AI_Lab_1

import sys
import bisect

infinity = float('inf')

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)

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 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

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)

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())



#koordinati na site prepreki vo shemata
Obstacles = [(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)]

#sostojba na nekoj atom ja definiram kako koordinati na site ostali atomi na primer H1x,H2x,Ox,Oy,H2x,H2y
def upAtomH1(A):
    tuple = ((A[2],A[3]),(A[4],A[5]))
    while(A[0] > 0 and A[0] < 8 and A[1]> 0 and A[1]< 10 and  #proveruvam dali mi iskacha od tablata
    ((A[0],A[1]) not in Obstacles) and #check wether i have landed on an obstacle
    ((A[0],A[1]) not in tuple)): # check wether i am in the same position as the other 2 atoms
        X=A[0] #the x coordinate of the atom is placed in the variable x
        X=X-1 #i reduce the x value because that is what happens when i move up in my coordinate system
        A=(X,A[1],A[2],A[3],A[4],A[5]) #vo A ja smestuvam novata sostojba na atomot so smeneta x coordinate

    Anew=(A[0]+1,A[1]) #vo Anew stavam koordinati, po izvrshuvanje na while. za da zavrshi while moralo da stignam negde kaj sho ne e okej
                        #zatoa mi sluzhi toa +1 za da se vratam edna poz nazad pred da napraam sranja za da iskocam od while
                        #whileot ustvari e za neprekinato pushing vo edna nasoka
    return Anew

def downAtomH1(A):
    tuple = ((A[2],A[3]),(A[4],A[5]))
    while(A[0] > 0 and A[0] < 8 and A[1]> 0 and A[1]< 10 and  #proveruvam dali mi iskacha od tablata
    ((A[0],A[1]) not in Obstacles) and #check wether i have landed on an obstacle
    ((A[0],A[1]) not in tuple)): # check wether i am in the same position as the other 2 atoms
        X=A[0] #the x coordinate of the atom is placed in the variable x
        X=X+1 #i reduce the x value because that is what happens when i move up in my coordinate system
        A=(X,A[1],A[2],A[3],A[4],A[5]) #vo A ja smestuvam novata sostojba na atomot so smeneta x coordinate

    Anew=(A[0]-1,A[1]) #vo Anew stavam koordinati, po izvrshuvanje na while. za da zavrshi while moralo da stignam negde kaj sho ne e okej
                        #zatoa mi sluzhi toa +1 za da se vratam edna poz nazad pred da napraam sranja za da iskocam od while
                        #whileot ustvari e za neprekinato pushing vo edna nasoka
    return Anew

def leftAtomH1(A):
    tuple = ((A[2],A[3]),(A[4],A[5]))
    while(A[0] > 0 and A[0] < 8 and A[1]> 0 and A[1]< 10 and  #proveruvam dali mi iskacha od tablata
    ((A[0],A[1]) not in Obstacles) and #check wether i have landed on an obstacle
    ((A[0],A[1]) not in tuple)): # check wether i am in the same position as the other 2 atoms
        Y=A[1] #the x coordinate of the atom is placed in the variable x
        Y=Y-1 #i reduce the x value because that is what happens when i move up in my coordinate system
        A=(A[0],Y,A[2],A[3],A[4],A[5]) #vo A ja smestuvam novata sostojba na atomot so smeneta x coordinate

    Anew=(A[0],A[1]+1) #vo Anew stavam koordinati, po izvrshuvanje na while. za da zavrshi while moralo da stignam negde kaj sho ne e okej
                        #zatoa mi sluzhi toa +1 za da se vratam edna poz nazad pred da napraam sranja za da iskocam od while
                        #whileot ustvari e za neprekinato pushing vo edna nasoka
    return Anew

def rightAtomH1(A):
    tuple = ((A[2],A[3]),(A[4],A[5]))
    while(A[0] > 0 and A[0] < 8 and A[1]> 0 and A[1]< 10 and  #proveruvam dali mi iskacha od tablata
    ((A[0],A[1]) not in Obstacles) and #check wether i have landed on an obstacle
    ((A[0],A[1]) not in tuple)): # check wether i am in the same position as the other 2 atoms
        Y = A[1]  # the x coordinate of the atom is placed in the variable x
        Y = Y + 1  # i reduce the x value because that is what happens when i move up in my coordinate system
        A = (A[0], Y, A[2], A[3], A[4], A[5])  # vo A ja smestuvam novata sostojba na atomot so smeneta x coordinate

    Anew = (A[0], A[1] - 1) #vo Anew stavam koordinati, po izvrshuvanje na while. za da zavrshi while moralo da stignam negde kaj sho ne e okej
                        #zatoa mi sluzhi toa +1 za da se vratam edna poz nazad pred da napraam sranja za da iskocam od while
                        #whileot ustvari e za neprekinato pushing vo edna nasoka
    return Anew

def upAtomO(A):
    tuple = ((A[0], A[1]), (A[4], A[5]))
    while (A[2] > 0 and A[2] < 8 and A[3] > 0 and A[3] < 10 and  # proveruvam dali mi iskacha od tablata
           ((A[2], A[3]) not in Obstacles) and  # check wether i have landed on an obstacle
           ((A[2], A[3]) not in tuple)):  # check wether i am in the same position as the other 2 atoms
        X=A[3]
        X=X-1
        A=(A[0],A[1],X,A[3],A[4],A[5])
    Anew=(A[2]+1,A[3])
    return Anew

def upAtomO(A):
    tuple = ((A[0], A[1]), (A[4], A[5]))
    while (A[2] > 0 and A[2] < 8 and A[3] > 0 and A[3] < 10 and  # proveruvam dali mi iskacha od tablata
           ((A[2], A[3]) not in Obstacles) and  # check wether i have landed on an obstacle
           ((A[2], A[3]) not in tuple)):  # check wether i am in the same position as the other 2 atoms
        X=A[3]
        X=X-1
        A=(A[0],A[1],X,A[3],A[4],A[5])
    Anew=(A[2]+1,A[3])
    return Anew

def downAtomO(A):
    tuple = ((A[0], A[1]), (A[4], A[5]))
    while (A[2] > 0 and A[2] < 8 and A[3] > 0 and A[3] < 10 and  # proveruvam dali mi iskacha od tablata
           ((A[2], A[3]) not in Obstacles) and  # check wether i have landed on an obstacle
           ((A[2], A[3]) not in tuple)):  # check wether i am in the same position as the other 2 atoms
        X=A[3]
        X=X+1
        A=(A[0],A[1],X,A[3],A[4],A[5])
    Anew=(A[2]-1,A[3])
    return Anew

def leftAtomO(A):
    tuple = ((A[0], A[1]), (A[4], A[5]))
    while (A[2] > 0 and A[2] < 8 and A[3] > 0 and A[3] < 10 and  # proveruvam dali mi iskacha od tablata
           ((A[2], A[3]) not in Obstacles) and  # check wether i have landed on an obstacle
           ((A[2], A[3]) not in tuple)):  # check wether i am in the same position as the other 2 atoms
        Y=A[3]
        Y=Y-1
        A=(A[0],A[1],A[2],Y,A[4],A[5])
    Anew=(A[2],A[3]+1)
    return Anew

def rightAtomO(A):
    tuple = ((A[0], A[1]), (A[4], A[5]))
    while (A[2] > 0 and A[2] < 8 and A[3] > 0 and A[3] < 10 and  # proveruvam dali mi iskacha od tablata
           ((A[2], A[3]) not in Obstacles) and  # check wether i have landed on an obstacle
           ((A[2], A[3]) not in tuple)):  # check wether i am in the same position as the other 2 atoms
        Y=A[3]
        Y=Y+1
        A=(A[0],A[1],A[2],Y,A[4],A[5])
    Anew=(A[2],A[3]-1)
    return Anew

def upAtomH2(A):
    tuple = ((A[2],A[3]),(A[4],A[5]))
    while(A[0] > 0 and A[0] < 8 and A[1]> 0 and A[1]< 10 and  #proveruvam dali mi iskacha od tablata
    ((A[0],A[1]) not in Obstacles) and #check wether i have landed on an obstacle
    ((A[0],A[1]) not in tuple)): # check wether i am in the same position as the other 2 atoms
        X=A[0] #the x coordinate of the atom is placed in the variable x
        X=X-1 #i reduce the x value because that is what happens when i move up in my coordinate system
        A=(X,A[1],A[2],A[3],A[4],A[5]) #vo A ja smestuvam novata sostojba na atomot so smeneta x coordinate

    Anew=(A[0]+1,A[1]) #vo Anew stavam koordinati, po izvrshuvanje na while. za da zavrshi while moralo da stignam negde kaj sho ne e okej
                        #zatoa mi sluzhi toa +1 za da se vratam edna poz nazad pred da napraam sranja za da iskocam od while
                        #whileot ustvari e za neprekinato pushing vo edna nasoka
    return Anew

def downAtomH2(A):
    tuple = ((A[2],A[3]),(A[4],A[5]))
    while(A[0] > 0 and A[0] < 8 and A[1]> 0 and A[1]< 10 and  #proveruvam dali mi iskacha od tablata
    ((A[0],A[1]) not in Obstacles) and #check wether i have landed on an obstacle
    ((A[0],A[1]) not in tuple)): # check wether i am in the same position as the other 2 atoms
        X=A[0] #the x coordinate of the atom is placed in the variable x
        X=X+1 #i reduce the x value because that is what happens when i move up in my coordinate system
        A=(X,A[1],A[2],A[3],A[4],A[5]) #vo A ja smestuvam novata sostojba na atomot so smeneta x coordinate

    Anew=(A[0]-1,A[1]) #vo Anew stavam koordinati, po izvrshuvanje na while. za da zavrshi while moralo da stignam negde kaj sho ne e okej
                        #zatoa mi sluzhi toa +1 za da se vratam edna poz nazad pred da napraam sranja za da iskocam od while
                        #whileot ustvari e za neprekinato pushing vo edna nasoka
    return Anew

def leftAtomH2(A):
    tuple = ((A[2],A[3]),(A[4],A[5]))
    while(A[0] > 0 and A[0] < 8 and A[1]> 0 and A[1]< 10 and  #proveruvam dali mi iskacha od tablata
    ((A[0],A[1]) not in Obstacles) and #check wether i have landed on an obstacle
    ((A[0],A[1]) not in tuple)): # check wether i am in the same position as the other 2 atoms
        Y=A[1] #the x coordinate of the atom is placed in the variable x
        Y=Y-1 #i reduce the x value because that is what happens when i move up in my coordinate system
        A=(A[0],Y,A[2],A[3],A[4],A[5]) #vo A ja smestuvam novata sostojba na atomot so smeneta x coordinate

    Anew=(A[0],A[1]+1) #vo Anew stavam koordinati, po izvrshuvanje na while. za da zavrshi while moralo da stignam negde kaj sho ne e okej
                        #zatoa mi sluzhi toa +1 za da se vratam edna poz nazad pred da napraam sranja za da iskocam od while
                        #whileot ustvari e za neprekinato pushing vo edna nasoka
    return Anew

def rightAtomH2(A):
    tuple = ((A[2],A[3]),(A[4],A[5]))
    while(A[0] > 0 and A[0] < 8 and A[1]> 0 and A[1]< 10 and  #proveruvam dali mi iskacha od tablata
    ((A[0],A[1]) not in Obstacles) and #check wether i have landed on an obstacle
    ((A[0],A[1]) not in tuple)): # check wether i am in the same position as the other 2 atoms
        Y = A[1]  # the x coordinate of the atom is placed in the variable x
        Y = Y + 1  # i reduce the x value because that is what happens when i move up in my coordinate system
        A = (A[0], Y, A[2], A[3], A[4], A[5])  # vo A ja smestuvam novata sostojba na atomot so smeneta x coordinate

    Anew = (A[0], A[1] - 1) #vo Anew stavam koordinati, po izvrshuvanje na while. za da zavrshi while moralo da stignam negde kaj sho ne e okej
                        #zatoa mi sluzhi toa +1 za da se vratam edna poz nazad pred da napraam sranja za da iskocam od while
                        #whileot ustvari e za neprekinato pushing vo edna nasoka
    return Anew

class Molekula(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(H1X == OX and OX == H2X and #proverka dali H1 i O se vo ista kolona posho za da se edni do drugi mora da se u ista kolona
               OY == H1Y +1 and #proverka dali i drugiot H2 atom e vo ista redica so ovie
               H2Y == OY+1) #dali se bash edni do drugi so rastojanie 0 megju sebe na sosedni kvadrati

    def successor(self,state):
        successors=dict() #definiram prazen rechnik
        H1 = state[0],state[1] #vo H1 stavam koordinati na H1 atomot shto gi dobivam od state
        O = state[2], state[3]  # vo HO stavam koordinati na H1 atomot shto gi dobivam od state
        H2 = state[4], state[5]  # vo H2 stavam koordinati na H1 atomot shto gi dobivam od state
        #podoly kako keyes vo dictionary gi staam iminjata na akciite a kako values gi staam states koi sledat od nekoja takva akcija
        #so sekoj nov state koj povikuva nekakva akcija od dict se generiraat novi possible states
        #zatoa na pocetokot successors sekogas se definira na prazen rechnik na pochetokot na funkcijava

        #GI DEFINIRAM SITE MOZHNI POTEZI I NIVNITE REZULTATI ZA H1 ATOM
        H1new = upAtomH1(state)
        Statenew= (H1new[0], H1new[1], O[0], O[1], H2[0], H2[1])
        successors['GoreH1'] = Statenew

        H1new = downAtomH1(state)
        Statenew = (H1new[0], H1new[1], O[0], O[1], H2[0], H2[1])
        successors['DoleH1'] = Statenew

        H1new = leftAtomH1(state)
        Statenew = (H1new[0], H1new[1], O[0], O[1], H2[0], H2[1])
        successors['LevoH1'] = Statenew

        H1new = rightAtomH1(state)
        Statenew = (H1new[0], H1new[1], O[0], O[1], H2[0], H2[1])
        successors['DesnoH1'] = Statenew

        # GI DEFINIRAM SITE MOZHNI POTEZI I NIVNITE REZULTATI ZA H2 ATOM
        H2new = upAtomH2(state)
        Statenew = (H1[0],H1[1], O[0], O[1],H2new[0], H2new[1])
        successors['GoreH2'] = Statenew

        H2new = downAtomH2(state)
        Statenew = (H1[0],H1[1], O[0], O[1],H2new[0], H2new[1])
        successors['DoleH2'] = Statenew

        H2new = leftAtomH2(state)
        Statenew = (H1[0],H1[1], O[0], O[1],H2new[0], H2new[1])
        successors['LevoH2'] = Statenew

        H2new = rightAtomH2(state)
        Statenew = (H1[0],H1[1], O[0], O[1],H2new[0], H2new[1])
        successors['DesnoH2'] = Statenew

        # GI DEFINIRAM SITE MOZHNI POTEZI I NIVNITE REZULTATI ZA O ATOM
        Onew = upAtomO(state)
        Statenew = (H1[0], H1[1], Onew[0], Onew[1], H2[0], H2[1])
        successors['GoreO'] = Statenew

        Onew = downAtomO(state)
        Statenew = (H1[0], H1[1], Onew[0], Onew[1], H2[0], H2[1])
        successors['DoleO'] = Statenew

        Onew = leftAtomO(state)
        Statenew = (H1[0], H1[1], Onew[0], Onew[1], H2[0], H2[1])
        successors['LevoO'] = Statenew

        Onew = rightAtomO(state)
        Statenew = (H1[0], H1[1], Onew[0], Onew[1], H2[0], H2[1])
        successors['DesnoO'] = Statenew

        return successors

    def actions(self, state):
        return self.successor(state).keys() #gi vrakjam site mozhni AKCII



    def result(self, state, action):
        possible = self.successor(state) #vrakjam koja sostojba e rezultat na dadena akcija pratena kako prarametar
        return possible[action]



#Vcituvanje na vleznite argumenti za test primerite
H1AtomRedica = int(input()) #atomot so link desno
H1AtomKolona = int(input())
OAtomRedica = int(input())
OAtomKolona = int(input())
H2AtomRedica = int(input()) #atomot so link levo
H2AtomKolona = int(input())

#Vasiot kod pisuvajte go pod ovoj komentar

MolekulaInstance = Molekula((H1AtomRedica, H1AtomKolona, OAtomRedica, OAtomKolona, H2AtomRedica, H2AtomKolona))

answer = breadth_first_graph_search(MolekulaInstance)
print (answer.solution())





import sys
import bisect

infinity = float('inf')

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)

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 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

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)

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 updateP1(P): #horisontal, to the left, start state: 2,2 and 2,3
    (X,Y,Nasoka) = P
    if(Y == 0 and Nasoka == 1) or (Y == 4 and Nasoka == -1): #ako sum doshla do nekoj od dzidovite sho me ogranichuvaat menjam nasoka
        Nasoka = Nasoka * (-1)
    Ynew = Y - Nasoka #na X mu se dodava/ odzema eden chekor zavisno od nasokata
    Pnew = (X, Ynew, Nasoka)
    return Pnew

def updateP2(P): #diagonal, upward right, start state: 8,2  8,3  7,2  7,3
    (X, Y, Nasoka) = P
    if (X == 10 and Nasoka == -1) or (X == 6 and Nasoka == 1):  # ako sum doshla do nekoj od dzidovite sho me ogranichuvaat menjam nasoka
        Nasoka = Nasoka * (-1)
    Xnew = X - Nasoka  # na X mu se dodava/ odzema eden chekor zavisno od nasokata
    Ynew = Y + Nasoka
    Pnew = (Xnew, Ynew, Nasoka)
    return Pnew

def updateP3(P): #vertical, down, 8,8  9,8
    (X,Y,Nasoka) = P
    if(X == 10 and Nasoka == 1) or (X == 6 and Nasoka == -1): #ako sum doshla do nekoj od dzidovite sho me ogranichuvaat menjam nasoka
        Nasoka = Nasoka * (-1)
    Xnew = X + Nasoka #na X mu se dodava/ odzema eden chekor zavisno od nasokata
    Pnew = (Xnew, Y, Nasoka)
    return Pnew

class Istrazuvac(Problem):

    def __init__(self, initial, goal):
        self.initial = initial
        self.goal = goal
    def goal_test(self, state):
        g = self.goal
        return (state [0] == g[0] and state[1] == g[1])

    def successor(self,state):
        successors = 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])

        #ako x e pomalo od 10 mozam da odam nadolu
        if(X < 10):
            Xnew = X + 1
            Ynew = Y
            P1new = updateP1(P1)
            P2new = updateP2(P2)
            P3new = updateP3(P3)
            #obstacles se site koordinati kade bi se nashle preckite vo slednata iteracija
            obstacles = (P1new[0], P1new[1]), (P1new[0], P1new[1]+1), (P2new[0], P2new[1]), (P2new[0]-1, P2new[1]), (P2new[0], P2new[1]+1), (P2new[0]-1, P2new[1]+1), (P3new[0], P3new[1]), (P3new[0]+1, P3new[1])
            if( (Xnew, Ynew) not in obstacles):
                Statenew = (Xnew, Ynew, P1new[0], P1new[1], P1new[2], P2new[0],P2new[1], P2new[2],P3new[0], P3new[1], P3new[2])
                #vo statenew mi e novoto stanje posle mrdanje dole ako pomine ifot odnosno ovaa promena na sostojba nastanuva samo ako site constraints se zadovoleni
                successors['Dolu'] = Statenew

         #ako x e pogolemo od 0 mozham da odam nagore
        if (X > 0):
            Xnew = X - 1
            Ynew = Y
            P1new = updateP1(P1)
            P2new = updateP2(P2)
            P3new = updateP3(P3)
            # obstacles se site koordinati kade bi se nashle preckite vo slednata iteracija
            obstacles = (P1new[0], P1new[1]), (P1new[0], P1new[1] + 1), (P2new[0], P2new[1]), (P2new[0] - 1, P2new[1]), (P2new[0], P2new[1] + 1), (P2new[0] - 1, P2new[1] + 1), (P3new[0], P3new[1]), (P3new[0] + 1, P3new[1])
            if (((Xnew, Ynew) not in obstacles) and ((Y < 5) or (X > 5))):
                Statenew = (
                Xnew, Ynew, P1new[0], P1new[1], P1new[2], P2new[0], P2new[1], P2new[2], P3new[0], P3new[1], P3new[2])
                # vo statenew mi e novoto stanje posle mrdanje dole ako pomine ifot odnosno ovaa promena na sostojba nastanuva samo ako site constraints se zadovoleni
                successors['Gore'] = Statenew

        #ako y>0 mozham da odam vo levo
        if (Y > 0):
            Xnew = X
            Ynew = Y - 1
            P1new = updateP1(P1)
            P2new = updateP2(P2)
            P3new = updateP3(P3)
            # obstacles se site koordinati kade bi se nashle preckite vo slednata iteracija
            obstacles = (P1new[0], P1new[1]), (P1new[0], P1new[1] + 1), (P2new[0], P2new[1]), (P2new[0] - 1, P2new[1]), (P2new[0], P2new[1] + 1), (P2new[0] - 1, P2new[1] + 1), (P3new[0], P3new[1]), (P3new[0] + 1, P3new[1])
            if ((Xnew, Ynew) not in obstacles):
                Statenew = (
                Xnew, Ynew, P1new[0], P1new[1], P1new[2], P2new[0], P2new[1], P2new[2], P3new[0], P3new[1], P3new[2])
                # vo statenew mi e novoto stanje posle mrdanje dole ako pomine ifot odnosno ovaa promena na sostojba nastanuva samo ako site constraints se zadovoleni
                successors['Levo'] = Statenew

        # ako y<10 mozham da odam vo desno
        if (Y > 0):
            Xnew = X
            Ynew = Y + 1
            P1new = updateP1(P1)
            P2new = updateP2(P2)
            P3new = updateP3(P3)
            # obstacles se site koordinati kade bi se nashle preckite vo slednata iteracija
            obstacles = (P1new[0], P1new[1]), (P1new[0], P1new[1] + 1), (P2new[0], P2new[1]), (
            P2new[0] - 1, P2new[1]), (P2new[0], P2new[1] + 1), (P2new[0] - 1, P2new[1] + 1), (
                                P3new[0], P3new[1]), (P3new[0] + 1, P3new[1])
            if (((Xnew, Ynew) not in obstacles) and ((X > 4) or (Y < 5))):
                Statenew = (Xnew, Ynew, P1new[0], P1new[1], P1new[2], P2new[0], P2new[1], P2new[2], P3new[0], P3new[1],
                    P3new[2])
                # vo statenew mi e novoto stanje posle mrdanje dole ako pomine ifot odnosno ovaa promena na sostojba nastanuva samo ako site constraints se zadovoleni
                successors['Desno'] = Statenew
        return successors


    def actions(self,state):
        return self.successor(state).keys() #gi vrakjam site mozhni AKCII

    def result(self,state,action):
        possible = self.successor(state) #vrakjam koja sostojba e rezultat na dadena akcija pratena kako prarametar
        return possible[action]

#Vcituvanje na vleznite argumenti za test primerite

CoveceRedica = int(input())
CoveceKolona = int(input())
KukjaRedica = int(input())
KukjaKolona = int(input())

#Vasiot kod pisuvajte go pod ovoj komentar

K = [KukjaRedica, KukjaKolona]
IstrazuvacInstance = Istrazuvac((CoveceRedica, CoveceKolona,2,1,1,7,3,1,9,8,1),K)

answer = breadth_first_graph_search(IstrazuvacInstance)
print (answer.solution())