【C】Problem solution (5-school joint examination 3day2)

analyze

This question looks disgusting. In fact, you can play DP only by recording four things: the point with the smallest y-coordinate shooting upward, the point with the largest y-coordinate shooting downward, and the point with the largest and smallest y-coordinate shooting right. The point is shifted obviously. Note that if the value of this state is zero it can be skipped, otherwise it will time out.

#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <iostream>
#include <algorithm>
#include <cstring>
using namespace std;
int a[60][3],f[2][57][57][57][57],xz[55],xy[55],ys[55],yx[55];
int n,m,tot;
void q(int l,int r)
{
    int i=l,j=r,mid=a[(l+r)/2][1],e;
    while(i<j)
    {
        while(a[i][1]<mid) i++;
        while(a[j][1]>mid) j--;
        if(i<=j)
        {
            e=a[i][1];
            a[i][1]=a[j][1];
            a[j][1]=e;
            e=a[i][2];
            a[i][2]=a[j][2];
            a[j][2]=e;
            i++;
            j--;
        }
    }
    if(i<r) q(i,r);
    if(l<j) q(l,j);
}
void q1(int l,int r)
{
    int i=l,j=r,mid=a[(l+r)/2][2],e;
    while(i<j)
    {
        while(a[i][2]<mid) i++;
        while(a[j][2]>mid) j--;
        if(i<=j)
        {
            e=a[i][1];
            a[i][1]=a[j][1];
            a[j][1]=e;
            e=a[i][2];
            a[i][2]=a[j][2];
            a[j][2]=e;
            i++;
            j--;
        }
    }
    if(i<r) q1(i,r);
    if(l<j) q1(l,j);
}
int main()
{
    cin>>n;
    int i,j,k,l,p,x,y;
    for(i=1;i<=n;i++)
    {
        cin>>a[i][1]>>a[i][2];
        xz[i]=xy[i]=ys[i]=yx[i]=56;
    }
    xz[0]=xy[0]=ys[0]=yx[0]=56;
    q1(1,n);
    tot=0;
    p=-2000000000;
    for(i=1;i<=n;i++)
    {
        if(a[i][2]==p)
        {
            a[i][2]=tot;
        }
        else
        {
            p=a[i][2];
            a[i][2]=++tot;
        }
    }
    q(1,n);
    tot=0;
    p=-2000000000;
    for(i=1;i<=n;i++)
    {
        if(a[i][1]==p)
        {
            a[i][1]=tot;
        }
        else
        {
            p=a[i][1];
            a[i][1]=++tot;
        }
        if(xz[a[i][2]]==56)
            xz[a[i][2]]=a[i][1];
        else
            xz[a[i][2]]=min(xz[a[i][2]],a[i][1]);
            
        if(xy[a[i][2]]==56)
            xy[a[i][2]]=a[i][1];
        else
            xy[a[i][2]]=max(xy[a[i][2]],a[i][1]);
            
        if(yx[a[i][1]]==56)
            yx[a[i][1]]=a[i][2];
        else
            yx[a[i][1]]=min(yx[a[i][1]],a[i][2]);
            
        if(ys[a[i][1]]==56)
            ys[a[i][1]]=a[i][2];
        else
            ys[a[i][1]]=max(ys[a[i][1]],a[i][2]);
    }
    int mo=998244353;
    f[0][n+1][0][0][n+1]=1;
    int ans=0;
    for(i=0;i<=n;i++)
    {
        memset(f[(i+1)%2],0,sizeof(f[(i+1)%2]));
        for(int up=0;up<=n+1;up++)
            for(int down=0;down<=n+1;down++)
                for(int mx=0;mx<=n+1;mx++)
                    for(int mn=0;mn<=n+1;mn++)
                        if(f[i%2][up][down][mx][mn])
                        {
                            int sum=0;
                            int t=f[i%2][up][down][mx][mn];
                            //上
                            if(a[i+1][2]==ys[a[i+1][1]] && mx<a[i+1][2])
                                (f[(i+1)%2][min(up,a[i+1][2])][down][mx][mn]+=t)%=mo,(sum+=t)%=mo; 
                            //下
                            if(a[i+1][2]==yx[a[i+1][1]] && mn>a[i+1][2])
                                (f[(i+1)%2][up][max(down,a[i+1][2])][mx][mn]+=t)%=mo,(sum+=t)%=mo; 
                            //左
                            if(a[i+1][1]==xz[a[i+1][2]] && up>a[i+1][2] &&  down<a[i+1][2])
                                (f[(i+1)%2][up][down][mx][mn]+=t)%=mo,(sum+=t)%=mo; 
                            //右
                            if(a[i+1][1]==xy[a[i+1][2]])
                                (f[(i+1)%2][up][down][max(mx,a[i+1][2])][min(mn,a[i+1][2])]+=t)%=mo,(sum+=t)%=mo;  
                            if(i==n-1) ans=(ans+sum)%mo;
                        } 
    }
    cout<<ans;
}