### util.py (original)

    # util.py
    # -------
    # Licensing Information: Please do not distribute or publish solutions to this
    # project. You are free to use and extend these projects for educational
    # purposes. The Pacman AI projects were developed at UC Berkeley, primarily by
    # John DeNero (denero@cs.berkeley.edu) and Dan Klein (klein@cs.berkeley.edu).
    # For more info, see http://inst.eecs.berkeley.edu/~cs188/sp09/pacman.html

    import sys
    import inspect
    import heapq, random

    """
     Data structures useful for implementing SearchAgents
    """

    class Stack:
        "A container with a last-in-first-out (LIFO) queuing policy."
        def __init__(self):
            self.list = []

        def push(self,item):
            "Push 'item' onto the stack"
            self.list.append(item)

        def pop(self):
            "Pop the most recently pushed item from the stack"
            return self.list.pop()

        def isEmpty(self):
            "Returns true if the stack is empty"
            return len(self.list) == 0

    class Queue:
        "A container with a first-in-first-out (FIFO) queuing policy."
        def __init__(self):
            self.list = []

        def push(self,item):
            "Enqueue the 'item' into the queue"
            self.list.insert(0,item)

        def pop(self):
            """
              Dequeue the earliest enqueued item still in the queue. This
              operation removes the item from the queue.
            """
            return self.list.pop()

        def isEmpty(self):
            "Returns true if the queue is empty"
            return len(self.list) == 0

    class PriorityQueue:
        """
          Implements a priority queue data structure. Each inserted item
          has a priority associated with it and the client is usually interested
          in quick retrieval of the lowest-priority item in the queue. This
          data structure allows O(1) access to the lowest-priority item.

          Note that this PriorityQueue does not allow you to change the priority
          of an item.  However, you may insert the same item multiple times with
          different priorities.
        """
        def  __init__(self):
            self.heap = []

        def push(self, item, priority):
            pair = (priority,item)
            heapq.heappush(self.heap,pair)

        def pop(self):
            (priority,item) = heapq.heappop(self.heap)
            return item

        def isEmpty(self):
            return len(self.heap) == 0

    class PriorityQueueWithFunction(PriorityQueue):
        """
        Implements a priority queue with the same push/pop signature of the
        Queue and the Stack classes. This is designed for drop-in replacement for
        those two classes. The caller has to provide a priority function, which
        extracts each item's priority.
        """
        def  __init__(self, priorityFunction):
            "priorityFunction (item) -> priority"
            self.priorityFunction = priorityFunction      # store the priority function
            PriorityQueue.__init__(self)        # super-class initializer

        def push(self, item):
            "Adds an item to the queue with priority from the priority function"
            PriorityQueue.push(self, item, self.priorityFunction(item))

    def manhattanDistance( xy1, xy2 ):
        "Returns the Manhattan distance between points xy1 and xy2"
        return abs( xy1[0] - xy2[0] ) + abs( xy1[1] - xy2[1] )

    """
      Data structures and functions useful for various course projects

      The search project should not need anything below this line.
    """

    class Counter(dict):
        """
        A counter keeps track of counts for a set of keys.

        The counter class is an extension of the standard python
        dictionary type.  It is specialized to have number values
        (integers or floats), and includes a handful of additional
        functions to ease the task of counting data.  In particular,
        all keys are defaulted to have value 0.  Using a dictionary:

        a = {}
        print a['test']

        would give an error, while the Counter class analogue:

        >>> a = Counter()
        >>> print a['test']
        0

        returns the default 0 value. Note that to reference a key
        that you know is contained in the counter,
        you can still use the dictionary syntax:

        >>> a = Counter()
        >>> a['test'] = 2
        >>> print a['test']
        2

        This is very useful for counting things without initializing their counts,
        see for example:

        >>> a['blah'] += 1
        >>> print a['blah']
        1

        The counter also includes additional functionality useful in implementing
        the classifiers for this assignment.  Two counters can be added,
        subtracted or multiplied together.  See below for details.  They can
        also be normalized and their total count and arg max can be extracted.
        """
        def __getitem__(self, idx):
            self.setdefault(idx, 0)
            return dict.__getitem__(self, idx)

        def incrementAll(self, keys, count):
            """
            Increments all elements of keys by the same count.

            >>> a = Counter()
            >>> a.incrementAll(['one','two', 'three'], 1)
            >>> a['one']
            1
            >>> a['two']
            1
            """
            for key in keys:
                self[key] += count

        def argMax(self):
            """
            Returns the key with the highest value.
            """
            if len(self.keys()) == 0: return None
            all = self.items()
            values = [x[1] for x in all]
            maxIndex = values.index(max(values))
            return all[maxIndex][0]

        def sortedKeys(self):
            """
            Returns a list of keys sorted by their values.  Keys
            with the highest values will appear first.

            >>> a = Counter()
            >>> a['first'] = -2
            >>> a['second'] = 4
            >>> a['third'] = 1
            >>> a.sortedKeys()
            ['second', 'third', 'first']
            """
            sortedItems = self.items()
            compare = lambda x, y:  sign(y[1] - x[1])
            sortedItems.sort(cmp=compare)
            return [x[0] for x in sortedItems]

        def totalCount(self):
            """
            Returns the sum of counts for all keys.
            """
            return sum(self.values())

        def normalize(self):
            """
            Edits the counter such that the total count of all
            keys sums to 1.  The ratio of counts for all keys
            will remain the same. Note that normalizing an empty
            Counter will result in an error.
            """
            total = float(self.totalCount())
            if total == 0: return
            for key in self.keys():
                self[key] = self[key] / total

        def divideAll(self, divisor):
            """
            Divides all counts by divisor
            """
            divisor = float(divisor)
            for key in self:
                self[key] /= divisor

        def copy(self):
            """
            Returns a copy of the counter
            """
            return Counter(dict.copy(self))

        def __mul__(self, y ):
            """
            Multiplying two counters gives the dot product of their vectors where
            each unique label is a vector element.

            >>> a = Counter()
            >>> b = Counter()
            >>> a['first'] = -2
            >>> a['second'] = 4
            >>> b['first'] = 3
            >>> b['second'] = 5
            >>> a['third'] = 1.5
            >>> a['fourth'] = 2.5
            >>> a * b
            14
            """
            sum = 0
            x = self
            if len(x) > len(y):
                x,y = y,x
            for key in x:
                if key not in y:
                    continue
                sum += x[key] * y[key]
            return sum

        def __radd__(self, y):
            """
            Adding another counter to a counter increments the current counter
            by the values stored in the second counter.

            >>> a = Counter()
            >>> b = Counter()
            >>> a['first'] = -2
            >>> a['second'] = 4
            >>> b['first'] = 3
            >>> b['third'] = 1
            >>> a += b
            >>> a['first']
            1
            """
            for key, value in y.items():
                self[key] += value

        def __add__( self, y ):
            """
            Adding two counters gives a counter with the union of all keys and
            counts of the second added to counts of the first.

            >>> a = Counter()
            >>> b = Counter()
            >>> a['first'] = -2
            >>> a['second'] = 4
            >>> b['first'] = 3
            >>> b['third'] = 1
            >>> (a + b)['first']
            1
            """
            addend = Counter()
            for key in self:
                if key in y:
                    addend[key] = self[key] + y[key]
                else:
                    addend[key] = self[key]
            for key in y:
                if key in self:
                    continue
                addend[key] = y[key]
            return addend

        def __sub__( self, y ):
            """
            Subtracting a counter from another gives a counter with the union of all keys and
            counts of the second subtracted from counts of the first.

            >>> a = Counter()
            >>> b = Counter()
            >>> a['first'] = -2
            >>> a['second'] = 4
            >>> b['first'] = 3
            >>> b['third'] = 1
            >>> (a - b)['first']
            -5
            """
            addend = Counter()
            for key in self:
                if key in y:
                    addend[key] = self[key] - y[key]
                else:
                    addend[key] = self[key]
            for key in y:
                if key in self:
                    continue
                addend[key] = -1 * y[key]
            return addend

    def raiseNotDefined():
        print "Method not implemented: %s" % inspect.stack()[1][3]
        sys.exit(1)

    def normalize(vectorOrCounter):
        """
        normalize a vector or counter by dividing each value by the sum of all values
        """
        normalizedCounter = Counter()
        if type(vectorOrCounter) == type(normalizedCounter):
            counter = vectorOrCounter
            total = float(counter.totalCount())
            if total == 0: return counter
            for key in counter.keys():
                value = counter[key]
                normalizedCounter[key] = value / total
            return normalizedCounter
        else:
            vector = vectorOrCounter
            s = float(sum(vector))
            if s == 0: return vector
            return [el / s for el in vector]

    def nSample(distribution, values, n):
        if sum(distribution) != 1:
            distribution = normalize(distribution)
        rand = [random.random() for i in range(n)]
        rand.sort()
        samples = []
        samplePos, distPos, cdf = 0,0, distribution[0]
        while samplePos < n:
            if rand[samplePos] < cdf:
                samplePos += 1
                samples.append(values[distPos])
            else:
                distPos += 1
                cdf += distribution[distPos]
        return samples

    def sample(distribution, values = None):
        if type(distribution) == Counter:
            items = distribution.items()
            distribution = [i[1] for i in items]
            values = [i[0] for i in items]
        if sum(distribution) != 1:
            distribution = normalize(distribution)
        choice = random.random()
        i, total= 0, distribution[0]
        while choice > total:
            i += 1
            total += distribution[i]
        return values[i]

    def sampleFromCounter(ctr):
        items = ctr.items()
        return sample([v for k,v in items], [k for k,v in items])

    def getProbability(value, distribution, values):
        """
          Gives the probability of a value under a discrete distribution
          defined by (distributions, values).
        """
        total = 0.0
        for prob, val in zip(distribution, values):
            if val == value:
                total += prob
        return total

    def flipCoin( p ):
        r = random.random()
        return r < p

    def chooseFromDistribution( distribution ):
        "Takes either a counter or a list of (prob, key) pairs and samples"
        if type(distribution) == dict or type(distribution) == Counter:
            return sample(distribution)
        r = random.random()
        base = 0.0
        for prob, element in distribution:
            base += prob
            if r <= base: return element

    def nearestPoint( pos ):
        """
        Finds the nearest grid point to a position (discretizes).
        """
        ( current_row, current_col ) = pos

        grid_row = int( current_row + 0.5 )
        grid_col = int( current_col + 0.5 )
        return ( grid_row, grid_col )

    def sign( x ):
        """
        Returns 1 or -1 depending on the sign of x
        """
        if( x >= 0 ):
            return 1
        else:
            return -1

    def arrayInvert(array):
        """
        Inverts a matrix stored as a list of lists.
        """
        result = [[] for i in array]
        for outer in array:
            for inner in range(len(outer)):
                result[inner].append(outer[inner])
        return result

    def matrixAsList( matrix, value = True ):
        """
        Turns a matrix into a list of coordinates matching the specified value
        """
        rows, cols = len( matrix ), len( matrix[0] )
        cells = []
        for row in range( rows ):
            for col in range( cols ):
                if matrix[row][col] == value:
                    cells.append( ( row, col ) )
        return cells

    def lookup(name, namespace):
        """
        Get a method or class from any imported module from its name.
        Usage: lookup(functionName, globals())
        """
        dots = name.count('.')
        if dots > 0:
            moduleName, objName = '.'.join(name.split('.')[:-1]), name.split('.')[-1]
            module = __import__(moduleName)
            return getattr(module, objName)
        else:
            modules = [obj for obj in namespace.values() if str(type(obj)) == "<type 'module'>"]
            options = [getattr(module, name) for module in modules if name in dir(module)]
            options += [obj[1] for obj in namespace.items() if obj[0] == name ]
            if len(options) == 1: return options[0]
            if len(options) > 1: raise Exception, 'Name conflict for %s'
            raise Exception, '%s not found as a method or class' % name

    def pause():
        """
        Pauses the output stream awaiting user feedback.
        """
        print "<Press enter/return to continue>"
        raw_input()

    ## code to handle timeouts
    import signal
    class TimeoutFunctionException(Exception):
        """Exception to raise on a timeout"""
        pass

    class TimeoutFunction:

        def __init__(self, function, timeout):
            "timeout must be at least 1 second. WHY??"
            self.timeout = timeout
            self.function = function

        def handle_timeout(self, signum, frame):
            raise TimeoutFunctionException()

        def __call__(self, *args):
            if not 'SIGALRM' in dir(signal):
                return self.function(*args)
            old = signal.signal(signal.SIGALRM, self.handle_timeout)
            signal.alarm(self.timeout)
            try:
                result = self.function(*args)
            finally:
                signal.signal(signal.SIGALRM, old)
            signal.alarm(0)
            return result