【线段树】基础版

1>区间加法+区间和询问

#include
#include
#define int long long
using namespace std;
int n,m;
const int N=1e6+3;
int d[N];
struct node
{
    int son1,son2;
    int sum,laz,len;
}tr[N<<2];
int root,cnt;
void updata(int rt)
{
    int a=tr[rt].son1 ,b=tr[rt].son2 ;
    tr[rt].sum =tr[a].sum +tr[b].sum ;
}
void build(int &rt,int l,int r)
{
    rt=++cnt;
    tr[rt].len =r-l+1;
    if(l==r) 
    {
        tr[rt].sum =d[l];
        return ;
    }
    int mid=(l+r)>>1;
    build(tr[rt].son1 ,l,mid);
    build(tr[rt].son2 ,mid+1,r);
    updata(rt);
}
void push_down(int rt)
{
    int a=tr[rt].son1 ,b=tr[rt].son2 ,v=tr[rt].laz ;
    tr[a].laz +=v,tr[b].laz +=v;
    tr[a].sum +=v*tr[a].len ,tr[b].sum +=v*tr[b].len ;
    tr[rt].laz =0;
}
void change(int rt,int l,int r,int ll,int rr,int vv)
{
    if(ll<=l && r<=rr)
    {
        tr[rt].laz +=vv,tr[rt].sum +=tr[rt].len *vv;
        return ;
    }
    if(tr[rt].laz ) push_down(rt);
    int mid=(l+r)>>1;
    if(rr<=mid) change(tr[rt].son1 ,l,mid,ll,rr,vv);
    else if(ll>mid) change(tr[rt].son2 ,mid+1,r,ll,rr,vv);
    else change(tr[rt].son1 ,l,mid,ll,mid,vv),change(tr[rt].son2 ,mid+1,r,mid+1,rr,vv);//有影响？？？ 
    updata(rt);
} 
int query(int rt,int l,int r,int ll,int rr)
{
    if(ll<=l && r<=rr)
        return tr[rt].sum ;
    if(tr[rt].laz ) push_down(rt);  
    int mid=(l+r)>>1;
    if(rr<=mid) return query(tr[rt].son1 ,l,mid,ll,rr); 
    else if(ll>mid) return query(tr[rt].son2 ,mid+1,r,ll,rr);
    return query(tr[rt].son1 ,l,mid,ll,rr)+query(tr[rt].son2 ,mid+1,r,ll,rr);
}

signed main()
{
    scanf("%lld%lld",&n,&m);
    for(int i=1;i<=n;i++)
        scanf("%lld",&d[i]);
    build(root,1,n);
    
    int op,ll,rr,vv;
    while(m--)
    {
        scanf("%lld%lld%lld",&op,&ll,&rr);
        if(op==1)
        {
            scanf("%lld",&vv);
            change(1,1,n,ll,rr,vv); 
        }
        else
            printf("%lld\n",query(1,1,n,ll,rr));
    }
    
    return 0;
}

2>区间加法+区间乘法+区间和询问

自设：d[i]*mul +add

#include
#include
#define int long long
using namespace std;
int n,m,mod;
const int N=1e5+3;
int d[N],root,cnt;

struct node
{
    int son1,son2,len;
    int sum,laz,LAZ;
    //加，乘两个标记，选择d*LAZ+laz
    //add时，直接加
    //mul时，如果laz!=0,就push_down再乘
    //push_down时，如果LAZ！=1  =》  将孩子的laz，LAZ，sum都*mul
    //再处理laz 
}tr[N*3];
void updata(int rt)
{
    tr[rt].sum=(tr[tr[rt].son1].sum +tr[tr[rt].son2].sum)%mod;
} 
void build(int &rt,int l,int r)
{
    rt=++cnt;
    tr[rt].LAZ =1,tr[rt].len =r-l+1;
    if(l==r)
    {
        tr[rt].sum=d[l]%mod;
        return ;
    }
    int mid=(l+r)>>1;
    build(tr[rt].son1 ,l,mid);
    build(tr[rt].son2 ,mid+1,r);
    updata(rt);
}

void push_down(int rt)
{
    int a=tr[rt].son1 ,b=tr[rt].son2 ;
    if(tr[rt].LAZ !=1)
    {
        int t=tr[rt].LAZ ;
        tr[a].sum =(tr[a].sum *t)%mod;
        tr[a].LAZ =(tr[a].LAZ *t)%mod;
        tr[a].laz =(tr[a].laz *t)%mod;
        tr[b].sum =(tr[b].sum *t)%mod;
        tr[b].LAZ =(tr[b].LAZ *t)%mod;
        tr[b].laz =(tr[b].laz *t)%mod;
        tr[rt].LAZ =1;
    }
    if(tr[rt].laz )
    {
        int t=tr[rt].laz ;
        tr[a].sum =(tr[a].sum +t*tr[a].len )%mod;
        tr[a].laz =(tr[a].laz +t)%mod;
        tr[b].sum =(tr[b].sum +t*tr[b].len )%mod;//写掉了len... 
        tr[b].laz =(tr[b].laz +t)%mod;
        tr[rt].laz =0;
    }
}
void add(int rt,int l,int r,int ql,int qr,int v)
{
    if(ql<=l && r<=qr)
    {
        tr[rt].sum =(tr[rt].sum + v*tr[rt].len%mod)%mod;
        tr[rt].laz =(tr[rt].laz + v)%mod;
        return ;
    }
    push_down(rt);

    int mid=(l+r)>>1;
    if(qr<=mid) add(tr[rt].son1 ,l,mid,ql,qr,v);
    else if(ql>mid) add(tr[rt].son2 ,mid+1,r,ql,qr,v);
    else add(tr[rt].son1 ,l,mid,ql,mid,v),add(tr[rt].son2 ,mid+1,r,mid+1,qr,v);
    updata(rt);
}
void mul(int rt,int l,int r,int ql,int qr,int v)
{
    if(ql<=l && r<=qr)
    {
        tr[rt].sum =(tr[rt].sum *v)%mod;
        tr[rt].laz =(tr[rt].laz *v)%mod;
        tr[rt].LAZ =(tr[rt].LAZ *v)%mod;
        return ;
    }
    push_down(rt);

    int mid=(l+r)>>1;
    if(qr<=mid) mul(tr[rt].son1 ,l,mid,ql,qr,v);
    else if(ql>mid) mul(tr[rt].son2 ,mid+1,r,ql,qr,v);
    else mul(tr[rt].son1 ,l,mid,ql,qr,v),mul(tr[rt].son2 ,mid+1,r,ql,qr,v);
    updata(rt);
}

int query(int rt,int l,int r,int ql,int qr)
{
    if(ql<=l && r<=qr)
        return tr[rt].sum ;
    push_down(rt);
    int mid=(l+r)>>1;
    if(qr<=mid) return query(tr[rt].son1 ,l,mid,ql,qr);
    else if(ql>mid) return query(tr[rt].son2 ,mid+1,r,ql,qr);
    else return (query(tr[rt].son1 ,l,mid,ql,mid)+query(tr[rt].son2 ,mid+1,r,mid+1,qr))%mod;
}

signed main()
{
    scanf("%lld%lld%lld",&n,&m,&mod);
    for(int i=1;i<=n;i++)
        scanf("%lld",&d[i]);
    build(root,1,n);
    
    int op,x,y,k;
    for(int i=1;i<=m;i++)
    {
        scanf("%lld%lld%lld",&op,&x,&y);
        if(op==3)
            printf("%lld\n",query(1,1,n,x,y));
        else if(op==1)
            scanf("%lld",&k),mul(1,1,n,x,y,k%mod);
        else if(op==2)
            scanf("%lld",&k),add(1,1,n,x,y,k%mod);
    }
    
    return 0;
}