NOI2005维修数列 splay

好题，错了不知道多少遍。这题其他几个操作都是比较经典的，多了一个最大子序列的。这时候对于当前的区间，最大子序列，可能使左区间的最值，可能是右区间的最值，也可能是整个区间的。所以维护lx[],rx[],mx[]。lx[rt] = max(lx[l],sum[l]+key[rt]+max(0,lx[r]));当前节点的左区间最值可能是左孩子的最值，也可能是左孩子加右孩子的一部分。

rx[]类似。mx[rt] = max(0,rx[l])+key[rt]+max(0,lx[r]);mx[rt] = max(mx[rt],max(mx[l],mx[r]));

#include<queue>
#include<stack>
#include<cmath>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#define INF 99999999
#define ll __int64
#define lson l,m,rt<<1
#define rson m+1,r,rt<<1|1
#define key_value ch[ch[root][1]][0]
using namespace std;
const int MAXN = 900005;
int pre[MAXN],ch[MAXN][2],siz[MAXN],sum[MAXN],rev[MAXN],lazy[MAXN],key[MAXN],root,tot1;
int n,a[MAXN],cnt,s[MAXN],tot2;
int mx[MAXN],lx[MAXN],rx[MAXN];
void Treavel(int x)
{
    if(x)
    {
        Treavel(ch[x][0]);
        printf("结点%2d:左儿子 %2d 右儿子 %2d 父结点 %2d size=%2d key=%2d lazy=%2d rev=%2d siz[0]=%2d
",x,ch[x][0],ch[x][1],pre[x],siz[x],key[x],lazy[x],rev[x],siz[0]);
        Treavel(ch[x][1]);
    }
}
void debug()
{
    printf("root:%d
",root);
    Treavel(root);
}
void Newnode(int &rt,int pa,int k)
{
    if(tot2){
        rt = s[tot2--];
    }
    else {
        rt = ++tot1;
    }
    pre[rt] = pa;
    sum[rt] = k;
    rev[rt] = 0;
    lazy[rt] = 0;
    siz[rt] = 1;
    key[rt] = lx[rt] = rx[rt] = mx[rt] = k;
    ch[rt][0] = ch[rt][1] = 0;
}
void pushup(int rt)
{
    int l = ch[rt][0];
    int r = ch[rt][1];
    siz[rt] = siz[l] + siz[r] + 1;
    sum[rt] = sum[l] + sum[r] + key[rt];
    lx[rt] = max(lx[l],sum[l]+key[rt]+max(0,lx[r]));
    rx[rt] = max(rx[r],sum[r]+key[rt]+max(0,rx[l]));
    mx[rt] = max(0,rx[l]) + key[rt] + max(0,lx[r]);
    mx[rt] = max(mx[rt],max(mx[l],mx[r]));
}
void updata_same(int rt,int k)
{
    if(!rt)
        return ;
    key[rt] = k;
    sum[rt] = k*siz[rt];
    lx[rt] = rx[rt] = mx[rt] = max(k,k*siz[rt]);
    lazy[rt] = 1;
}
void updata_rev(int rt)
{
    rev[rt] ^= 1;
    swap(ch[rt][0],ch[rt][1]);
    swap(lx[rt],rx[rt]);
}
void pushdown(int rt)
{
    if(lazy[rt]){
        updata_same(ch[rt][0],key[rt]);
        updata_same(ch[rt][1],key[rt]);
        lazy[rt] = 0;
    }
    if(rev[rt]){
        updata_rev(ch[rt][0]);
        updata_rev(ch[rt][1]);
        rev[rt] = 0;
    }
}
void build(int &rt,int l,int r,int pa)
{
    if(l > r){
        return ;
    }
    int m = (l+r)/2;
    Newnode(rt,pa,a[m]);
    build(ch[rt][0],l,m-1,rt);
    build(ch[rt][1],m+1,r,rt);
    pushup(rt);
}
void Init()
{
    root = tot1 = tot2 = 0;
    pre[root] = sum[root] = key[root] = lazy[root] = rev[root] = siz[root] = 0;
    lx[root] = rx[root] = mx[root] = -INF;//重要
    ch[root][0] = ch[root][1] = 0;
    Newnode(root,0,0);
    Newnode(ch[root][1],root,0);
    build(key_value,1,n,ch[root][1]);
    pushup(ch[root][1]);
    pushup(root);
}
int Get_kth(int rt,int k)
{
    pushdown(rt);
    int t = siz[ch[rt][0]] + 1;
    if(t == k){
        return rt;
    }
    else if(t > k){
        return Get_kth(ch[rt][0],k);
    }
    else {
        return Get_kth(ch[rt][1],k-t);
    }
}
void Rotate(int rt,int kind)
{
    int y = pre[rt];
    pushdown(y);
    pushdown(rt);
    ch[y][!kind] = ch[rt][kind];
    pre[ch[rt][kind]] = y;
    if(pre[y]){
        ch[pre[y]][ch[pre[y]][1]==y] = rt;
    }
    pre[rt] = pre[y];
    ch[rt][kind] = y;
    pre[y] = rt;
    pushup(y);
}
void splay(int rt,int goal)
{
    pushdown(rt);
    while(pre[rt] != goal)
    {
        if(pre[pre[rt]] == goal){
            pushdown(pre[rt]);
            pushdown(rt);
            Rotate(rt,ch[pre[rt]][0]==rt);
        }
        else {
            pushdown(pre[pre[rt]]);
            pushdown(pre[rt]);
            pushdown(rt);
            int y = pre[rt];
            int kind = ch[pre[y]][0]==y;
            if(ch[y][kind] == rt){
                Rotate(rt,!kind);
                Rotate(rt,kind);
            }
            else {
                Rotate(y,kind);
                Rotate(rt,kind);
            }
        }
    }
    if(goal == 0)
        root = rt;
    pushup(rt);
}
void erase(int rt)
{
    if(!rt)
        return;
    s[++tot2] = rt;
    erase(ch[rt][0]);
    erase(ch[rt][1]);
}
int main()
{
    int m,i,j;
    while(scanf("%d%d",&n,&m)!=EOF)
    {
        for(i=1; i<=n; i++){
            scanf("%d",&a[i]);
        }
        Init();
        char c[20];
        while(m--)
        {
            scanf("%s",c);
            if(c[0] == 'I'){
                int x,y;
                scanf("%d%d",&x,&y);
                for(i=1; i<=y; i++){
                    scanf("%d",&a[i]);
                }
                splay(Get_kth(root,x+1),0);
                splay(Get_kth(root,x+2),root);
                build(key_value,1,y,ch[root][1]);
                pushup(ch[root][1]);
                pushup(root);
            }
            else if(c[0] == 'D'){
                int x,y;
                scanf("%d%d",&x,&y);
                splay(Get_kth(root,x),0);
                splay(Get_kth(root,x+y+1),root);
                erase(key_value);
                pre[key_value] = 0;
                key_value = 0;
                pushup(ch[root][1]);
                pushup(root);
            }
            else if(c[0] == 'M' && c[2] == 'K'){
                int x,y,z;
                scanf("%d%d%d",&x,&y,&z);
                splay(Get_kth(root,x),0);
                splay(Get_kth(root,x+y+1),root);
                updata_same(key_value,z);
                pushup(ch[root][1]);
                pushup(root);
            }
            else if(c[0] == 'R'){
                int x,y;
                scanf("%d%d",&x,&y);
                splay(Get_kth(root,x),0);
                splay(Get_kth(root,x+y+1),root);
                updata_rev(key_value);
                pushup(ch[root][1]);
                pushup(root);
            }
            else if(c[0] == 'G'){
                int x,y;
                scanf("%d%d",&x,&y);
                
                splay(Get_kth(root,x),0);
                splay(Get_kth(root,x+y+1),root);
                printf("%d
",sum[key_value]);
            }
            else{
                splay(Get_kth(root,1),0);
                splay(Get_kth(root,siz[root]),root);
                printf("%d
",mx[key_value]);
            }
        }
    }
}