search.py

"""

** Complete search module **

This search module is loosely based on the AIMA book.
Search (Chapters 3-4)

The way to use this code is to subclass the class 'Problem' to create
your own class of problems,  then create problem instances and solve them with
calls to the various search functions.

Last modified 2017-03-18
by f.maire@qut.edu.au
  simplified  depth_first_graph_search()

"""

from __future__ import print_function
from __future__ import division

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
#                           UTILS

import itertools


def memoize(fn):
    """Memoize fn: make it remember the computed value for any argument list"""
    def memoized_fn(*args):
        if not args in memoized_fn.cache:
            memoized_fn.cache[args] = fn(*args)
        return memoized_fn.cache[args]
    memoized_fn.cache = {}
    return memoized_fn

def update(x, **entries):
    """Update a dict; or an object with slots; according to entries.
    >>> update({'a': 1}, a=10, b=20)
    {'a': 10, 'b': 20}
    >>> update(Struct(a=1), a=10, b=20)
    Struct(a=10, b=20)
    """
    if isinstance(x, dict):
        x.update(entries)
    else:
        x.__dict__.update(entries)
    return x

#______________________________________________________________________________
# Queues: LIFOQueue (also known as Stack), FIFOQueue, PriorityQueue

class Queue:
    """
    Queue is an abstract class/interface. There are three types:
        LIFOQueue(): A Last In First Out Queue.
        FIFOQueue(): A First In First Out Queue.
        PriorityQueue(order, f): Queue in sorted order (min-first).
    Each type of queue 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?
    """

    def __init__(self):
        raise NotImplementedError

    def extend(self, items):
        for item in items: self.append(item)

def LIFOQueue():
    """
    Return an empty list, suitable as a Last-In-First-Out Queue.
    Last-In-First-Out Queues are also called stacks
    """
    return []


import collections # for dequeue
class FIFOQueue(collections.deque):
    """
    A First-In-First-Out Queue.
    """
    def __init__(self):
        collections.deque.__init__(self)
    def pop(self):
        return self.popleft()


import heapq
class PriorityQueue(Queue):
    """
    A queue in which the minimum  element (as determined by f) is returned first.
    The item with minimum f(x) is returned first
    """
    def __init__(self, f=lambda x: x):
        self.A = []  # list of pairs  (f(item), item)
        self.f = f
        self.counter = itertools.count() # unique sequence count
    def append(self, item):
        # thw pair  (f(item), item)  is pushed on the internal heapq
        heapq.heappush(self.A, (self.f(item), next(self.counter), item))
    def __len__(self):
        return len(self.A)
    def __str__(self):
        return str(self.A)
    def pop(self):
        return heapq.heappop(self.A)[2]
        # (self.f(item), item) is returned by heappop
        # (self.f(item), item)[1]   is item
    def __contains__(self, item):
        # Note that on the next line a generator is used!
        # the _ corresponds to f(x)
        return any(x==item for _,_, x in self.A)
    def __getitem__(self, key):
        for _,_, item in self.A:
            if item == key:
                return item
    def __delitem__(self, key):
        for i, (value,count,item) in enumerate(self.A):
            if item == key:
                self.A.pop(i)
                return
#______________________________________________________________________________

class Problem(object):
    """The abstract class for a formal problem.  You should subclass
    this and implement the methods actions and result, 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 actions(self, state):
        """Return the actions that can be executed in the given
        state. The result would typically be a list, but if there are
        many actions, consider yielding them one at a time in an
        iterator, rather than building them all at once."""
        raise NotImplementedError

    def result(self, state, action):
        """Return the state that results from executing the given
        action in the given state. The action must be one of
        self.actions(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. Override 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, state):
        """For optimization problems, each state has a value.  Hill-climbing
        and related algorithms try to maximize this value."""
        raise NotImplementedError
#______________________________________________________________________________

# Code to compare searchers on various problems.

class InstrumentedProblem(Problem):
    """Delegates to a problem, and keeps statistics."""

    def __init__(self, problem):
        assert isinstance(problem, Problem)
        self.problem = problem
        self.succs = self.goal_tests = self.states = 0
        self.found = False

    def actions(self, state):
        self.succs += 1
        return self.problem.actions(state)

    def result(self, state, action):
        self.states += 1
        return self.problem.result(state, action)

    def goal_test(self, state):
        self.goal_tests += 1
        result = self.problem.goal_test(state)
        if result:
            self.found = True
        return result

    def path_cost(self, c, state1, action, state2):
        return self.problem.path_cost(c, state1, action, state2)

    def value(self, state):
        return self.problem.value(state)

    def __getattr__(self, attr):
        return getattr(self.problem, attr)

    def __repr__(self):
        '''
        Once a search has been performed on an InstrumentedProblem  ip,
        Some stats can be displayed by using,
            print ip
        '''
        return '#succs = %d, #goal test = %d, #states = %d, goal found = %s' % (self.succs, self.goal_tests,
                                     self.states, str(self.found))

#______________________________________________________________________________

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."
        update(self, state=state, parent=parent, action=action,
               path_cost=path_cost, depth=0)
        if parent:
            self.depth = parent.depth + 1

    def __repr__(self):
        return "<Node %s>" % (self.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):
        "Fig. 3.10"
        next = problem.result(self.state, action)
        return Node(next, # next is a state
                    self, # parent is a node
                    action, # from this state to next state
                    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 path(self):
        "Return a list of nodes forming the path from the root to this node."
        node, path_back = self, []
        while node:
            path_back.append(node)
            node = node.parent
        return list(reversed(path_back))

    # 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)

#______________________________________________________________________________

# Uninformed Search algorithms

def tree_search(problem, frontier):
    """
        Search through the successors of a problem to find a goal.
        The argument frontier should be an empty queue.
        Don't worry about repeated paths to a state. [Fig. 3.7]
        Return
             the node of the first goal state found
             or None is no goal state is found
    """
    assert isinstance(problem, Problem)
    frontier.append(Node(problem.initial))
    while frontier:
        print(frontier)
        node = frontier.pop()
        if problem.goal_test(node.state):
            return node
        frontier.extend(node.expand(problem))
    return None

def graph_search(problem, frontier):
    """
    Search through the successors of a problem to find a goal.
    The argument frontier should be an empty queue.
    If two paths reach a state, only use the first one. [Fig. 3.7]
    Return
        the node of the first goal state found
        or None is no goal state is found
    """
    assert isinstance(problem, Problem)
    frontier.append(Node(problem.initial))
    explored = set() # initial empty set of explored states
    while frontier:
        node = frontier.pop()
        if problem.goal_test(node.state):
            return node
        explored.add(node.state)
        # Python note: next line uses of a generator
        frontier.extend(child for child in node.expand(problem)
                        if child.state not in explored
                        and child not in frontier)
    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, LIFOQueue())


def depth_first_graph_search(problem):
    "Search the deepest nodes in the search tree first."
    return graph_search(problem, LIFOQueue())


def breadth_first_graph_search(problem):
    "Graph search version of BFS.  [Fig. 3.11]"
    return graph_search(problem, FIFOQueue())

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

def best_first_tree_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.
    """
    node = Node(problem.initial)
    if problem.goal_test(node.state):
        return node
    frontier = PriorityQueue(f)
    frontier.append(node)
    while frontier:
        node = frontier.pop()
        if problem.goal_test(node.state):
            return node
        for child in node.expand(problem):
            if child not in frontier:
                frontier.append(child)
            elif child in frontier:
                incumbent = frontier[child] # incumbent is a node
                if f(child) < f(incumbent):
                    del frontier[incumbent]
                    frontier.append(child)
    return None



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)
    node = Node(problem.initial)
    if problem.goal_test(node.state):
        return node
    frontier = PriorityQueue(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] # incumbent is a node
                if f(child) < f(incumbent):
                    del frontier[incumbent]
                    frontier.append(child)
    return None

def uniform_cost_search(problem):
    "[Fig. 3.14]"
    return best_first_graph_search(problem, lambda node: node.path_cost)

def depth_limited_search(problem, limit=50):
    "[Fig. 3.17]"
    def recursive_dls(node, problem, limit):
        if problem.goal_test(node.state):
            return node
        elif node.depth == limit:
            return 'cutoff'
        else:
            cutoff_occurred = False
            for child in node.expand(problem):
                result = recursive_dls(child, problem, limit)
                if result == 'cutoff':
                    cutoff_occurred = True
                elif result is not 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):
    "[Fig. 3.18]"
    for depth in itertools.count():
        result = depth_limited_search(problem, depth)
        if result != 'cutoff':
            return result

#______________________________________________________________________________
# Informed (Heuristic) Search

greedy_best_first_graph_search = best_first_graph_search
    # Greedy best-first search is accomplished by specifying f(n) = h(n).

def astar_graph_search(problem, h=None):
    """A* search is best-first graph search with f(n) = g(n)+h(n).
    You need to specify the h function when you call astar_search, or
    else in your Problem subclass."""
    h = memoize(h or problem.h)
    return best_first_graph_search(problem, lambda n: n.path_cost + h(n))


def astar_tree_search(problem, h=None):
    """A* search is best-first graph search with f(n) = g(n)+h(n).
    You need to specify the h function when you call astar_search, or
    else in your Problem subclass."""
    h = h or problem.h
    return best_first_tree_search(problem, lambda n: n.path_cost + h(n))

#______________________________________________________________________________
#

# + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
#                              CODE CEMETARY
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