线段树，树状数组学习笔记

具体内容在代码里面都有了

树状数组：

#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
#define lc p<<1
#define rc p<<1|1
#define N 500005
int n,w[N];
struct node{
  int l,r,sum;
}tr[N*4];

void pushup(int p){//向上更新
  tr[p].sum=tr[lc].sum+tr[rc].sum;
}
void build(int p,int l,int r){//建树 
  tr[p]={l,r,w[l]};
  if(l==r) return; //是叶子则返回 
  int m=l+r>>1; //不是叶子则裂开 
  build(lc,l,m);
  build(rc,m+1,r);
  pushup(p);
}
void update(int p,int x,int k){//点修改 
  if(tr[p].l==x&&tr[p].r==x){//叶子则修改 
    tr[p].sum+=k;
    return;
  }
  int m=tr[p].l+tr[p].r>>1;//非叶子则裂开 
  if(x<=m) update(lc,x,k);
  if(x>m) update(rc,x,k);
  pushup(p);
}
int query(int p,int x,int y){//区间查询 
  if(x<=tr[p].l&&tr[p].r<=y)//覆盖则返回 
    return tr[p].sum;
  int m=tr[p].l+tr[p].r>>1;//不覆盖则裂开 
  int sum=0;
  if(x<=m) sum+=query(lc,x,y);
  if(y>m) sum+=query(rc,x,y);
  return sum;
}
int main(){
    ios::sync_with_stdio(0);
  int m,op,x,y;  
  cin>>n>>m;
  for(int i=1;i<=n;i++) cin>>w[i];
  build(1,1,n);
  
  while(m--){
    cin>>op>>x>>y;
    if(op==1) update(1,x,y);
    else cout<<query(1,x,y)<<endl;
  }
  return 0;
}

带懒标记的就是理解为父母存钱，等用了再下发给每个孩子

//线段树浅学习
//基于分治思想，用来维护区间信息（区间和，区间最值，区间gcd）
//可以在logn的时间内执行区间修改和区间查询
#include<iostream>
using namespace std;
//定义左儿子，右儿子
#define lc p<<1//这个是2 * p
#define rc p<<1|1//这个是2 * p + 1 
const int N = 10010;
int w[N];
struct node
{
    int l,int r,int sum;
}tree[N * 4];
//构造线段树
void built(int p,int l,int r)//p表示根节点
{
    tree[p] = {l,r,w[l]};//刚开始w[l]没有意义
    if(l == r)return;
    //开始裂开
    int mid = l+r>>1;
    built(lc,l,mid);
    built(lr,mid+1,r);

    tree[p].sum = tree[lc].sum + tree[rc].sum;
}

//点修改
void xiugai(int p,int x,int k)//k表示要修改的值
{   
    if(tree[p].l == x && tree[p].r == x)
    {
        tree[p].sum += k;
        return;
    }

    int mid = tree[p].l + tree[p].r >> 1;
    if(x <= m)xiugai(lc,x,k);
    if(x > m)xiugai(rc,x,k);

    tree[p].sum = tree[lc].sum + tree[rc].sum;
}
int query(int p,int x,int y)
{
    if(x <= tree[p].l && tree[p].r <= y)return tree[p].sum;

    int mid = tree[p].l + tree[p].r >> 1;
    int sum = 0;
    if(x <= m)sum += query(lc,x,y);
    if(x > m) sum += query(rc,x,y);
}   return sum;




//带有懒标记的线段树
#include<bits/stdc++.h>
using namespace std;
const int N = 100010;
int w[N];
int m,n;
#define lc p << 1
#define rc p<<1 | 1
struct node
{
    int l,int r,int add;
}tree[N * 4];
void pushup(int p)
{
    tree[p].sum = tree[lc].sum + tree[rc].sum;
}

void pushdown(int p,int x,int y,int k)
{
    if(tree[p].add)
    {
        tree[lc].sum += tree[p].add * (tree[lc].r - tree[lc].l+1);
        tree[rc].sum += tree[p].add * (tree[rc].r - tree[rc].l+1);
        tree[lc].add += tree[p].add;
        tree[rc].add += tree[p].add;
        tree[p].add = 0;
    }
}


void built(int p,int l,int r)
{
    tree[p] = {l,r,w[l],0};
    if(l == r)return;
    int mid = l+r>>1;
    built(lc,l,mid);
    built(rc,mid+1,r);
    pushup(p);
}


void xiugai(int p,int x,int y,int k)
{
    if(x <= tree[p].l && tree[p].r <= y)
    {
        tree[p].sum += (tree[p].r - tree[p].l+1)*k;
        tree[p].add += k;
        return;
    }
    int mid = tree[p].l + tree[p].r >> 1;
    pushdown(p);
    if(x <= m)xiugai(lc,x,y,k);
    if(x > m)xiugai(rc,x,y,k);
    pushup(p);
}


int query(int p,int x,int y)
{
    if(x <= tree[p].l && tree[p].r <= y)return tree[p].sum;

    int mid = tree[p].l + tree[p].r >> 1;
    pushdown(p);
    if(x <= m)sum += query(lc,x,y);
    if(x > m)sum += query(rc,x,y);
    return sum;
}
signed main()
{
    scanf("%d",&n);//n个节点 
    build(1,1,n);//建树 
    scanf("%d",&m);//m种操作 
    for(int i=1;i<=m;i++)
    {
        scanf("%d",&p);
        ans = 0;
        if(p == 1)
        {
            scanf("%d",&x);
            //单点查询,输出第x个数 
            printf("%d",ans);
        } 
        else if(p==2)
        {
            scanf("%d%d",&x,&y);
            
        }
        else if(p==3)
        {
            scanf("%d%d",&a,&b);//区间查询 
            
            printf("%d\n",ans);
        }
        else
        {
             scanf("%d%d%d",&a,&b,&y);//区间修改 
             
        }
    }
    return 0;
}

实战模式： 

线段树模板1 

【模板】线段树 1 - 洛谷 

//带有懒标记的线段树
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
#define lc p<<1
#define rc p<<1|1
#define N 100005
#define LL long long
LL n,w[N];
struct node{
  LL l,r,sum,add;
}tr[N*4];

void pushup(LL p){
  tr[p].sum=tr[lc].sum + tr[rc].sum;
}
void pushdown(LL p){
  auto &u=tr[p],&l=tr[lc],&r=tr[rc];
  if(u.add){
    l.sum+=u.add*(l.r-l.l+1),
    r.sum+=u.add*(r.r-r.l+1),
    l.add+=u.add,
    r.add+=u.add,
    u.add=0;      
    }
}
void build(LL p,LL l,LL r){
  tr[p]={l,r,w[l],0};
  if(l==r) return; //是叶子则返回 
  LL m=l+r>>1; //不是叶子则裂开 
  build(lc,l,m);
  build(rc,m+1,r);
  pushup(p);
}
void update(LL p,LL x,LL y,LL k){
  if(x<=tr[p].l&&tr[p].r<=y)
  {
  //覆盖则修改 
    tr[p].sum+=(tr[p].r-tr[p].l+1)*k;
    tr[p].add+=k;
    return;
  }
  LL m=tr[p].l+tr[p].r>>1; //不覆盖则裂开 
  pushdown(p);
  if(x<=m) update(lc,x,y,k);
  if(y>m) update(rc,x,y,k);
  pushup(p);
}
LL query(LL p,LL x,LL y){
  if(x<=tr[p].l&&tr[p].r<=y)//覆盖则返回 
    return tr[p].sum;
  LL m=tr[p].l+tr[p].r>>1;//不覆盖则裂开 
  pushdown(p);
  LL sum=0;
  if(x<=m) sum+=query(lc,x,y);
  if(y>m) sum+=query(rc,x,y);
  return sum;
}
int main()
{
  LL m,op,x,y,k;  
  cin>>n>>m;
  for(LL i=1; i<=n; i ++) cin>>w[i];
  build(1,1,n);
  
  while(m--)
  {
    cin>>op>>x>>y;
    if(op==2)cout<<query(1,x,y)<<endl;
    else cin>>k,update(1,x,y,k);
  }
  return 0;
}