树状数组b站博主
灵神博主

tree数组：Tree[i] 存储的是原本的数组中num[i - (i&-i)+1]到nums[i]的和
更新的时候，num[i[更新，逐一修改num[i+(i & -i)]

307.区间和检索-数组可修改

题目实战

总的代码：

class NumArray:
    __slots__ = 'nums', 'tree'

    def __init__(self, nums: List[int]):
        n = len(nums)
        # 注意，nums 是从0-n-1的下标，tree是1-n的下标
        self.nums = [0] * n  # 使 update 中算出的 delta = nums[i]
        self.tree = [0] * (n + 1)
        for i, x in enumerate(nums):
            self.update(i, x)

    def update(self, index: int, val: int) -> None:
        delta = val - self.nums[index]
        self.nums[index] = val
        i = index + 1
        # 注意这个+1的操作是下标的对应的操作
        while i < len(self.tree):
            self.tree[i] += delta
            i += i & -i

    def prefixSum(self, i: int) -> int:
        s = 0
        while i:
            s += self.tree[i]
            i &= i - 1  # i -= i & -i 的另一种写法
        return s

    def sumRange(self, left: int, right: int) -> int:
        return self.prefixSum(right + 1) - self.prefixSum(left)