Range Sum Query - Mutable

weixin_34090643

于 2019-07-03 04:35:31 发布

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CC 4.0 BY-SA版权

原文链接：http://www.cnblogs.com/sherylwang/p/5912620.html

本文介绍了一种使用段树数据结构实现动态数组区间求和和更新的方法。通过构建段树，可以高效地进行区间求和和单点更新操作，避免了传统遍历求和的效率低下。文章详细解释了段树的构建、查询和更新过程，并提供了完整的Python代码实现。

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class SegmentTreeNode(object):
    def __init__(self, start, end):
        self.start = start
        self.end = end
        self.sum = 0
        self.left = None
        self.right = None
        
class NumArray(object):
    def __init__(self, nums):
        """
        initialize your data structure here.
        :type nums: List[int]
        """
        n = len(nums)
        self.root = self.buildTree(nums, 0, n-1)
        

    def update(self, i, val):
        """
        :type i: int
        :type val: int
        :rtype: int
        """
        self.modifyTree(i,val, self.root)
        

    def sumRange(self, i, j):
        """
        sum of elements nums[i..j], inclusive.
        :type i: int
        :type j: int
        :rtype: int
        """
        return self.queryTree(i, j, self.root)
        
    def buildTree(self, nums, start, end):
        if start > end: return None#not valid
        root = SegmentTreeNode(start, end)
        if start == end:
            root.sum = nums[start]
            return root
        mid = start + (end - start)/2
        root.left = self.buildTree(nums, start, mid)
        root.right = self.buildTree(nums, mid+1, end)
        root.sum = root.left.sum + root.right.sum
        return root
        
    def modifyTree(self, i, val, root):
        if not root:
            return 0
        if root.start==i and root.end == i: 
            diff = val - root.sum
            root.sum = val
            return diff
        mid = (root.start + root.end)/2
        if i > mid:
            diff = self.modifyTree(i, val, root.right)
        else:
            diff = self.modifyTree(i, val, root.left)
        root.sum = root.sum + diff
        return diff
        
    def queryTree(self, i, j, root):
        if not root:
            return 0
        if root.start == i and root.end == j:
            return root.sum
        mid = (root.start + root.end)/2
        if i > mid:
            return self.queryTree(i, j, root.right)
        if j <= mid:
            return self.queryTree(i, j, root.left)
            
        return self.queryTree(i, mid, root.left)+self.queryTree(mid+1, j , root.right)
        
        

# Your NumArray object will be instantiated and called as such:
# numArray = NumArray(nums)
# numArray.sumRange(0, 1)
# numArray.update(1, 10)
# numArray.sumRange(1, 2)