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Copy pathVan Emde Boas.py
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Van Emde Boas.py
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import math
class VEBTree:
def __init__(self, size):
self.universe_size = size
self.minimum = -1
self.maximum = -1
self.summary = None
self.cluster = []
if size > 2:
upper_size = math.ceil(math.sqrt(size))
lower_size = math.floor(math.sqrt(size))
self.summary = VEBTree(upper_size)
self.cluster = [VEBTree(lower_size) for _ in range(upper_size)]
def insert(self, key):
if self.minimum == -1:
self.minimum = self.maximum = key
return
if key < self.minimum:
key, self.minimum = self.minimum, key
if self.universe_size > 2:
if self.cluster[key // int(math.sqrt(self.universe_size))].minimum == -1:
self.summary.insert(key // int(math.sqrt(self.universe_size)))
self.cluster[key // int(math.sqrt(self.universe_size))].insert(key % int(math.sqrt(self.universe_size)))
if key > self.maximum:
self.maximum = key
def remove(self, key):
if self.minimum == self.maximum:
self.minimum = self.maximum = -1
return
if self.universe_size == 2:
if key == 0:
self.minimum = 1
else:
self.minimum = 0
self.maximum = self.minimum
return
if key == self.minimum:
first_cluster = self.summary.minimum
key = first_cluster * int(math.sqrt(self.universe_size)) + self.cluster[first_cluster].minimum
self.minimum = key
self.cluster[key // int(math.sqrt(self.universe_size))].remove(key % int(math.sqrt(self.universe_size)))
if self.cluster[key // int(math.sqrt(self.universe_size))].minimum == -1:
self.summary.remove(key // int(math.sqrt(self.universe_size)))
if key == self.maximum:
if self.summary.minimum == -1:
self.maximum = self.minimum
else:
last_cluster = self.summary.maximum
self.maximum = last_cluster * int(math.sqrt(self.universe_size)) + self.cluster[last_cluster].maximum
def successor(self, key):
if self.universe_size == 2:
if key == 0 and self.maximum == 1:
return 1
else:
return -1
if self.minimum != -1 and key < self.minimum:
return self.minimum
max_low = self.cluster[key // int(math.sqrt(self.universe_size))].maximum
if max_low != -1 and key % int(math.sqrt(self.universe_size)) < max_low:
offset = self.cluster[key // int(math.sqrt(self.universe_size))].successor(
key % int(math.sqrt(self.universe_size)))
return key // int(math.sqrt(self.universe_size)) * int(math.sqrt(self.universe_size)) + offset
succ_cluster = self.summary.successor(key // int(math.sqrt(self.universe_size)))
if succ_cluster == -1:
return -1
offset = self.cluster[succ_cluster].minimum
return succ_cluster * int(math.sqrt(self.universe_size)) + offset
def predecessor(self, key):
if self.universe_size == 2:
if key == 1 and self.minimum == 0:
return 0
else:
return -1
if self.maximum != -1 and key > self.maximum:
return self.maximum
min_low = self.cluster[key // int(math.sqrt(self.universe_size))].minimum
if min_low != -1 and key % int(math.sqrt(self.universe_size)) > min_low:
offset = self.cluster[key // int(math.sqrt(self.universe_size))].predecessor(
key % int(math.sqrt(self.universe_size)))
return key // int(math.sqrt(self.universe_size)) * int(math.sqrt(self.universe_size)) + offset
pred_cluster = self.summary.predecessor(key // int(math.sqrt(self.universe_size)))
if pred_cluster == -1:
if self.minimum != -1 and key > self.minimum:
return self.minimum
else:
return -1
offset = self.cluster[pred_cluster].maximum
return pred_cluster * int(math.sqrt(self.universe_size)) + offset
def contains(self, key):
if key == self.minimum or key == self.maximum:
return True
if self.universe_size == 2:
return False
return self.cluster[key // int(math.sqrt(self.universe_size))].contains(
key % int(math.sqrt(self.universe_size)))
veb_tree = VEBTree(16)
veb_tree.insert(4)
veb_tree.insert(1)
veb_tree.insert(8)
veb_tree.insert(10)
print(veb_tree.contains(4)) # Output: True
print(veb_tree.contains(5)) # Output: False
print(veb_tree.successor(4)) # Output: 8
print(veb_tree.predecessor(4)) # Output: 1
veb_tree.remove(4)
print(veb_tree.contains(4)) # Output: False