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VEBTree.py
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VEBTree.py
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from math import floor, ceil, log2
from contextlib import suppress
from typing import List
class VEBTree:
# input_range must be 2^k
def __init__(self, input_range: int):
self.min = self.max = -1
self.children = ()
if input_range > 2:
average_bits = log2(input_range) / 2
small, big = 2 ** floor(average_bits), 2 ** ceil(average_bits)
self.children = [VEBTree(small) for _ in range(big)] # type: List[VEBTree]
self.child_range = small
self.cache = VEBTree(big)
def range_min(self, range_from: int = 0, range_to: int = -1) -> int:
if self.min == -1:
raise Exception
if range_from <= self.min and (self.min <= range_to or range_to == -1):
return self.min
if range_from == self.max:
return self.max
if len(self.children) == 0:
raise Exception
index_from, remainder_from = divmod(range_from, self.child_range)
if range_to == -1:
index_to, remainder_to = len(self.children) - 1, self.child_range - 1
else:
index_to, remainder_to = divmod(range_to, self.child_range)
child = self.children[index_from]
if child.min != -1:
drift = index_from * self.child_range
if index_from < index_to:
remainder_to = self.child_range - 1
if remainder_from <= child.min <= remainder_to:
return drift + child.min
if child.min < remainder_from <= child.max:
return drift + child.range_min(remainder_from, remainder_to)
if index_from < index_to:
index_min = self.cache.range_min(index_from + 1, index_to)
result = index_min * self.child_range + self.children[index_min].min
if result <= range_to:
return result
raise Exception
def range_max(self, range_from: int = 0, range_to: int = -1) -> int:
if self.min == -1:
raise Exception
if range_from <= self.max and (self.max <= range_to or range_to == -1):
return self.max
if range_to == self.min:
return self.min
if len(self.children) == 0:
raise Exception
index_from, remainder_from = divmod(range_from, self.child_range)
if range_to == -1:
index_to, remainder_to = len(self.children) - 1, self.child_range - 1
else:
index_to, remainder_to = divmod(range_to, self.child_range)
with suppress(Exception):
child = self.children[index_to]
if child.min != -1:
drift = index_to * self.child_range
if index_from < index_to:
remainder_from = 0
if remainder_from <= child.max <= remainder_to:
return drift + child.max
if child.min <= remainder_to < child.max:
return drift + child.range_max(remainder_from, remainder_to)
if index_from < index_to:
index_max = self.cache.range_max(index_from, index_to - 1)
result = index_max * self.child_range + self.children[index_max].max
if result >= range_from:
return result
# find nothing bigger than self.min
if range_from <= self.min <= range_to:
return self.min
raise Exception
def insert(self, number: int):
if self.min == -1:
self.min = self.max = number
else:
if number < self.min:
number, self.min = self.min, number
elif number > self.max:
self.max = number
if number != self.min and len(self.children) > 0:
index, remainder = divmod(number, self.child_range)
child = self.children[index]
if child.min == -1:
self.cache.insert(index)
child.min = child.max = remainder
else:
child.insert(remainder)
def delete(self, number: int):
if self.min == -1 or not self.min <= number <= self.max:
raise Exception
if self.min == self.max:
self.min = self.max = -1
elif len(self.children) == 0:
if number == 0:
self.min = self.max = 1
else:
self.min = self.max = 0
else:
if number == self.min:
number = self.min = self.cache.min * self.child_range + self.children[self.cache.min].min
index, remainder = divmod(number, self.child_range)
child = self.children[index]
if not child.min <= remainder <= child.max:
raise Exception
if child.min == child.max:
self.cache.delete(index)
child.delete(remainder)
if number == self.max:
if child.min == -1:
child_cache = self.children[self.cache.max]
if child_cache.max == -1:
self.max = self.min
else:
self.max = self.cache.max * self.child_range + child_cache.max
else:
self.max = index * self.child_range + child.max
def search(self, number: int) -> bool:
if self.min == number or self.max == number:
return True
if self.min == -1 or len(self.children) == 0:
return False
index, remainder = divmod(number, self.child_range)
return self.children[index].search(remainder)
def __iter__(self) -> int:
if self.min != -1:
yield self.min
if self.min == self.max:
return
if len(self.children) == 0:
yield self.max
else:
for i in range(self.min // self.child_range, self.max // self.child_range + 1):
child = self.children[i]
drift = i * self.child_range
for value in child:
yield drift + value
if __name__ == '__main__':
from random import randint, shuffle
def main_0():
tree = VEBTree(1024)
compare_set = set()
for i in range(1000):
random = randint(0, 1023)
compare_set.add(random)
tree.insert(random)
compare_list = list(compare_set)
tree_list = list(tree)
tree_set = set(tree_list)
print('compare_list', len(compare_list))
print('tree_list', len(tree_list))
print('tree_set', len(tree_set))
for i in compare_list:
if i not in tree_set or not tree.search(i):
print(i, 'NO')
raise Exception
else:
print(i, 'OK')
def main_1():
bucket = [0 for _ in range(16)]
sample = tuple(randint(0, 15) for _ in range(20))
for i in sample:
bucket[i] = 1
tree = VEBTree(16)
for i in sample:
tree.insert(i)
for _ in range(10000):
random_0 = randint(0, 15)
random_1 = randint(random_0, 15)
value = -1
for i in range(random_0, random_1 + 1):
if bucket[i]:
value = i
break
if value == -1:
try:
result = tree.range_min(random_0, random_1)
except Exception:
print('OK')
else:
print()
print('error result:', result)
print('from:to', random_0, random_1)
raise Exception
else:
result = tree.range_min(random_0, random_1)
print('result:', result)
print('from:to', random_0, random_1)
print('expected:', value)
assert value == result
def main_2():
bucket = [0 for _ in range(16)]
sample = tuple(randint(0, 15) for _ in range(20))
for i in sample:
bucket[i] = 1
tree = VEBTree(16)
for i in sample:
tree.insert(i)
for _ in range(10000):
random_0 = randint(0, 15)
random_1 = randint(random_0, 15)
value = -1
for i in reversed(range(random_0, random_1 + 1)):
if bucket[i]:
value = i
break
if value == -1:
try:
result = tree.range_max(random_0, random_1)
except Exception:
print('OK')
else:
print()
print('error result:', result)
print('from:to', random_0, random_1)
raise Exception
else:
result = tree.range_max(random_0, random_1)
print('result:', result)
print('from:to', random_0, random_1)
print('expected:', value)
def main_3():
for i in range(100):
sample = [randint(0, 15) for _ in range(10)]
sample = list(set(sample))
shuffle(sample)
tree = VEBTree(16)
for i in sample:
tree.insert(i)
while sample:
print()
a = list(tree)
b = list(sample)
a.sort()
b.sort()
print('a', a)
assert a == b
exist_del_value = sample.pop()
print('try to del exist', exist_del_value)
tree.delete(exist_del_value)
a = list(tree)
b = list(sample)
a.sort()
b.sort()
print('a', a)
assert a == b
null_del_value = randint(0, 15)
if null_del_value not in sample:
print('try to del null value', null_del_value)
try:
tree.delete(null_del_value)
except:
print('a', list(tree))
else:
print('MISSED EXCEPTION')
raise Exception
def main_4():
sample = [7, 8, 11, 15]
tree = VEBTree(16)
for i in sample:
tree.insert(i)
with suppress(Exception):
tree.delete(12)
tree.delete(15)
print()
main_3()