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 | float: """ 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) -> str: return str([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)