POJ 3580 SuperMemo

最新推荐文章于 2019-03-11 21:39:00 发布

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最新推荐文章于 2019-03-11 21:39:00 发布

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本文介绍了一种使用裸Splay实现的区间操作方法，包括内存池、区间加减、区间翻转、插入、删除及最值维护等功能。通过具体实例展示了如何在一系列操作和查询中高效地更新和查询序列中的数值。

裸Splay区间操作: 内存池+区间加减+区间翻转+插入+删除+维护最值

SuperMemo

Time Limit: 5000MS		Memory Limit: 65536K
Total Submissions: 8552		Accepted: 2801
Case Time Limit: 2000MS

Description

Your friend, Jackson is invited to a TV show called SuperMemo in which the participant is told to play a memorizing game. At first, the host tells the participant a sequence of numbers, {A₁,A₂, ... A_n}. Then the host performs a series of operations and queries on the sequence which consists:

ADD x y D: Add D to each number in sub-sequence {A_x ... A_y}. For example, performing "ADD 2 4 1" on {1, 2, 3, 4, 5} results in {1, 3, 4, 5, 5}
REVERSE x y: reverse the sub-sequence {A_x ... A_y}. For example, performing "REVERSE 2 4" on {1, 2, 3, 4, 5} results in {1, 4, 3, 2, 5}
REVOLVE x y T: rotate sub-sequence {A_x ... A_y} T times. For example, performing "REVOLVE 2 4 2" on {1, 2, 3, 4, 5} results in {1, 3, 4, 2, 5}
INSERT x P: insert P after A_x. For example, performing "INSERT 2 4" on {1, 2, 3, 4, 5} results in {1, 2, 4, 3, 4, 5}
DELETE x: delete A_x. For example, performing "DELETE 2" on {1, 2, 3, 4, 5} results in {1, 3, 4, 5}
MIN x y: query the participant what is the minimum number in sub-sequence {A_x ... A_y}. For example, the correct answer to "MIN 2 4" on {1, 2, 3, 4, 5} is 2

To make the show more interesting, the participant is granted a chance to turn to someone else that means when Jackson feels difficult in answering a query he may call you for help. You task is to watch the TV show and write a program giving the correct answer to each query in order to assist Jackson whenever he calls.

Input

The first line contains n (n ≤ 100000).

The following n lines describe the sequence.

Then follows M (M ≤ 100000), the numbers of operations and queries.

The following M lines describe the operations and queries.

Output

For each "MIN" query, output the correct answer.

Sample Input

Sample Output

Source

POJ Founder Monthly Contest – 2008.04.13, Yao Jinyu

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#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;

const int maxn=220000;
const int INF=0x3f3f3f3f;
#define Key_Value ch[ch[root][1]][0]

int ch[maxn][2],rev[maxn],add[maxn],sz[maxn],pre[maxn],key[maxn],minn[maxn];
int root,tot1;
int s[maxn],tot2;

int n,q,a[maxn];

void NewNode(int& x,int father,int k)
{
    if(tot2) x=s[tot2--];
    else x=++tot1;

    ch[x][0]=ch[x][1]=rev[x]=add[x]=0;
    sz[x]=1; pre[x]=father; key[x]=minn[x]=k;
}

void Erase(int r)
{
    if(r)
    {
        s[++tot2]=r;
        Erase(ch[r][0]);
        Erase(ch[r][1]);
    }
}

void Upd_Rev(int x)
{
    if(!x) return ;
    swap(ch[x][0],ch[x][1]);
    rev[x]^=1;
}

void Upd_Add(int x,int d)
{
    if(!x) return ;
    key[x]+=d; minn[x]+=d;
    add[x]+=d;
}

void Push_Up(int x)
{
    sz[x]=sz[ch[x][1]]+sz[ch[x][0]]+1;
    minn[x]=key[x];
    if(ch[x][0]) minn[x]=min(minn[x],minn[ch[x][0]]);
    if(ch[x][1]) minn[x]=min(minn[x],minn[ch[x][1]]);
}

void Push_Down(int x)
{
    if(rev[x])
    {
        Upd_Rev(ch[x][0]); Upd_Rev(ch[x][1]);
        rev[x]=0;
    }
    if(add[x])
    {
        Upd_Add(ch[x][0],add[x]); Upd_Add(ch[x][1],add[x]);
        add[x]=0;
    }
}

void Build(int& x,int l,int r,int fa)
{
    if(l>r) return ;
    int mid=(l+r)/2;
    NewNode(x,fa,a[mid]);
    Build(ch[x][0],l,mid-1,x);
    Build(ch[x][1],mid+1,r,x);
    Push_Up(x);
}

void Init()
{
    root=tot1=tot2=0;
    ch[root][0]=ch[root][1]=pre[root]=sz[root]=0;
    minn[root]=key[root]=INF;
    NewNode(root,0,INF);
    NewNode(ch[root][1],root,INF);
    Build(Key_Value,1,n,ch[root][1]);
    Push_Up(ch[root][1]);
    Push_Up(root);
}

void Rotate(int x,int kind)
{
    int y=pre[x];
    Push_Down(y);
    Push_Down(x);
    ch[y][!kind]=ch[x][kind];
    pre[ch[x][kind]]=y;
    if(pre[y]) ch[pre[y]][ch[pre[y]][1]==y]=x;
    pre[x]=pre[y];
    pre[y]=x;
    ch[x][kind]=y;
    Push_Up(y);
}

void Splay(int r,int goal)
{
    Push_Down(r);
    while(pre[r]!=goal)
    {
        if(pre[pre[r]]==goal)
        {
            Push_Down(pre[r]);
            Push_Down(r);
            Rotate(r,ch[pre[r]][0]==r);
        }
        else
        {
            Push_Down(pre[pre[r]]);
            Push_Down(pre[r]);
            Push_Down(r);
            int y=pre[r];
            int kind=(ch[pre[y]][0]==y);
            if(ch[y][kind]==r) Rotate(r,!kind);
            else Rotate(y,kind);
            Rotate(r,kind);
        }
    }
    Push_Up(r);
    if(goal==0) root=r;
}

int Get_Kth(int r,int k)
{
    Push_Down(r);
    int t=sz[ch[r][0]]+1;
    if(k==t) return r;
    if(t<k) return Get_Kth(ch[r][1],k-t);
    else return Get_Kth(ch[r][0],k);
}

int Get_Min(int r)
{
    Push_Down(r);
    while(ch[r][0])
    {
        r=ch[r][0];
        Push_Down(r);
    }
    return r;
}

int Get_Max(int r)
{
    Push_Down(r);
    while(ch[r][1])
    {
        r=ch[r][1];
        Push_Down(r);
    }
    return r;
}

///.......do..it........

void ADD(int l,int r,int d)
{
    Splay(Get_Kth(root,l),0);
    Splay(Get_Kth(root,r+2),root);
    Upd_Add(Key_Value,d);
    Push_Up(ch[root][1]);
    Push_Up(root);
}

void REVERSE(int l,int r)
{
    Splay(Get_Kth(root,l),0);
    Splay(Get_Kth(root,r+2),root);
    Upd_Rev(Key_Value);
    Push_Up(ch[root][1]);
    Push_Up(root);
}

void DELETE(int p)
{
    Splay(Get_Kth(root,p),0);
    Splay(Get_Kth(root,p+2),root);
    Erase(Key_Value);
    pre[Key_Value]=0;
    Key_Value=0;
    Push_Up(ch[root][1]);
    Push_Up(root);
}

void INSERT(int p,int v)
{
    Splay(Get_Kth(root,p+1),0);
    Splay(Get_Kth(root,p+2),root);
    NewNode(Key_Value,ch[root][1],v);
    Push_Up(ch[root][1]);
    Push_Up(root);
}

int MIN(int l,int r)
{
    Splay(Get_Kth(root,l),0);
    Splay(Get_Kth(root,r+2),root);
    return minn[Key_Value];
}

void REVOLVE(int l,int r,int t)
{
    int len=r-l+1;
    t=(t%len+len)%len;
    if(t==0) return ;
    int c=r-t+1;
    ///[l..c-1] and [c..r]
    Splay(Get_Kth(root,c),0);
    Splay(Get_Kth(root,r+2),root);
    int temp=Key_Value;
    Key_Value=0;
    Push_Up(ch[root][1]);
    Push_Up(root);

    Splay(Get_Kth(root,l),0);
    Splay(Get_Kth(root,l+1),root);
    Key_Value=temp;
    pre[Key_Value]=ch[root][1];
    Push_Up(ch[root][1]);
    Push_Up(root);
}
/****************Debug*********************/

void showit(int x)
{
    if(x)
    {
        Push_Down(x);
        showit(ch[x][0]);
        printf("结点: %2d key: %2d 左儿子: %2d 右儿子: %2d 父结点: %2d sz: %2d min: %2d \n",
               x,key[x],ch[x][0],ch[x][1],pre[x],sz[x],minn[x]);
        showit(ch[x][1]);
    }
}

void Debug()
{
    cout<<"---------------------------\n";
    cout<<"root: "<<root<<endl;
    showit(root);
}


int main()
{
    while(scanf("%d",&n)!=EOF)
    {
        for(int i=1;i<=n;i++) scanf("%d",a+i);
        Init();
       // Debug();
        scanf("%d",&q);
        char op[100]; int x,y,z;
        while(q--)
        {
            scanf("%s",op);
            if(strcmp(op,"ADD")==0)
            {
                scanf("%d%d%d",&x,&y,&z);
                ADD(x,y,z);
            }
            else if(strcmp(op,"REVERSE")==0)
            {
                scanf("%d%d",&x,&y);
                REVERSE(x,y);
            }
            else if(strcmp(op,"REVOLVE")==0)
            {
                 scanf("%d%d%d",&x,&y,&z);
                 REVOLVE(x,y,z);
            }
            else if(strcmp(op,"INSERT")==0)
            {
                scanf("%d%d",&x,&y);
                INSERT(x,y);
            }
            else if(strcmp(op,"DELETE")==0)
            {
                scanf("%d",&x);
                DELETE(x);
            }
            else if(strcmp(op,"MIN")==0)
            {
                scanf("%d%d",&x,&y);
                printf("%d\n",MIN(x,y));
            }
           // Debug();
        }
    }
    return 0;
}