bzoj5299 [Cqoi2018] Unlock the screen [shape pressure dp]

portal

Problem solving ideas:

shape pressure dp.

Assume$f[i][s]$means currently in$i$, after the state is$s$number of scenarios, in preprocessing$g[i][j]$for$i$arrive$j$point on the path. The time complexity is$O(n^22^n)$

#include<bits/stdc++.h>
#define ll long long
using namespace std;
int getint()
{
    int i=0,f=1;char c;
    for(c=getchar();(c!='-')&&(c<'0'||c>'9');c=getchar());
    if(c=='-')c=getchar(),f=-1;
    for(;c>='0'&&c<='9';c=getchar())i=(i<<3)+(i<<1)+c-'0';
    return i*f;
}
const int N=20,mod=1e8+7;
inline void add(int &x,int y){x=x+y>=mod?x+y-mod:x+y;}
struct point
{
    int x,y;
    point(){}
    point(int _x,int _y):x(_x),y(_y){}
    inline friend point operator - (const point &a,const point &b){return point(a.x-b.x,a.y-b.y);}
    inline friend int operator ^ (const point &a,const point &b){return a.x*b.y-a.y*b.x;}
    inline friend int operator * (const point &a,const point &b){return a.x*b.x+a.y*b.y;}
}p[N];
inline bool online(point a,point b,point c)
{
    a=a-c,b=b-c;
    return ((a^b)==0)&&(a*b<=0);
}
int n,ans,S,f[N][1<<20],bin[1<<20],g[N][N];
int main()
{
    //freopen("android.in","r",stdin);
    //freopen("android.out","w",stdout);
    n=getint();S=(1<<n);
    for(int i=1;i<S;i++)bin[i]=bin[i>>1]+(i&1);
    for(int i=1;i<=n;i++)p[i].x=getint(),p[i].y=getint();
    for(int i=1;i<=n;i++)
        for(int j=i+1;j<=n;j++)
            for(int k=1;k<=n;k++)if(k!=i&&k!=j)
                if(online(p[i],p[j],p[k]))
                    g[i][j]|=(1<<k-1),g[j][i]|=(1<<k-1);
    for(int i=1;i<=n;i++)f[i][1<<i-1]=1;
    for(int s=1;s<S;s++)
        for(int i=1;i<=n;i++)if(f[i][s])
            for(int j=1;j<=n;j++)if(!(s&(1<<j-1)))
            {
                if((s&g[i][j])!=g[i][j])continue;
                add(f[j][s|(1<<j-1)],f[i][s]);
            }
    for(int s=1;s<S;s++)if(bin[s]>=4)
        for(int i=1;i<=n;i++)add(ans,f[i][s]);
    cout<<ans<<'\n';
    return 0;
}