| 4 | |
| 5 | |
| 6 | class SegmentTree: |
| 7 | def __init__(self, size: int) -> None: |
| 8 | self.size = size |
| 9 | # approximate the overall size of segment tree with given value |
| 10 | self.segment_tree = [0 for i in range(4 * size)] |
| 11 | # create array to store lazy update |
| 12 | self.lazy = [0 for i in range(4 * size)] |
| 13 | self.flag = [0 for i in range(4 * size)] # flag for lazy update |
| 14 | |
| 15 | def left(self, idx: int) -> int: |
| 16 | """ |
| 17 | >>> segment_tree = SegmentTree(15) |
| 18 | >>> segment_tree.left(1) |
| 19 | 2 |
| 20 | >>> segment_tree.left(2) |
| 21 | 4 |
| 22 | >>> segment_tree.left(12) |
| 23 | 24 |
| 24 | """ |
| 25 | return idx * 2 |
| 26 | |
| 27 | def right(self, idx: int) -> int: |
| 28 | """ |
| 29 | >>> segment_tree = SegmentTree(15) |
| 30 | >>> segment_tree.right(1) |
| 31 | 3 |
| 32 | >>> segment_tree.right(2) |
| 33 | 5 |
| 34 | >>> segment_tree.right(12) |
| 35 | 25 |
| 36 | """ |
| 37 | return idx * 2 + 1 |
| 38 | |
| 39 | def build( |
| 40 | self, idx: int, left_element: int, right_element: int, a: list[int] |
| 41 | ) -> None: |
| 42 | if left_element == right_element: |
| 43 | self.segment_tree[idx] = a[left_element - 1] |
| 44 | else: |
| 45 | mid = (left_element + right_element) // 2 |
| 46 | self.build(self.left(idx), left_element, mid, a) |
| 47 | self.build(self.right(idx), mid + 1, right_element, a) |
| 48 | self.segment_tree[idx] = max( |
| 49 | self.segment_tree[self.left(idx)], self.segment_tree[self.right(idx)] |
| 50 | ) |
| 51 | |
| 52 | def update( |
| 53 | self, idx: int, left_element: int, right_element: int, a: int, b: int, val: int |
| 54 | ) -> bool: |
| 55 | """ |
| 56 | update with O(lg n) (Normal segment tree without lazy update will take O(nlg n) |
| 57 | for each update) |
| 58 | |
| 59 | update(1, 1, size, a, b, v) for update val v to [a,b] |
| 60 | """ |
| 61 | if self.flag[idx] is True: |
| 62 | self.segment_tree[idx] = self.lazy[idx] |
| 63 | self.flag[idx] = False |