线段树

 

线段树：http://blog.csdn.net/shiqi_614/article/details/8228102（帖子总结的很好，可以参考题目)

http://blog.csdn.net/metalseed/article/details/8039326

特性：平衡二叉树，查询和插入都是log(n)

线段树：

1）单点更新

2）区间更新，用延迟标记，避免区间左右儿子进行更新操作；只有当query时才需要进行更新；

3）区间合并 

线段树的类：实现区间增加一个值，并延迟更新

#define LL(x) (x<<1)
#define RR(x) (x<<1|1)
#define MID(a,b) (a+((b-a)>>1))
const int N=100005;
typedef long long LL;
struct node
{
int lft,rht;
    LL sum,add;
int mid(){return MID(lft,rht);}
void fun(LL tmp)
    {
        add+=tmp;
        sum+=(rht-lft+1)*tmp;
    }
};
int y[N];
struct Segtree
{
    node tree[N*4];
void relax(int ind)
    {
if(tree[ind].add)
        {
            tree[LL(ind)].fun(tree[ind].add);
            tree[RR(ind)].fun(tree[ind].add);
            tree[ind].add=0;
        }
    }
void build(int lft,int rht,int ind)
    {
        tree[ind].lft=lft;  tree[ind].rht=rht;
        tree[ind].sum=0;    tree[ind].add=0;
if(lft==rht) tree[ind].sum=y[lft];
else
        {
int mid=tree[ind].mid();
            build(lft,mid,LL(ind));
            build(mid+1,rht,RR(ind));
            tree[ind].sum=tree[LL(ind)].sum+tree[RR(ind)].sum;
        }
    }
void updata(int st,int ed,int ind,int add)
    {
int lft=tree[ind].lft,rht=tree[ind].rht;
if(st<=lft&&rht<=ed) tree[ind].fun(add);
else
        {
            relax(ind);
int mid=tree[ind].mid();
if(st<=mid) updata(st,ed,LL(ind),add);
if(ed> mid) updata(st,ed,RR(ind),add);
            tree[ind].sum=tree[LL(ind)].sum+tree[RR(ind)].sum;
        }
    }
    LL query(int st,int ed,int ind)
    {
int lft=tree[ind].lft,rht=tree[ind].rht;
if(st<=lft&&rht<=ed) return tree[ind].sum;
else
        {
            relax(ind);
int mid=tree[ind].mid();
            LL sum1=0,sum2=0;
if(st<=mid) sum1=query(st,ed,LL(ind));
if(ed> mid) sum2=query(st,ed,RR(ind));
return sum1+sum2;
        }
    }
}seg;

基本实现：主要实现单点更新

1. #include<iostream>
2. using namespace std;
3. struct TreeNode{
4.   int start;
5.   int end;
6.   int cnt;
7.   TreeNode *left;
8.   TreeNode *right;
9.   TreeNode(int start,int end):start(start),end(end){
10.     left = NULL;
11.     right = NULL;
12.     cnt=0;
13.   }
14. };
15. void update(TreeNode *root, int i,int cnt,bool flag) {
16.     if(root==NULL) return;
17.     if(root->start <= i && i<=root->end) {
18.         if(flag == true) root->cnt += cnt;
19.         else root->cnt -= cnt;
20.         int mid = root->start + (root->end - root->start)/2;
21.         if(i>mid) update(root->right,i,cnt,flag);
22.         else update(root->left,i,cnt,flag);
23.     }
24. }
25. int query(TreeNode *root,int i,int j) {
26.     if(root==NULL) return 0;
27.     if(i>j) return 0;
28.     int start = root->start;
29.     int end = root->end;
30.     int mid = start + (end-start)/2;
31.     if(start==i && j==end) return root->cnt;
32.     if(j<=mid) return query(root->left,i,j);
33.     else if(i<=mid) return query(root->left,i,mid) + query(root->right,mid+1,j); 
34.     else return query(root->right,i,j);
35. }
36. TreeNode *  addSegTree(int start,int end) {
37.         TreeNode * root = new TreeNode(start,end);
38.         if(start!=end) {
39.             int mid = start + (end-start)/2;
40.             root->left  = addSegTree(start,mid);
41.             root->right = addSegTree(mid+1,end);
42.         }
43.         return root;
44. }
45. void preorder(TreeNode *root) {
46.     if(root==NULL) return;
47.     cout<<"["<<root->start<<","<<root->end<<"]"<<endl;
48.     preorder(root->left);
49.     preorder(root->right);
50. }
51. int main(){
52.     int start=1;
53.     int end=10;
54.     // cin>>start>>end;
55.      TreeNode *root = addSegTree(start,end);
56.      for(int i=1;i<=10;i++)
57.          update(root,i,i,true);
58.      cout<<query(root,1,3)<<endl;
59.      update(root,3,6,true);
60.      cout<<query(root,2,7)<<endl;
61.      update(root,10,2,false);
62.      update(root,6,3,true);
63.      cout<<query(root,3,10)<<endl;
64.     // preorder(root);
65.      return 0;
66. }