leetcode307

class segTree:
    def __init__(self,nums):
        n = len(nums)
        for i in range(1,31):
            low,high = 2 ** (i-1),2 ** i
            if n > low and n < high:
                fillzero = high - n
                break
        self.sTree = [0] * 2 * n
        for i in range(n,2*n):
            self.sTree[i] = nums[i-n]
        for i in range(n-1,0,-1):
            self.sTree[i] = self.sTree[2*i] + self.sTree[2*i+1]
            
class NumArray:
    def __init__(self, nums: 'List[int]'):
        self.segmentTree = segTree(nums)
        self.n = len(nums)
        

    def update(self, i: int, val: int) -> None:
        i = i + self.n
        self.segmentTree.sTree[i] = val
        while i > 1:
            i = i // 2
            self.segmentTree.sTree[i] = self.segmentTree.sTree[2*i] + self.segmentTree.sTree[2*i+1]

    def sumRange(self, i: int, j: int) -> int:
        left = i + self.n
        right = j + self.n + 1
        sums = 0
        while left < right:
            if left % 2 == 1:
                sums += self.segmentTree.sTree[left]
                left += 1
            if right % 2 == 1:
                right -= 1
                sums += self.segmentTree.sTree[right]
            left //= 2
            right //= 2
        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)。