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- # Python modul vo koj se implementirani algoritmite za informirano prebaruvanje
- # ______________________________________________________________________________________________
- # Improtiranje na dopolnitelno potrebni paketi za funkcioniranje na kodovite
- 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
- def tree_search(problem, fringe):
- """Search through the successors of a problem to find a goal.
- The argument fringe should be an empty queue."""
- fringe.append(Node(problem.initial))
- while fringe:
- node = fringe.pop()
- print(node.state)
- if problem.goal_test(node.state):
- return node
- fringe.extend(node.expand(problem))
- return None
- def breadth_first_tree_search(problem):
- "Search the shallowest nodes in the search tree first."
- return tree_search(problem, FIFOQueue())
- def depth_first_tree_search(problem):
- "Search the deepest nodes in the search tree first."
- return tree_search(problem, Stack())
- # ________________________________________________________________________________________________________
- # Neinformirano prebaruvanje vo ramki na graf
- # Osnovnata razlika e vo toa sto ovde ne dozvoluvame jamki t.e. povtoruvanje na sostojbi
- def graph_search(problem, fringe):
- """Search through the successors of a problem to find a goal.
- The argument fringe should be an empty queue.
- If two paths reach a state, only use the best one."""
- closed = {}
- fringe.append(Node(problem.initial))
- while fringe:
- node = fringe.pop()
- if problem.goal_test(node.state):
- return node
- if node.state not in closed:
- closed[node.state] = True
- fringe.extend(node.expand(problem))
- return None
- def breadth_first_graph_search(problem):
- "Search the shallowest nodes in the search tree first."
- return graph_search(problem, FIFOQueue())
- def depth_first_graph_search(problem):
- "Search the deepest nodes in the search tree first."
- return graph_search(problem, Stack())
- def uniform_cost_search(problem):
- "Search the nodes in the search tree with lowest cost first."
- return graph_search(problem, PriorityQueue(lambda a, b: a.path_cost < b.path_cost))
- def depth_limited_search(problem, limit=50):
- "depth first search with limited depth"
- def recursive_dls(node, problem, limit):
- "helper function for depth limited"
- cutoff_occurred = False
- if problem.goal_test(node.state):
- return node
- elif node.depth == limit:
- return 'cutoff'
- else:
- for successor in node.expand(problem):
- result = recursive_dls(successor, problem, limit)
- if result == 'cutoff':
- cutoff_occurred = True
- elif result != None:
- return result
- if cutoff_occurred:
- return 'cutoff'
- else:
- return None
- # Body of depth_limited_search:
- return recursive_dls(Node(problem.initial), problem, limit)
- Prepreki = [(1, 4), (1, 6), (1, 8), (2, 3), (2, 9), (4, 2), (4, 7), (4, 8), (5, 5), (5, 7), (6, 1), (6, 2), (6, 4),
- (6, 7)]
- def desnoh1(state):
- while (((state[0], state[1]) != (state[2], state[3])) and ((state[0], state[1]) != (state[4], state[5])) and (
- (state[0], state[1]) not in Prepreki)
- and (state[1] < 10 and state[1] > 0) and (state[0] > 0 and state[0] < 8)):
- Y = state[1]
- Y = Y + 1
- state = state[0], Y, state[2], state[3], state[4], state[5]
- newState = state[0], state[1] - 1
- return newState
- def levoh1(state):
- while (((state[0], state[1]) != (state[2], state[3])) and ((state[0], state[1]) != (state[4], state[5])) and (
- (state[0], state[1]) not in Prepreki)
- and (state[1] < 10 and state[1] > 0) and (state[0] > 0 and state[0] < 8)):
- Y = state[1]
- Y = Y - 1
- state = state[0], Y, state[2], state[3], state[4], state[5]
- newState = state[0], state[1] + 1
- return newState
- def goreh1(state):
- while (((state[0], state[1]) != (state[2], state[3])) and ((state[0], state[1]) != (state[4], state[5])) and (
- (state[0], state[1]) not in Prepreki)
- and (state[1] < 10 and state[1] > 0) and (state[0] > 0 and state[0] < 8)):
- X = state[0]
- X = X - 1
- state = X, state[1], state[2], state[3], state[4], state[5]
- newState = state[0] + 1, state[1]
- return newState
- def doluh1(state):
- while (((state[0], state[1]) != (state[2], state[3])) and ((state[0], state[1]) != (state[4], state[5])) and (
- (state[0], state[1]) not in Prepreki)
- and (state[1] < 10 and state[1] > 0) and (state[0] > 0 and state[0] < 8)):
- X = state[0]
- X = X + 1
- state = X, state[1], state[2], state[3], state[4], state[5]
- newState = state[0] - 1, state[1]
- return newState
- def desnoO(state):
- while (((state[2], state[3]) != (state[0], state[1])) and ((state[2], state[3]) != (state[4], state[5])) and (
- (state[2], state[3]) not in Prepreki)
- and (state[3] < 10 and state[3] > 0) and (state[2] > 0 and state[2] < 8)):
- Y = state[3]
- Y = Y + 1
- state = state[0], state[1], state[2], Y, state[4], state[5]
- newState = state[2], state[3] - 1
- return newState
- def levoO(state):
- while (((state[2], state[3]) != (state[0], state[1])) and ((state[2], state[3]) != (state[4], state[5])) and (
- (state[2], state[3]) not in Prepreki)
- and (state[3] < 10 and state[3] > 0) and (state[2] > 0 and state[2] < 8)):
- Y = state[3]
- Y = Y - 1
- state = state[0], state[1], state[2], Y, state[4], state[5]
- newState = state[2], state[3] + 1
- return newState
- def goreO(state):
- while (((state[2], state[3]) != (state[0], state[1])) and ((state[2], state[3]) != (state[4], state[5])) and (
- (state[2], state[3]) not in Prepreki)
- and (state[3] < 10 and state[3] > 0) and (state[2] > 0 and state[2] < 8)):
- X = state[2]
- X = X - 1
- state = state[0], state[1], X, state[3], state[4], state[5]
- newState = state[2] + 1, state[3]
- return newState
- def doluO(state):
- while (((state[2], state[3]) != (state[0], state[1])) and ((state[2], state[3]) != (state[4], state[5])) and (
- (state[2], state[3]) not in Prepreki)
- and (state[3] < 10 and state[3] > 0) and (state[2] > 0 and state[2] < 8)):
- X = state[2]
- X = X + 1
- state = state[0], state[1], X, state[3], state[4], state[5]
- newState = state[2] - 1, state[3]
- return newState
- def desnoh2(state):
- while (((state[4], state[5]) != (state[0], state[1])) and ((state[4], state[5]) != (state[2], state[3])) and (
- (state[4], state[5]) not in Prepreki)
- and (state[5] < 10 and state[5] > 0) and (state[4] > 0 and state[4] < 8)):
- Y = state[5]
- Y = Y + 1
- state = state[0], state[1], state[2], state[3], state[4], Y
- newState = state[4], state[5] - 1
- return newState
- def levoh2(state):
- while (((state[4], state[5]) != (state[0], state[1])) and ((state[4], state[5]) != (state[2], state[3])) and (
- (state[4], state[5]) not in Prepreki)
- and (state[5] < 10 and state[5] > 0) and (state[4] > 0 and state[4] < 8)):
- Y = state[5]
- Y = Y - 1
- state = state[0], state[1], state[2], state[3], state[4], Y
- newState = state[4], state[5] + 1
- return newState
- def goreh2(state):
- while (((state[4], state[5]) != (state[0], state[1])) and ((state[4], state[5]) != (state[2], state[3])) and (
- (state[4], state[5]) not in Prepreki)
- and (state[5] < 10 and state[5] > 0) and (state[4] > 0 and state[4] < 8)):
- X = state[4]
- X = X - 1
- state = state[0], state[1], state[2], state[3], X, state[5]
- newState = state[4] + 1, state[5]
- return newState
- def doluh2(state):
- while (((state[4], state[5]) != (state[0], state[1])) and ((state[4], state[5]) != (state[2], state[3])) and (
- (state[4], state[5]) not in Prepreki)
- and (state[5] < 10 and state[5] > 0) and (state[4] > 0 and state[4] < 8)):
- X = state[4]
- X = X + 1
- state = state[0], state[1], state[2], state[3], X, state[5]
- newState = state[4] - 1, state[5]
- return newState
- class PMolekula(Problem):
- def __init__(self, initial):
- self.initial = initial
- def goal_test(self, state):
- h1X = state[0]
- h1Y = state[1]
- oX = state[2]
- oY = state[3]
- h2X = state[4]
- h2Y = state[5]
- return (oX == h1X + 1 and h2X == oX + 1 and h1Y == oY and oY == h2Y)
- def successor(self, state):
- successors = dict()
- h1 = state[0], state[1]
- o = state[2], state[3]
- h2 = state[4], state[5]
- # gore h1
- h1new = goreh1(state)
- newState = h1new[0], h1new[1], o[0], o[1], h2[0], h2[1]
- successors['GoreH1'] = newState
- # dolu h1
- h1new = doluh1(state)
- newState = h1new[0], h1new[1], o[0], o[1], h2[0], h2[1]
- successors['DoluH1'] = newState
- # desno h1
- h1new = desnoh1(state)
- newState = h1new[0], h1new[1], o[0], o[1], h2[0], h2[1]
- successors['DesnoH1'] = newState
- # levo h1
- h1new = levoh1(state)
- newState = h1new[0], h1new[1], o[0], o[1], h2[0], h2[1]
- successors['LevoH1'] = newState
- # desno o
- onew = desnoO(state)
- newState = h1[0], h1[1], onew[0], onew[1], h2[0], h2[1]
- successors['DesnoO'] = newState
- # dolu o
- onew = doluO(state)
- newState = h1[0], h1[1], onew[0], onew[1], h2[0], h2[1]
- successors['DoluO'] = newState
- # levo 0
- onew = levoO(state)
- newState = h1[0], h1[1], onew[0], onew[1], h2[0], h2[1]
- successors['LevoO'] = newState
- # gore o
- onew = goreO(state)
- newState = h1[0], h1[1], onew[0], onew[1], h2[0], h2[1]
- successors['GoreO'] = newState
- # dolu h2
- h2new = doluh2(state)
- newState = h1[0], h1[1], o[0], o[1], h2new[0], h2new[1]
- successors['DoluH2'] = newState
- # gore h2
- h2new = goreh2(state)
- newState = h1[0], h1[1], o[0], o[1], h2new[0], h2new[1]
- successors['GoreH2'] = newState
- # levo h2
- h2new = levoh2(state)
- newState = h1[0], h1[1], o[0], o[1], h2new[0], h2new[1]
- successors['LevoH2'] = newState
- # desno h2
- h2new = desnoh2(state)
- newState = h1[0], h1[1], o[0], o[1], h2new[0], h2new[1]
- successors['DesnoH2'] = newState
- return successors
- def actions(self, state):
- return self.successor(state).keys()
- # called only for informed search
- def h(self, node):
- pos = node.state
- goalState = self.goal
- return abs(pos[0] - goalState[0]) + abs(pos[1] - goalState[1])
- def result(self, state, action):
- possible = self.successor(state)
- return possible[action]
- h1redica = int(input())
- h1kolona = int(input())
- oredica = int(input())
- okolona = int(input())
- h2redica = int(input())
- h2kolona = int(input())
- molekulaProblem = PMolekula((h1redica, h1kolona, oredica, okolona, h2redica, h2kolona))
- answer = breadth_first_graph_search(molekulaProblem)
- print(answer.solution())
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