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