高级树状数组讲解：https://www.cnblogs.com/RabbitHu/p/BIT.html
树状数组
一维树状数组
单点修改，区间查询
#include<bits/stdc++.h>
#define INF 0x3f3f3f3f
#define DOF 0x7f7f7f7f
#define endl '
'
#define mem(a,b) memset(a,b,sizeof(a))
#define debug(case,x); cout<<case<<" : "<<x<<endl;
#define open freopen("ii.txt","r",stdin)
#define close freopen("oo.txt","w",stdout)
#define IO ios::sync_with_stdio(false);cin.tie(0);cout.tie(0)
#define pb push_back
using namespace std;
#define int long long
int n;
const int maxn=1e6+10;
int d[maxn];
inline int lowbit(int x){return -x&x;}
void add(int x,int y){
while(x<=n){
d[x]+=y;x+=lowbit(x);
}
}
int get_sum(int x){
int res=0;
while(x){
res+=d[x];x-=lowbit(x);
}
return res;
}
signed main(){
int q;cin>>n>>q;
for(int i=1;i<=n;++i){
int t;cin>>t;
add(i,t);
}
while(q--){
int p,x,y;cin>>p>>x>>y;
if(p==1){
add(x,y);
}else{
cout<<(get_sum(y)-get_sum(x-1))<<endl;
}
}
}
区间修改，单点查询
#include<bits/stdc++.h>
#define INF 0x3f3f3f3f
#define DOF 0x7f7f7f7f
#define endl '
'
#define mem(a,b) memset(a,b,sizeof(a))
#define debug(case,x); cout<<case<<" : "<<x<<endl;
#define open freopen("ii.txt","r",stdin)
#define close freopen("oo.txt","w",stdout)
#define IO ios::sync_with_stdio(false);cin.tie(0);cout.tie(0)
#define pb push_back
using namespace std;
#define int long long
int n;
const int maxn=1e6+10;
int d[maxn],cha[maxn];
inline int lowbit(int x){return -x&x;}
void add(int x,int y){
while(x<=n){
d[x]+=y;x+=lowbit(x);
}
}
int get_sum(int x){
int res=0;
while(x){
res+=d[x];x-=lowbit(x);
}
return res;
}
signed main(){
int q;cin>>n>>q;
for(int i=1;i<=n;++i){
cin>>cha[i];
add(i,cha[i]-cha[i-1]);
}
while(q--){
int op;cin>>op;
if(op==1){
int l,r,x;cin>>l>>r>>x;
add(l,x);
add(r+1,-x);
}else{
int i;cin>>i;
cout<<get_sum(i)<<endl;
}
}
}
区间修改，区间查询
#include<bits/stdc++.h>
#define INF 0x3f3f3f3f
#define DOF 0x7f7f7f7f
#define endl '
'
#define mem(a,b) memset(a,b,sizeof(a))
#define debug(case,x); cout<<case<<" : "<<x<<endl;
#define open freopen("ii.txt","r",stdin)
#define close freopen("oo.txt","w",stdout)
#define IO ios::sync_with_stdio(false);cin.tie(0);cout.tie(0)
#define pb push_back
using namespace std;
#define int long long
int n;
const int maxn=1e6+10;
int t[maxn];
inline int lowbit(int x){return -x&x;}
class Tree_arry{
public:
int d[maxn];
void add(int x,int y){
while(x<=n){
d[x]+=y;x+=lowbit(x);
}
}
int query(int x){
int res=0;
while(x){
res+=d[x];x-=lowbit(x);
}
return res;
}
}b,bi;
int get_xum(int x){
int res=0;
res=(x+1)*b.query(x)-bi.query(x);
return res;
}
signed main(){
int q;cin>>n>>q;
for(int i=1;i<=n;++i){
cin>>t[i];
b.add(i,t[i]-t[i-1]);
bi.add(i,i*(t[i]-t[i-1]));
}
while(q--){
int op;cin>>op;
int l,r,x;cin>>l>>r;
if(op==1){
cin>>x;
b.add(l,x);
b.add(r+1,-x);
bi.add(l,x*l);
bi.add(r+1,-x*(r+1));
}else{
cout<<(get_xum(r)-get_xum(l-1))<<endl;
}
}
}
二维树状数组
单点修改，区间查询
https://loj.ac/submission/868327
#include<bits/stdc++.h>
#define INF 0x3f3f3f3f
#define DOF 0x7f7f7f7f
#define endl '
'
#define mem(a,b) memset(a,b,sizeof(a))
#define debug(case,x); cout<<case<<" : "<<x<<endl;
#define open freopen("ii.txt","r",stdin)
#define close freopen("oo.txt","w",stdout)
#define IO ios::sync_with_stdio(false);cin.tie(0);cout.tie(0)
#define pb push_back
using namespace std;
#define int long long
int n,m;
const int maxn=1e6+10;
const int MAXN=(1<<12)+10;
int d[MAXN][MAXN];
inline int lowbit(int x){return -x&x;}
void add(int x,int y,int val){
while(x<=n){
int ty=y;
while(ty<=m){
d[x][ty]+=val;ty+=lowbit(ty);
}
x+=lowbit(x);
}
}
int query(int x,int y){
int res=0;
while(x){
int ty=y;
while(ty){
res+=d[x][ty];
ty-=lowbit(ty);
}
x-=lowbit(x);
}
return res;
}
int get_xum(int a,int b,int c,int d){
return query(c,d)-query(c,b-1)-query(a-1,d)+query(a-1,b-1);
}
signed main(){
cin>>n>>m;
int op,a,b,c,d,k;
while(cin>>op){
if(op==1){
cin>>a>>b>>k;
add(a,b,k);
}else{
cin>>a>>b>>c>>d;
cout<<get_xum(a,b,c,d)<<endl;
}
}
}
区间修改，单点查询
#include<bits/stdc++.h>
#define INF 0x3f3f3f3f
#define DOF 0x7f7f7f7f
#define endl '
'
#define mem(a,b) memset(a,b,sizeof(a))
#define debug(case,x); cout<<case<<" : "<<x<<endl;
#define open freopen("ii.txt","r",stdin)
#define close freopen("oo.txt","w",stdout)
#define IO ios::sync_with_stdio(false);cin.tie(0);cout.tie(0)
#define pb push_back
using namespace std;
#define int long long
int n,m;
const int maxn=1e6+10;
const int MAXN=(1<<12)+10;
int d[MAXN][MAXN];
inline int lowbit(int x){return -x&x;}
void add(int x,int y,int val){
while(x<=n){
int ty=y;
while(ty<=m){
d[x][ty]+=val;ty+=lowbit(ty);
}
x+=lowbit(x);
}
}
int query(int x,int y){
int res=0;
while(x){
int ty=y;
while(ty){
res+=d[x][ty];
ty-=lowbit(ty);
}
x-=lowbit(x);
}
return res;
}
void update_add(int a,int b,int c,int d,int k){
add(a,b,k);
add(a,d+1,-k);
add(c+1,b,-k);
add(c+1,d+1,k);
}
signed main(){
cin>>n>>m;
int op,a,b,c,d,k;
while(cin>>op>>a>>b){
if(op==1){
cin>>c>>d>>k;
update_add(a,b,c,d,k);
}else{
cout<<query(a,b)<<endl;
}
}
}
区间修改，区间查询
#include<bits/stdc++.h>
#define INF 0x3f3f3f3f
#define DOF 0x7f7f7f7f
#define endl '
'
#define mem(a,b) memset(a,b,sizeof(a))
#define debug(case,x); cout<<case<<" : "<<x<<endl;
#define open freopen("ii.txt","r",stdin)
#define close freopen("oo.txt","w",stdout)
#define IO ios::sync_with_stdio(false);cin.tie(0);cout.tie(0)
#define pb push_back
using namespace std;
#define int long long
int n,m;
const int maxn=1e6+10;
inline int lowbit(int x){return -x&x;}
class Tree_arry{
public:
int d[3000][3000];
void add(int x,int y,int val){
while(x<=n){
int ty=y;
while(ty<=m){
d[x][ty]+=val;ty+=lowbit(ty);
}
x+=lowbit(x);
}
}
int query(int x,int y){
int res=0;
while(x){
int ty=y;
while(ty){
res+=d[x][ty];
ty-=lowbit(ty);
}
x-=lowbit(x);
}
return res;
}
}b,bi,bj,bij;
void add_all(int x,int y,int val){
b.add(x,y,val);
bi.add(x,y,val*x);
bj.add(x,y,val*y);
bij.add(x,y,val*x*y);
}
void update_add(int x1,int y1,int x2,int y2,int k){
add_all(x1,y1,k);
add_all(x2+1,y2+1,k);
add_all(x2+1,y1,-k);
add_all(x1,y2+1,-k);
}
int get_xum(int x,int y){
return (x+1)*(y+1)*b.query(x,y)-(y+1)*bi.query(x,y)-(x+1)*bj.query(x,y)+bij.query(x,y);
}
int get_sum(int x1,int y1,int x2,int y2){
return get_xum(x2,y2)-get_xum(x2,y1-1)-get_xum(x1-1,y2)+get_xum(x1-1,y1-1);
}
signed main(){
cin>>n>>m;
int op,x1,y1,x2,y2,d;
while(cin>>op){
cin>>x1>>y1>>x2>>y2;
if(op==1){
cin>>d;
update_add(x1,y1,x2,y2,d);
}else{
cout<<get_sum(x1,y1,x2,y2)<<endl;
}
}
}