NWERC 2017(Connect the Dots-几何+搜索)

题意：4*4个格点，要求一笔从小到大依次经过这16个点。求使用的最小线段数。

暴搜。
考虑任意一条线段一定满足
1.斜率为2个不超过20的整数的比值；2.至少经过1个点。
搜索状态为（当前画到了第几个点，当前所在射线的方向）
转移为：
在这个点转一下方向，
直接画到下一个点。
画到下一个点，中间转一次方向。

#include<bits/stdc++.h>using namespace std;#define For(i,n) for(int i=1;i<=n;i++)#define Fork(i,k,n) for(int i=k;i<=n;i++)#define Rep(i,n) for(int i=0;i<n;i++)#define ForD(i,n) for(int i=n;i;i--)#define ForkD(i,k,n) for(int i=n;i>=k;i--)#define RepD(i,n) for(int i=n;i>=0;i--)#define Forp(x) for(int p=Pre[x];p;p=Next[p])#define Forpiter(x) for(int &p=iter[x];p;p=Next[p])  #define Lson (o<<1)#define Rson ((o<<1)+1)#define MEM(a) memset(a,0,sizeof(a));#define MEMI(a) memset(a,127,sizeof(a));#define MEMi(a) memset(a,128,sizeof(a));#define INF (2139062143)#define F (100000007)#define pb push_back#define mp make_pair #define fi first#define se second#define vi vector<int> #define pi pair<int,int>#define SI(a) ((a).size())#define ALL(x) (x).begin(),(x).end()typedef long long ll;typedef long double ld;typedef unsigned long long ull;ll mul(ll a,ll b){return (a*b)%F;}ll add(ll a,ll b){return (a+b)%F;}ll sub(ll a,ll b){return (a-b+llabs(a-b)/F*F+F)%F;}void upd(ll &a,ll b){a=(a%F+b%F)%F;}int read(){    int x=0,f=1; char ch=getchar();    while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();}    while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();}    return x*f;} ll sqr(ll a){return a*a;}ld sqr(ld a){return a*a;}double sqr(double a){return a*a;}const double eps=1e-10;int dcmp(double x) {    if (fabs(x)<eps) return 0; else return x<0 ? -1 : 1; }ld PI = 3.141592653589793238462643383;class P{public:    ll x,y;    P(ll x=0,ll y=0):x(x),y(y){}    friend ll Dot(P A,P B) {return A.x*B.x+A.y*B.y; }    friend P operator- (P A,P B) { return P(A.x-B.x,A.y-B.y); }    friend P operator+ (P A,P B) { return P(A.x+B.x,A.y+B.y); }    friend P operator* (P A,double p) { return P(A.x*p,A.y*p); }    friend P operator/ (P A,double p) { return P(A.x/p,A.y/p); }    friend bool operator< (const P& a,const P& b) {return dcmp(a.x-b.x)<0 ||(dcmp(a.x-b.x)==0&& dcmp(a.y-b.y)<0 );}    P operator-()const {return P(-x,-y);}}; P read_point() {    P a;    scanf("%lld%lld",&a.x,&a.y);    return a;   } bool operator==(const P& a,const P& b) {    return a.x==b.x&&a.y==b.y;} bool operator!=(const P& a,const P& b) {    return a.x!=b.x||a.y!=b.y;} typedef P V;ll Cross(V A,V B) {return A.x*B.y - A.y*B.x;}int n=4,a[1000][100];P p[1000];bool OnRay(P a,V v,P b){    return  (dcmp(Cross(b-a,v))==0 && dcmp(Dot(b-a,v))>=0) ; }double x_max=10000;P c;bool RayIntesection(P a,V v,P b,V w){    int det=Cross(v,w);    if(dcmp(det)==0) {        if (!OnRay(a,v,b) && !OnRay(b,w,a)) return false;    } else {        int s = Cross(b-a,w), t = Cross(b-a,v);        if (s*det < 0 || t*det < 0) return false;        double ss = double(s)/det;        double cx = a.x+ss*v.x,cy = a.y+ss*v.y;        if (abs(cx) > x_max || abs(cy) > x_max) return false;    }    return true;} typedef pair<int,P> state;int dist[100][100][100];int main(){    memset(dist,0x3f3f3f3f,sizeof(dist));//  freopen("c.in","r",stdin);//  freopen("c.out","w",stdout);    For(i,4) {        For(j,4) {            a[i][j]=read();            p[a[i][j]-1]=P(j,-i+5);        }    }    vector<P> vs;    Fork(x,-30,30) Fork(y,-30,30) if(abs(__gcd(x,y))==1) {        vs.pb(P(x,y));    }     deque<state> q;    for(auto v:vs) {        dist[v.x+50][v.y+50][0] = 1;        q.emplace_back(0,v);    }    auto relax = [&] (state s,state t,int len){        if(dist[t.se.x+50][t.se.y+50][t.fi]>dist[s.se.x+50][s.se.y+50][s.fi]+len) {            dist[t.se.x+50][t.se.y+50][t.fi]=dist[s.se.x+50][s.se.y+50][s.fi]+len;            if(!len) q.push_front(t);            else q.push_back(t);        }    };    int ans=1e9+7;    int an[16];    Rep(i,16) an[i]=INF;    while(!q.empty()){        int i; P v;        tie(i,v) = q.front();        q.pop_front();        an[i]=min(an[i],dist[v.x+50][v.y+50][i]);        if (i==15) {            ans=min(ans,dist[v.x+50][v.y+50][i])    ;            continue;        }        for(auto w:vs) {            if (v!=w) {                relax({i,v},{i,w},1); //正好在点i改变方向             }        }        if(OnRay(p[i],v,p[i+1])) {            relax({i,v},{i+1,v},0); //不改变方向 //          cerr<<i<<' '<<dist[v.x+50][v.y+50][i+1]<<endl;        }        for(auto w:vs) {            if (v!=w) {                if (!RayIntesection(p[i],v,p[i+1],-w)) continue;                relax({i,v},{i+1,w},1); //在i点延长出去某点改变方向            }        }    }//  Rep(i,16) cerr<<an[i]<<' ';puts("");    cout<<ans<<endl;    return 0;}