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Merged
merged 11 commits into from
Aug 12, 2022
102 changes: 102 additions & 0 deletions data_structures/binary_tree/maximum_fenwick_tree.py
Original file line number Diff line number Diff line change
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class MaxFenwickTree:
"""
Maximum Fenwick Tree

More info: https://cp-algorithms.com/data_structures/fenwick.html
---------
>>> ft = MaxFenwickTree(5)
>>> ft.query(0, 5)
0
>>> ft.update(4, 100)
>>> ft.query(0, 5)
100
>>> ft.update(4, 0)
>>> ft.update(2, 20)
>>> ft.query(0, 5)
20
>>> ft.update(4, 10)
>>> ft.query(2, 5)
10
>>> ft.query(1, 5)
20
>>> ft.update(2, 0)
>>> ft.query(0, 5)
10
>>> ft = MaxFenwickTree(10000)
>>> ft.update(255, 30)
>>> ft.query(0, 10000)
30
"""

def __init__(self, size: int) -> None:
"""
Create empty Maximum Fenwick Tree with specified size

Parameters:
size: size of Array

Returns:
None
"""
self.size = size
self.arr = [0] * size
self.tree = [0] * size

@staticmethod
def get_next(index: int) -> int:
"""
Get next index in O(1)
"""
return index + (index & -index)

@staticmethod
def get_prev(index: int) -> int:
"""
Get previous index in O(1)
"""
return index - (index & -index)

def update(self, index: int, value: int) -> None:
"""
Set index to value in O(lg^2 N)

Parameters:
index: index to update
value: value to set

Returns:
None
"""
self.arr[index] = value
while index < self.size:
self.tree[index] = max(value, self.query(self.get_prev(index), index))
index = self.get_next(index)

def query(self, left: int, right: int) -> int:
"""
Answer the query of maximum range [l, r) in O(lg^2 N)

Parameters:
left: left index of query range (inclusive)
right: right index of query range (exclusive)

Returns:
Maximum value of range [left, right)
"""
right -= 1 # Because of right is exclusive
result = 0
while left < right:
current_left = self.get_prev(right)
if left < current_left:
result = max(result, self.tree[right])
right = current_left
else:
result = max(result, self.arr[right])
right -= 1
return result


if __name__ == "__main__":
import doctest

doctest.testmod()