import sys
import inspect
import heapq, random
"""
Utility classes
Data structures useful for implementing SearchAgents
"""
class Stack:
"""
Data structure that implements a last-in-first-out (LIFO)
queue 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:
"""
Data structure that implements a first-in-first-out (FIFO)
queue 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.
"""
def __init__(self):
"""
heap: A binomial heap storing [priority,item]
lists.
dict: Dictionary storing item -> [priorirty,item]
maps so we can reach into heap for a given
item and update the priorirty and heapify
"""
self.heap = []
self.dict = {}
def push(self,item,priority):
"""
Sets the priority of the 'item' to
priority. If the 'item' is already
in the queue, then its key is changed
to the new priority, regardless if it
is higher or lower than the current
priority.
"""
if item in self.dict:
self.dict[item][0] = priority
heapq.heapify(self.heap)
else:
pair = [priority,item]
heapq.heappush(self.heap,pair)
self.dict[item] = pair
def getPriority(self,item):
"""
Get priority of 'item'. If
'item' is not in the queue returns None
"""
if not item in self.dict:
return None
return self.dict[item][0]
def pop(self):
"""
Returns lowest-priority item in priority queue, or
None if the queue is empty
"""
if self.isEmpty(): return None
(priority,item) = heapq.heappop(self.heap)
del self.dict[item]
return item
def isEmpty(self):
"""
Returns True if the queue is empty
"""
return len(self.heap) == 0
class FasterPriorityQueue:
"""
Implements a priority queue data structure. This differs from the
PriorityQueue in that it allows multiple copies of the same object,
and doesn't support getPriority or changing priority.
"""
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 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.getCount('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
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 incrementCount(self, key, count):
"""
Increases the count of key by the specified count. If
the counter does not contain the key, then the count for
key will be set to count.
>>> a = Counter()
>>> a.incrementCount('test', 1)
>>> a.getCount('hello')
0
>>> a.getCount('test')
1
"""
if key in self:
self[key] += count
else:
self[key] = count
def incrementAll(self, keys, count):
"""
Increments all elements of keys by the same count.
>>> a = Counter()
>>> a.incrementAll(['one','two', 'three'], 1)
>>> a.getCount('one')
1
>>> a.getCount('two')
1
"""
for key in keys:
self.incrementCount(key, count)
def getCount(self, key):
"""
Returns the count of key, defaulting to zero.
>>> a = Counter()
>>> print a.getCount('test')
0
>>> a['test'] = 2
>>> print a.getCount('test')
2
"""
if key in self:
return self[key]
else:
return 0
def argMax(self):
"""
Returns the key with the highest value.
"""
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())
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 __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.getCount('first')
1
"""
for key, value in y.items():
self.incrementCount(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).getCount('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).getCount('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(vector):
s = float(sum(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):
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 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 manhattanDistance( xy1, xy2 ):
"""
Returns the Manhattan distance between points xy1 and xy2
"""
return abs( xy1[0] - xy2[0] ) + abs( xy1[1] - xy2[1] )
def chooseFromDistribution( 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