forked from TheAlgorithms/Python
-
Notifications
You must be signed in to change notification settings - Fork 0
Expand file tree
/
Copy pathlazy_segment_tree.py
More file actions
136 lines (123 loc) · 4.73 KB
/
lazy_segment_tree.py
File metadata and controls
136 lines (123 loc) · 4.73 KB
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
from __future__ import annotations
import math
class SegmentTree:
def __init__(self, size: int) -> None:
self.size = size
# approximate the overall size of segment tree with given value
self.segment_tree = [0 for i in range(0, 4 * size)]
# create array to store lazy update
self.lazy = [0 for i in range(0, 4 * size)]
self.flag = [0 for i in range(0, 4 * size)] # flag for lazy update
def left(self, idx: int) -> int:
"""
>>> segment_tree = SegmentTree(15)
>>> segment_tree.left(1)
2
>>> segment_tree.left(2)
4
>>> segment_tree.left(12)
24
"""
return idx * 2
def right(self, idx: int) -> int:
"""
>>> segment_tree = SegmentTree(15)
>>> segment_tree.right(1)
3
>>> segment_tree.right(2)
5
>>> segment_tree.right(12)
25
"""
return idx * 2 + 1
def build(
self, idx: int, left_element: int, right_element: int, A: list[int]
) -> None:
if left_element == right_element:
self.segment_tree[idx] = A[left_element - 1]
else:
mid = (left_element + right_element) // 2
self.build(self.left(idx), left_element, mid, A)
self.build(self.right(idx), mid + 1, right_element, A)
self.segment_tree[idx] = max(
self.segment_tree[self.left(idx)], self.segment_tree[self.right(idx)]
)
def update(
self, idx: int, left_element: int, right_element: int, a: int, b: int, val: int
) -> bool:
"""
update with O(lg n) (Normal segment tree without lazy update will take O(nlg n)
for each update)
update(1, 1, size, a, b, v) for update val v to [a,b]
"""
if self.flag[idx] is True:
self.segment_tree[idx] = self.lazy[idx]
self.flag[idx] = False
if left_element != right_element:
self.lazy[self.left(idx)] = self.lazy[idx]
self.lazy[self.right(idx)] = self.lazy[idx]
self.flag[self.left(idx)] = True
self.flag[self.right(idx)] = True
if right_element < a or left_element > b:
return True
if left_element >= a and right_element <= b:
self.segment_tree[idx] = val
if left_element != right_element:
self.lazy[self.left(idx)] = val
self.lazy[self.right(idx)] = val
self.flag[self.left(idx)] = True
self.flag[self.right(idx)] = True
return True
mid = (left_element + right_element) // 2
self.update(self.left(idx), left_element, mid, a, b, val)
self.update(self.right(idx), mid + 1, right_element, a, b, val)
self.segment_tree[idx] = max(
self.segment_tree[self.left(idx)], self.segment_tree[self.right(idx)]
)
return True
# query with O(lg n)
def query(
self, idx: int, left_element: int, right_element: int, a: int, b: int
) -> int:
"""
query(1, 1, size, a, b) for query max of [a,b]
>>> A = [1, 2, -4, 7, 3, -5, 6, 11, -20, 9, 14, 15, 5, 2, -8]
>>> segment_tree = SegmentTree(15)
>>> segment_tree.build(1, 1, 15, A)
>>> segment_tree.query(1, 1, 15, 4, 6)
7
>>> segment_tree.query(1, 1, 15, 7, 11)
14
>>> segment_tree.query(1, 1, 15, 7, 12)
15
"""
if self.flag[idx] is True:
self.segment_tree[idx] = self.lazy[idx]
self.flag[idx] = False
if left_element != right_element:
self.lazy[self.left(idx)] = self.lazy[idx]
self.lazy[self.right(idx)] = self.lazy[idx]
self.flag[self.left(idx)] = True
self.flag[self.right(idx)] = True
if right_element < a or left_element > b:
return -math.inf
if left_element >= a and right_element <= b:
return self.segment_tree[idx]
mid = (left_element + right_element) // 2
q1 = self.query(self.left(idx), left_element, mid, a, b)
q2 = self.query(self.right(idx), mid + 1, right_element, a, b)
return max(q1, q2)
def __str__(self) -> None:
return [self.query(1, 1, self.size, i, i) for i in range(1, self.size + 1)]
if __name__ == "__main__":
A = [1, 2, -4, 7, 3, -5, 6, 11, -20, 9, 14, 15, 5, 2, -8]
size = 15
segt = SegmentTree(size)
segt.build(1, 1, size, A)
print(segt.query(1, 1, size, 4, 6))
print(segt.query(1, 1, size, 7, 11))
print(segt.query(1, 1, size, 7, 12))
segt.update(1, 1, size, 1, 3, 111)
print(segt.query(1, 1, size, 1, 15))
segt.update(1, 1, size, 7, 8, 235)
print(segt)