1 class segTree: 2 def __init__(self,nums): 3 n = len(nums) 4 for i in range(1,31): 5 low,high = 2 ** (i-1),2 ** i 6 if n > low and n < high: 7 fillzero = high - n 8 break 9 self.sTree = [0] * 2 * n 10 for i in range(n,2*n): 11 self.sTree[i] = nums[i-n] 12 for i in range(n-1,0,-1): 13 self.sTree[i] = self.sTree[2*i] + self.sTree[2*i+1] 14 15 class NumArray: 16 def __init__(self, nums: 'List[int]'): 17 self.segmentTree = segTree(nums) 18 self.n = len(nums) 19 20 21 def update(self, i: int, val: int) -> None: 22 i = i + self.n 23 self.segmentTree.sTree[i] = val 24 while i > 1: 25 i = i // 2 26 self.segmentTree.sTree[i] = self.segmentTree.sTree[2*i] + self.segmentTree.sTree[2*i+1] 27 28 def sumRange(self, i: int, j: int) -> int: 29 left = i + self.n 30 right = j + self.n + 1 31 sums = 0 32 while left < right: 33 if left % 2 == 1: 34 sums += self.segmentTree.sTree[left] 35 left += 1 36 if right % 2 == 1: 37 right -= 1 38 sums += self.segmentTree.sTree[right] 39 left //= 2 40 right //= 2 41 return sums
算法思路：SegmentTree(线段树)。线段树是完全二叉树(不一定必须是满二叉树)。
线段树，查询操作时间复杂度O(logn)，更新操作时间复杂度O(logn)。
