区间求和 II -LintCode

在类的构造函数中给一个整数数组, 实现两个方法 query(start, end) 和 modify(index, value):

对于 query(start, end), 返回数组中下标 start 到 end 的 和。

对于 modify(index, value), 修改数组中下标为 index 上的数为 value.

注意事项：

在做此题前，建议先完成以下三题：

线段树的构造

线段树的查询

线段树的修改

样例：

给定数组 A = [1,2,7,8,5].

query(0, 2), 返回 10.

modify(0, 4), 将 A[0] 修改为 4.

query(0, 1), 返回 6.

modify(2, 1), 将 A[2] 修改为 1.

query(2, 4), 返回 14.

挑战 ：

O(logN) time for query and modify.

#ifndef C207_H
#define C207_H
#include<iostream>
#include<vector>
using namespace std;
class SegmentNode{
public:
int start, end;
long long sum;
SegmentNode *left, *right;
SegmentNode(int start, int end, long long sum=0)
{
this->start = start, this->end = end, this->sum = sum;
this->left = this->right = NULL;
}
static SegmentNode *build(vector<int> &A, int start, int end){
if (start > end)
return NULL;
SegmentNode* root = new SegmentNode(start, end, A[start]);
if (start == end)
return root;
int mid = (start + end) / 2;
root->left = build(A,start, mid);
root->right = build(A,mid + 1, end);

root->sum = 0;
if (root->left)
root->sum += root->left->sum;
if (root->right)
root->sum += root->right->sum;
return root;
}
static void modifyRecur(SegmentNode* root, int index, int value){
if (root->start == root->end)
{
if (root->start == index)
root->sum = value;
return;
}
int mid = (root->start + root->end) / 2;
if (index > mid)
modifyRecur(root->right, index, value);
else
modifyRecur(root->left, index, value);
root->sum = 0;
if (root->left)
root->sum += root->left->sum;
if (root->right)
root->sum += root->right->sum;
}
static long long queryRecur(SegmentNode* root, int start, int end){
if (start > root->end || end<root->start)
return 0;
if (start <= root->start && end >= root->end)
return root->sum;
int l = queryRecur(root->left, start, end);
int r = queryRecur(root->right, start, end);
return l + r;
}
};
class Solution {
public:
/* you may need to use some attributes here */

/*
* @param A: An integer array
*/
Solution(vector<int> A) {
// do intialization if necessary
node = SegmentNode::build(A, 0, A.size() - 1);
}
/*
* @param start: An integer
* @param end: An integer
* @return: The sum from start to end
*/
long long query(int start, int end) {
// write your code here
return SegmentNode::queryRecur(node, start, end);
}
/*
* @param index: An integer
* @param value: An integer
* @return: nothing
*/
void modify(int index, int value) {
// write your code here
SegmentNode::modifyRecur(node, index, value);
}
SegmentNode* node;
};
#endif