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https://github.com/TheAlgorithms/Python.git
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2eaacee7b4
* adding static type checking to basic_binary_tree.py * Add static type checking to functions with None return type * Applying code review comments * Added missing import statement * fix spaciing * "cleaned up depth_of_tree" * Add doctests and then streamline display() and is_full_binary_tree() * added static typing to lazy_segment_tree.py * added missing import statement * modified variable names for left and right elements * added static typing to lowest_common_ancestor.py * fixed formatting * modified files to meet style guidelines, edited docstrings and added some doctests * added and fixed doctests in lazy_segment_tree.py * fixed errors in doctests Co-authored-by: Christian Clauss <cclauss@me.com>
135 lines
4.6 KiB
Python
135 lines
4.6 KiB
Python
import math
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from typing import List
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class SegmentTree:
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def __init__(self, N: int) -> None:
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self.N = N
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# approximate the overall size of segment tree with array N
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self.st: List[int] = [0 for i in range(0, 4 * N)]
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# create array to store lazy update
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self.lazy: List[int] = [0 for i in range(0, 4 * N)]
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self.flag: List[int] = [0 for i in range(0, 4 * N)] # flag for lazy update
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def left(self, idx: int) -> int:
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"""
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>>> segment_tree = SegmentTree(15)
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>>> segment_tree.left(1)
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2
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>>> segment_tree.left(2)
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4
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>>> segment_tree.left(12)
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24
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"""
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return idx * 2
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def right(self, idx: int) -> int:
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"""
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>>> segment_tree = SegmentTree(15)
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>>> segment_tree.right(1)
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3
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>>> segment_tree.right(2)
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5
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>>> segment_tree.right(12)
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25
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"""
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return idx * 2 + 1
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def build(
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self, idx: int, left_element: int, right_element: int, A: List[int]
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) -> None:
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if left_element == right_element:
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self.st[idx] = A[left_element - 1]
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else:
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mid = (left_element + right_element) // 2
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self.build(self.left(idx), left_element, mid, A)
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self.build(self.right(idx), mid + 1, right_element, A)
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self.st[idx] = max(self.st[self.left(idx)], self.st[self.right(idx)])
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def update(
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self, idx: int, left_element: int, right_element: int, a: int, b: int, val: int
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) -> bool:
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"""
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update with O(lg N) (Normal segment tree without lazy update will take O(Nlg N)
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for each update)
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update(1, 1, N, a, b, v) for update val v to [a,b]
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"""
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if self.flag[idx] is True:
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self.st[idx] = self.lazy[idx]
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self.flag[idx] = False
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if left_element != right_element:
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self.lazy[self.left(idx)] = self.lazy[idx]
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self.lazy[self.right(idx)] = self.lazy[idx]
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self.flag[self.left(idx)] = True
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self.flag[self.right(idx)] = True
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if right_element < a or left_element > b:
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return True
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if left_element >= a and right_element <= b:
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self.st[idx] = val
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if left_element != right_element:
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self.lazy[self.left(idx)] = val
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self.lazy[self.right(idx)] = val
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self.flag[self.left(idx)] = True
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self.flag[self.right(idx)] = True
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return True
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mid = (left_element + right_element) // 2
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self.update(self.left(idx), left_element, mid, a, b, val)
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self.update(self.right(idx), mid + 1, right_element, a, b, val)
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self.st[idx] = max(self.st[self.left(idx)], self.st[self.right(idx)])
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return True
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# query with O(lg N)
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def query(
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self, idx: int, left_element: int, right_element: int, a: int, b: int
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) -> int:
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"""
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query(1, 1, N, a, b) for query max of [a,b]
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>>> A = [1, 2, -4, 7, 3, -5, 6, 11, -20, 9, 14, 15, 5, 2, -8]
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>>> segment_tree = SegmentTree(15)
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>>> segment_tree.build(1, 1, 15, A)
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>>> segment_tree.query(1, 1, 15, 4, 6)
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7
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>>> segment_tree.query(1, 1, 15, 7, 11)
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14
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>>> segment_tree.query(1, 1, 15, 7, 12)
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15
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"""
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if self.flag[idx] is True:
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self.st[idx] = self.lazy[idx]
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self.flag[idx] = False
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if left_element != right_element:
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self.lazy[self.left(idx)] = self.lazy[idx]
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self.lazy[self.right(idx)] = self.lazy[idx]
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self.flag[self.left(idx)] = True
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self.flag[self.right(idx)] = True
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if right_element < a or left_element > b:
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return -math.inf
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if left_element >= a and right_element <= b:
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return self.st[idx]
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mid = (left_element + right_element) // 2
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q1 = self.query(self.left(idx), left_element, mid, a, b)
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q2 = self.query(self.right(idx), mid + 1, right_element, a, b)
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return max(q1, q2)
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def show_data(self) -> None:
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showList = []
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for i in range(1, N + 1):
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showList += [self.query(1, 1, self.N, i, i)]
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print(showList)
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if __name__ == "__main__":
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A = [1, 2, -4, 7, 3, -5, 6, 11, -20, 9, 14, 15, 5, 2, -8]
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N = 15
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segt = SegmentTree(N)
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segt.build(1, 1, N, A)
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print(segt.query(1, 1, N, 4, 6))
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print(segt.query(1, 1, N, 7, 11))
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print(segt.query(1, 1, N, 7, 12))
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segt.update(1, 1, N, 1, 3, 111)
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print(segt.query(1, 1, N, 1, 15))
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segt.update(1, 1, N, 7, 8, 235)
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segt.show_data()
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