poj 3468 (splay)

最近在学splay，就用这道题来记一下模板。

splay是二叉搜索树，满足中序遍历有序的性质；同时，splay操作可以在不改变中序序列的前提下改变树的结构。因此，splay可以十分方便地维护区间信息。

#include<cstdio>
using namespace std;

const int maxn = 1e5 + 5;
typedef long long ll;

int fa[maxn], ch[maxn][2], val[maxn], siz[maxn];
ll sum[maxn], lazy[maxn];
int a[maxn];

int tot, root, N, Q;
#define rrt ch[root][1]
#define ls ch[rt][0]
#define rs ch[rt][1]
bool get(int x)
{
    return ch[fa[x]][1] == x;
}

void connect(int x,int f,int which)
{
    fa[x] = f;
    ch[f][which] = x;
}

void pushup(int rt)
{
    siz[rt] = siz[ls] + siz[rs] + 1;
    sum[rt] = sum[ls] + sum[rs] + val[rt];
}

void pushdown(int rt)
{
    if(lazy[rt])
    {
        lazy[ls] += lazy[rt];
        lazy[rs] += lazy[rt];
        sum[ls] += (ll)siz[ls] * lazy[rt];
        sum[rs] += (ll)siz[rs] * lazy[rt];
        val[rt] += lazy[rt];
        lazy[rt] = 0;
    }
}

int y,z,yson,zson,xson;
void rotate(int x)
{
    y = fa[x];
    z = fa[y];
    pushdown(y);
    pushdown(x);
    yson = get(x);
    zson = get(y);
    xson = ch[x][yson^1];
    if(z) connect(x,z,zson);
    fa[x] = z;
    connect(y,x,yson^1);
    connect(xson,y,yson);
    pushup(y);
}

void splay(int x,int to)//把x移动到to的下面
{
    pushdown(x);
    while(fa[x] != to)
    {
        if(fa[fa[x]] == to) rotate(x);
        else if(get(x) == get(fa[x])) rotate(fa[x]), rotate(x);//三点共线
        else rotate(x), rotate(x);
    }
    pushup(x);
    if(to == 0)//x移动到根了
        root = x;//更新根
}

void newnode(int &x,int v,int f)
{
    x = ++tot;
    ch[x][0] = ch[x][1]  = lazy[x] = 0;
    siz[x] = 1;
    sum[x] = v;
    fa[x] = f;
    val[x] = v;
}

void build(int &rt,int l,int r,int f)
{
    if(l>r) return ;
    int m = l + r >> 1;
    newnode(rt,a[m],f);
    build(ls,l,m-1,rt);
    build(rs,m+1,r,rt);
    pushup(rt);
}

void initbuild()
{
    root = tot = 0;
    ch[0][0] = ch[0][1] = siz[0] = sum[0] = lazy[0] = fa[0] = val[0] = 0;
    newnode(root,0,0);//0
    newnode(rrt,0,root);//N+1
    for(int i=1;i<=N;++i)
        scanf("%d",&a[i]);
    build(ch[rrt][0],1,N,rrt);
    pushup(rrt);
    pushup(root);
}

int get_kth(int rt,int k)
{
    pushdown(rt);
    int temp = siz[ls] + 1;
    if(temp == k) return rt;
    if(temp > k) return get_kth(ls,k);
    return get_kth(rs,k-temp);
}

void update(int l,int r,int v)
{
    splay(get_kth(root,l),0);//因为加了虚节点0(占了下标1)，实际区间的下标为2到N+1
    splay(get_kth(root,r+2),root);//所以区间中的第l-1个元素就是树上的第l个点

    lazy[ch[rrt][0]] += v;
    sum[ch[rrt][0]] += ll(v * siz[ch[rrt][0]]);
    pushup(root);
    pushup(rrt);
}

ll query(int l,int r)
{
    splay(get_kth(root,l),0);
    splay(get_kth(root,r+2),root);

    return sum[ch[rrt][0]];
}

int main()
{
    char op[2];
    int l, r, v;
    scanf("%d%d",&N,&Q);
    initbuild();
    while(Q--)
    {
        scanf("%s%d%d",op,&l,&r);
        if(op[0]=='C')
        {
            scanf("%d",&v);
            update(l,r,v);
        }
        else
            printf("%lld\n",query(l,r));
    }
    return 0;
}