PodvizniPrepreki

# Python modul vo koj se implementirani algoritmite za neinformirano i 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)


# ________________________________________________________________________________________________________
#Neinformirano prebaruvanje vo ramki na drvo
#Vo ramki na drvoto ne razresuvame jamki

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)


def iterative_deepening_search(problem):

    for depth in xrange(sys.maxint):
        result = depth_limited_search(problem, depth)
        if result is not 'cutoff':
            return result



# _________________________________________________________________________________________________________
#Vasiot kod pisuvajte go pod ovoj komentar

# Python modul vo koj se implementirani algoritmite za neinformirano i 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)


# ________________________________________________________________________________________________________
#Neinformirano prebaruvanje vo ramki na drvo
#Vo ramki na drvoto ne razresuvame jamki

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)


def iterative_deepening_search(problem):

    for depth in xrange(sys.maxint):
        result = depth_limited_search(problem, depth)
        if result is not 'cutoff':
            return result


# ________________________________________________________________________________________________________
#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


# 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



# _________________________________________________________________________________________________________
#Vcituvanje na vleznite argumenti za test primerite

def precka1(P):
    x=P[0]
    y=P[1]
    n=P[2]

    if x==2 and y==0 and n==-1:
        x=x
        y=y+1
        n=n*(-1)
    elif x==2 and y==4 and n==+1:
        x=x
        y=y-1
        n=n*(-1)
    else:
        x=x
        y=y+n
        n=n

    Pnew=x,y,n
    return Pnew

def precka2(P):
    x=P[0]
    y=P[1]
    n=P[2]
    if x==9 and y==1 and n==-1:
        x=x-1
        y=y+1
        n=n*(-1)
    elif x==5 and y==5 and n==+1:
        x=x+1
        y=y-1
        n=n*(-1)
    else:
        x=x-n
        y=y+n
        n=n

    Pnew=x,y,n
    return Pnew

def precka3(P):
    x=P[0]
    y=P[1]
    n=P[2]

    if x==6 and y==8 and n==-1:
        x=x+1
        y=y
        n=n*(-1)
    elif x==10 and y==8 and n==+1:
        x=x-1
        y=y
        n=n*(-1)
    else:
        x=x+n
        y=y
        n=n

    Pnew=x,y,n
    return Pnew

def validno(V):
    Cx=V[0]
    Cy=V[1]
    p1x=V[2]
    p1y=V[3]
    p2x=V[4]
    p2y=V[5]
    p3x=V[6]
    p3y=V[7]

    t=False
    if (Cx != p1x or Cy != p1y) and (Cx != p1x or Cy != p1y+1) and (Cx != p2x or Cy != p2y) and (Cx != p2x or Cy != p2y-1) and (Cx != p2x+1 or Cy != p2y-1) and (Cx != p2x+1 or Cy != p2y) and (Cx != p3x or Cy != p3y) and (Cx != p3x+1 or Cy != p3y):
        t=True
    else:
        t=False
    return t


class PP(Problem):

    def __init__(self, initial, goal):
        self.initial = initial
        self.goal = goal

    def successor(self, state):
        succs = dict()

        x=state[0]
        y=state[1]
        p1=(state[2],state[3],state[4])
        p2=(state[5],state[6],state[7])
        p3=(state[8],state[9],state[10])

        if (y<5 and y>=0 and x >=0 and x<5) or (y<10 and y>=0 and x>4 and x<11):
            Xnew=x
            Ynew=y+1
            p1New=precka1(p1)
            p2New=precka2(p2)
            p3New=precka3(p3)
            V=(Xnew,Ynew,p1New[0],p1New[1],p2New[0],p2New[1],p3New[0],p3New[1])
            v=validno(V)
            if(v==True):
                StateNew=(Xnew,Ynew,p1New[0],p1New[1],p1New[2],p2New[0],p2New[1],p2New[2],p3New[0],p3New[1],p3New[2])
                succs['Desno']=StateNew

        if (y>0 and y<6 and x>=0 and x<5) or (y>0 and y<11 and x>4 and x<11):
            Xnew=x
            Ynew=y-1
            p1New=precka1(p1)
            p2New=precka2(p2)
            p3New=precka3(p3)
            V=(Xnew,Ynew,p1New[0],p1New[1],p2New[0],p2New[1],p3New[0],p3New[1])
            v=validno(V)
            if(v==True):
                StateNew=(Xnew,Ynew,p1New[0],p1New[1],p1New[2],p2New[0],p2New[1],p2New[2],p3New[0],p3New[1],p3New[2])
                succs['Levo']=StateNew


        if (x>0 and x<11 and y>=0 and y<6) or (x>5 and x<11 and y>5 and y<11):
            Xnew=x-1
            Ynew=y
            p1New=precka1(p1)
            p2New=precka2(p2)
            p3New=precka3(p3)
            V=(Xnew,Ynew,p1New[0],p1New[1],p2New[0],p2New[1],p3New[0],p3New[1])
            v=validno(V)
            if(v==True):
                StateNew=(Xnew,Ynew,p1New[0],p1New[1],p1New[2],p2New[0],p2New[1],p2New[2],p3New[0],p3New[1],p3New[2])
                succs['Gore']=StateNew

        if (x<10 and x>=0 and y>=0 and y<6) or (x<10 and x>4 and y>5 and y<11):
            Xnew=x+1
            Ynew=y
            p1New=precka1(p1)
            p2New=precka2(p2)
            p3New=precka3(p3)
            V=(Xnew,Ynew,p1New[0],p1New[1],p2New[0],p2New[1],p3New[0],p3New[1])
            v=validno(V)
            if(v==True):
                StateNew=(Xnew,Ynew,p1New[0],p1New[1],p1New[2],p2New[0],p2New[1],p2New[2],p3New[0],p3New[1],p3New[2])
                succs['Dolu']=StateNew

        return succs


    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])



CoveceRedica = int(input())
CoveceKolona = int(input())
KukaRedica = int(input())
KukaKolona = int(input())

K = [KukaRedica,KukaKolona]
PPinstanca = PP((CoveceRedica, CoveceKolona, 2, 2, -1, 7, 3, +1, 8, 8, +1), K)
answer = breadth_first_graph_search(PPinstanca)
print answer.solution()