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115 lines
2.7 KiB
Python
115 lines
2.7 KiB
Python
class MaxFenwickTree:
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"""
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Maximum Fenwick Tree
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More info: https://cp-algorithms.com/data_structures/fenwick.html
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---------
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>>> ft = MaxFenwickTree(5)
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>>> ft.query(0, 5)
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0
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>>> ft.update(4, 100)
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>>> ft.query(0, 5)
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100
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>>> ft.update(4, 0)
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>>> ft.update(2, 20)
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>>> ft.query(0, 5)
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20
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>>> ft.update(4, 10)
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>>> ft.query(2, 5)
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20
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>>> ft.query(1, 5)
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20
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>>> ft.update(2, 0)
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>>> ft.query(0, 5)
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10
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>>> ft = MaxFenwickTree(10000)
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>>> ft.update(255, 30)
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>>> ft.query(0, 10000)
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30
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>>> ft = MaxFenwickTree(6)
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>>> ft.update(5, 1)
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>>> ft.query(5, 6)
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1
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>>> ft = MaxFenwickTree(6)
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>>> ft.update(0, 1000)
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>>> ft.query(0, 1)
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1000
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"""
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def __init__(self, size: int) -> None:
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"""
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Create empty Maximum Fenwick Tree with specified size
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Parameters:
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size: size of Array
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Returns:
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None
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"""
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self.size = size
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self.arr = [0] * size
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self.tree = [0] * size
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@staticmethod
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def get_next(index: int) -> int:
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"""
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Get next index in O(1)
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"""
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return index | (index + 1)
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@staticmethod
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def get_prev(index: int) -> int:
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"""
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Get previous index in O(1)
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"""
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return (index & (index + 1)) - 1
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def update(self, index: int, value: int) -> None:
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"""
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Set index to value in O(lg^2 N)
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Parameters:
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index: index to update
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value: value to set
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Returns:
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None
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"""
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self.arr[index] = value
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while index < self.size:
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current_left_border = self.get_prev(index) + 1
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if current_left_border == index:
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self.tree[index] = value
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else:
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self.tree[index] = max(value, current_left_border, index)
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index = self.get_next(index)
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def query(self, left: int, right: int) -> int:
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"""
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Answer the query of maximum range [l, r) in O(lg^2 N)
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Parameters:
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left: left index of query range (inclusive)
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right: right index of query range (exclusive)
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Returns:
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Maximum value of range [left, right)
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"""
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right -= 1 # Because of right is exclusive
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result = 0
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while left <= right:
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current_left = self.get_prev(right)
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if left <= current_left:
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result = max(result, self.tree[right])
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right = current_left
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else:
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result = max(result, self.arr[right])
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right -= 1
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return result
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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