok, prepreka 2 ima goren lev kvadrat na 2,7 odi gore desno (1)
- # prepreka 3 ima gore kvadrat na 8,7 odi nagore na pocetok(-1)
- IstrazuvacInstance = Istrazuvac((CoveceRedica, CoveceKolona, (2, 2, -1), (7, 2, 1), (7, 8, 1)),
- (KukaRedica, KukaKolona))
- answer = astar_search(IstrazuvacInstance).solution()
- print(answer)
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