def merge_sorted_lists():
k = 10
n = 10
min_value = 0
max_value = 30
sorted_lists = generate_sorted_lists(k,n,min_value,max_value)
sorted_list = SingleLinkedList()
heap = MinHeap([], 0)
# fill in the 1st batch
for i, l in sorted_lists.items():
heap.add(IdAndValue(i, l.pop(0)))
while len(sorted_lists) > 0:
item = heap.pop()
sorted_list.append(item.get_value())
list_id = item.get_id()
if list_id in sorted_lists:
value = sorted_lists[list_id].pop(0)
if len(sorted_lists[list_id]) <= 0:
sorted_lists.pop(list_id)
heap.add(IdAndValue(list_id, value))
else:
list_id, list = sorted_lists.items()[0]
heap.add(IdAndValue(list_id, list.pop(0)))
if len(list) <= 0:
sorted_lists.pop(list_id)
while not heap.is_empty():
sorted_list.append(heap.pop())
print k*n, len(sorted_list), sorted_list
def test_empty(self):
mh = MinHeap()
self.assertTrue(mh.empty())
mh.append(1)
self.assertFalse(mh.empty())
mh.pop()
self.assertTrue(mh.empty())
def test_0():
# 0
# 1 2 3
# 4 5 6 7 8 9 10 11 12
heap = MinHeap(*range(13), n=3)
assert heap.height == 3
assert heap.parent(0) is None
assert heap.child(0, 0) == 1
assert heap.child(0, 1) == 2
assert heap.child(0, 2) == 3
assert heap.first(0) == 1
assert heap.last(0) == 3
assert heap.parent(1) == 0
assert heap.child(1, 0) == 4
assert heap.child(1, 1) == 5
assert heap.child(1, 2) == 6
assert heap.first(1) == 4
assert heap.last(1) == 6
assert heap.parent(2) == 0
assert heap.child(2, 0) == 7
assert heap.child(2, 1) == 8
assert heap.child(2, 2) == 9
assert heap.first(2) == 7
assert heap.last(2) == 9
assert heap.parent(3) == 0
assert heap.child(3, 0) == 10
assert heap.child(3, 1) == 11
assert heap.child(3, 2) == 12
assert heap.first(3) == 10
assert heap.last(3) == 12
assert heap.parent(4) == 1
assert heap.parent(5) == 1
assert heap.parent(6) == 1
assert heap.parent(7) == 2
assert heap.parent(8) == 2
assert heap.parent(9) == 2
assert heap.parent(10) == 3
assert heap.parent(11) == 3
assert heap.parent(12) == 3
assert heap.is_valid()
assert tuple(heap.walk_up(4)) == ((1, 4), (0, 1))
assert tuple(heap.walk_up(5)) == ((1, 5), (0, 1))
assert tuple(heap.walk_up(6)) == ((1, 6), (0, 1))
assert tuple(heap.walk_up(7)) == ((2, 7), (0, 2))
assert tuple(heap.walk_up(12)) == ((3, 12), (0, 3))
assert tuple(heap.walk_down()) == ((0, 1), (1, 4))
heap.push(14)
assert heap.is_valid()
heap.push(6)
assert heap.is_valid()
assert heap.pop() == 0
assert heap.is_valid()
assert heap.pop() == 1
assert heap.is_valid()
assert heap.pop() == 2
assert heap.is_valid()
def test_len(self):
mh = MinHeap()
self.assertTrue(len(mh) == 0)
mh.append(1)
self.assertTrue(len(mh) == 1)
mh.append(1)
self.assertTrue(len(mh) == 2)
mh.pop()
self.assertTrue(len(mh) == 1)
mh.pop()
self.assertTrue(len(mh) == 0)
class HuffmanEncoder:
frequencies = {}
def __init__(self, frequencies):
self.frequencies = frequencies
self.nodes = MinHeap()
def to_nodes(self):
for i in self.frequencies.keys():
self.nodes.insert(Node(self.frequencies[i], None, None, i))
def generate_coding(self):
d = {}
e = {}
tree = self.construct_huffman_tree()
self.encode_huffman_tree_r(tree, d, e)
return d, e
def encode_huffman_tree_r(self, node, d, e, val=''):
if node.right is None and node.left is None:
d[node.character] = val
e[val] = node.character
if node.left is not None:
self.encode_huffman_tree_r(node.left, d, e, val + '0')
if node.right is not None:
self.encode_huffman_tree_r(node.right, d, e, val + '1')
return d, e
def construct_huffman_tree(self):
self.to_nodes()
t = Node(0)
while self.nodes.length() != 1:
left = self.nodes.pop()
right = self.nodes.pop()
if right.character is not None and left.character is None:
t = Node(left.value + right.value, right, left)
else:
t = Node(left.value + right.value, left, right)
self.nodes.insert(t)
return t
def encode(self, symbols=None): """ Huffman-encoding symbols symbols: [(w1, s1), (w2, s2), ..., (wn, sn)] where wi, si are ith symbol's weight/freq """ pq = MinHeap() symbols = copy.deepcopy(symbols) symbols = [(s[0], HuffmanNode(value=s[1], left=None, right=None)) for s in symbols] # initialize symbols to nodes pq.heapify(symbols) while len(symbols) > 1: l, r = pq.pop(symbols), pq.pop(symbols) lw, ls, rw, rs = l[0], l[1], r[0], r[1] # left weight, left symbol, right wreight, right symbol parent = HuffmanNode(value=None, left=ls, right=rs) pq.add(heap=symbols, item=(lw+rw, parent)) self._root = pq.pop(symbols)[1] # tree is complete, pop root node self._symbol2codes() # create symbol: code dictionary self._maxDepth = len(max(self._codes.values(), key=len)) # max depth self._minDepth = len(min(self._codes.values(), key=len)) # min depth self._avgDepth = sum([len(d) for d in self._codes.values()]) / len(self._codes) # mean depth
def test_min_heap_sorting(self):
# seed for consistant testing and reproductibility
for seed in xrange(10):
random.seed(seed)
heap = MinHeap()
shuffled_nums = [int(random.random() * 20 - 10) for _ in xrange(1000)]
nums = sorted(shuffled_nums)
for n in shuffled_nums:
heap.insert(n)
for n in nums:
self.assertEqual(n, heap.pop())
heap.heapify(shuffled_nums)
for n in nums:
self.assertEqual(n, heap.pop())
def test_min(self):
mh = MinHeap()
with self.assertRaises(IndexError):
mh.min()
mh.append(1)
self.assertEqual(1, mh.min())
self.assertEqual(1, mh.min())
mh.append(1)
self.assertEqual(1, mh.min())
mh.pop()
self.assertEqual(1, mh.min())
mh.pop()
with self.assertRaises(IndexError):
mh.min()
mh.append(3)
self.assertEqual(3, mh.min())
mh.append(1)
self.assertEqual(1, mh.min())
mh.pop()
self.assertEqual(3, mh.min())
def sort(array):
heap = MinHeap()
for i in array:
heap.push(i)
out = []
while True:
try:
out.append(heap.pop())
except:
break
return out
class PriorityQueue: def __init__(self): self.heap = MinHeap() def enqueue(self, priority, item): self.heap.push(PriorityQueueItem(priority, item)) def dequeue(self): try: return self.heap.pop().value except: return None
def test_pop(self):
mh = MinHeap()
with self.assertRaises(IndexError):
mh.pop()
mh.append(1)
self.assertEqual(1, mh.pop())
with self.assertRaises(IndexError):
mh.pop()
mh.append(9)
mh.append(6)
mh.append(5)
mh.append(3)
self.assertEqual(3, mh.pop())
self.assertEqual(5, mh.pop())
self.assertEqual(6, mh.pop())
self.assertEqual(9, mh.pop())
with self.assertRaises(IndexError):
mh.pop()
def algorithm(self, graph): edges = sorted(graph.E, key=self.edge_wt_sort) hp = MinHeap() hp.insert(edges[0]) while(not hp.empty()): edge = hp.pop() graph.remove_edge(edge) if(edge.v1 in self.tree.V() \ and edge.v2 in self.tree.V()): continue self.tree.add_edge(edge) self.min_weight += edge.wt neighborhood = graph.edges(edge.v1) + graph.edges(edge.v2) hp.insert_all(neighborhood)
class SinglePercentileTracker(object):
''' A class that tracks a single percentile'''
def __init__(self, percentile):
self.percentile_tracked = percentile
self.lheap = MaxHeap()
self.rheap = MinHeap()
self.size = 0
self.percentile = None
def add(self, num):
# An addition to a list is O(log n) since look up is O(1)
# insertions are O(log n), and worst case pop is O(log n)
# and everything is done a constant number of times. In these
# cases, n is the size of the larger of the two heaps
self.size += 1
n = (self.percentile_tracked / 100.0) * (self.size + 1)
# The left heap should always be the floor of n, so we have the
# floor(n)th ranked node as the max node in the left heap, and the
# min node of the right heap will be the nth+1 ranked node.
lsize = int(math.floor(n))
# Push the num on to the proper heap
if num > self.percentile:
self.rheap.push(num)
else:
self.lheap.push(num)
# if the left heap isn't the right size, push or pop the nodes
# to make sure it is.
if self.lheap.size() < lsize:
self.lheap.push(self.rheap.pop())
elif self.lheap.size() > lsize:
self.rheap.push(self.lheap.pop())
# Take the integer part of n and grab the nth and nth+1
# ranked nodes. Then take the nth node as the base
# and add the fractional part of n * nth+1 ranked node to get a
# weighted value between the two. This is your percentile.
ir = int(n)
fr = n - ir
low_data = self.lheap.get(0)
high_data = self.rheap.get(0)
self.percentile = fr * (high_data - low_data) + low_data
def add_list(self, lst):
# Add list is O(k * log n) where k is len(lst) and n is
# the size of the larger of the two heaps
for l in lst:
self.add(l)
class HeapMedian:
''' solution using min-, max- heaps '''
def __init__(self):
self.upper = MinHeap()
self.lower = MaxHeap()
def add(self, i):
assert self.lower.size() >= self.upper.size()
if self.lower.size()==0 or\
i <= self.lower.peek():
self.lower.push(i)
else:
self.upper.push(i)
if self.lower.size() < self.upper.size():
self.lower.push(self.upper.pop())
elif self.lower.size() > self.upper.size()+1:
self.upper.push(self.lower.pop())
def get(self):
return self.lower.peek()
from heap import MinHeap
from random import randint
from time import clock
# TODO use my mergesort for comparison?
fill = []
for i in range(30):
x = randint(0,10000)
fill.append((x,x))
test = MinHeap(fill)
print(test.heap)
res = []
for i in range(test.size):
res.append(test.pop()[1])
print(test.heap)
fill.sort(key=lambda tup : tup[0])
res2 = list(map(lambda x : x[0], fill))
print("Expect:",res2)
print("Get: ",res)
print("Now for excitement!")
heapElapsed = 0
listElapsed = 0
err = False
for i in range(10000):
fill = []
for i in range(100):
x = randint(0,10000)
def find_shortest(self):
return len(self.encoding)
def find_longest(self):
return len(self.encoding)
with open("huffman.txt", "r") as infile:
infile = [int(i) for i in infile.readlines()[1:]]
infile = list(enumerate(infile))
##infile = [(0,1), (1,5), (2,7), (3,2), (4,3)]
min_heap = MinHeap()
for i in infile:
min_heap.insert(i[1], HCLeafNode(i[0], i[1]))
#do until only one node left, the root
while min_heap.size() > 1:
#get two smallest nodes
small = min_heap.pop().get_data()[0]
small.add_prefix("0")
two_small = min_heap.pop().get_data()[0]
two_small.add_prefix("1")
#merge them together
merged = HCMiddleNode(small, two_small)
min_heap.insert(merged.get_frequency(), merged)
tree = min_heap.pop().get_data()[0]
minheap = MinHeap()
start_vertex = 1
#store shortest distances, by default is infinite length to reach
shortest_distance = {start_vertex: 0}
added_vertices = [1]
curr = start_vertex
curr_vertex = g.get_graph()[curr]
for neighbour, weight in curr_vertex.get_neighbours().items():
#key is the weight of getting to each vertex in the unexplored area
#first vertex in data is the source and second is the destination
minheap.insert(weight, curr, neighbour)
while not minheap.is_empty():
popped = minheap.pop()
curr = popped.get_data()[1]
if curr in shortest_distance:
#just delete and move on since this vertex has already been seen
continue
#the vertex from the searched that points to the new element
curr_parent = popped.get_data()[0]
#add current vertex to shortest distance so the distance has been set
shortest_distance[curr] = popped.get_key()
for neighbour, weight in g.graph[curr].get_neighbours().items():
#popping from min heap and ignoring those that were seen before, so the shortest paths will keep coming up first, so no need to delete
#the check if curr in shortest distance also ensures that our duplicate entries for same vertex will be ignored since they would
#have previously been inserted into minheap
#for below, new distance to each neighbour from the current would be the shortest distance to current + weight of edge between them
minheap.insert(shortest_distance[curr] + weight, curr, neighbour)
