【poj3608】 Bridge Across Islands

时间：2023-03-08 16:15:05

http://poj.org/problem?id=3608 (题目链接)

题意

　　求两凸包间最短距离

Solution

　　难写难调，旋转卡壳，还真是卡死我了。

　　先分别选出两凸包最上点和最下点，从这两点开始向逆时针方向旋转卡壳。用叉乘判断是否旋转旋转，具体操作跟求凸包直径差不多。

poj discuss蒯下来的数据制造器：

#include<algorithm>

#include<iostream>

#include<cstdlib>

#include<cstdio>

#include<cmath>

using namespace std;

struct point{double x,y;};

struct polygon

{

    int n;

    point data[10];

};

#define N   16

polygon p[N]={

    {4,{{0,0},{-1,0},{-1,-1},{0,-1}}},

    {4,{{2,0},{2,-1},{3,-1},{3,0}}},

    {4,{{247,208},{247,235},{375,235},{375,208}}},

    {3,{{85 ,101},{116 ,168},{168 ,103}}},

    {3,{{131 ,189},{216 ,148},{196 ,209}}},

    {3,{{180 ,127},{246 ,127},{202 ,144}}},

    {3,{{226 ,201},{297 ,201},{242 ,151}}},

    {3,{{42 ,225},{61 ,261},{100,222}}},

    {3,{{84 ,261},{99 ,246},{102,260}}},

    {3,{{72,309},{157,224},{167,309}}},

    {3,{{170,221},{229,221},{199,245}}},

    {3,{{190,90},{153,47},{225,108}}},

    {3,{{165,230},{168,242},{172,233}}},

    {6,{{143,146},{133,156},{138,170},{150,173},{161,166},{161,152}}},

    {5,{{109,208},{100,236},{111,253},{122,250},{161,206}}},

    {6,{{177,273},{174,309},{202,377},{417,375},{490,270},{268,239}}}

    };

int main()

{

    srand(time(NULL));

    //freopen("aaa.in","w",stdout);

    int i=0,j=0,k,num=0;

    while (i==j) i=rand()%N,j=rand()%N;

    num++;

    //if(num>35||num<=33)continue;

    printf("%d %d\n",p[i].n,p[j].n);

    for(k=0;k<p[i].n;k++)

        printf("%lf %lf\n",p[i].data[k].x,p[i].data[k].y);

    for(k=0;k<p[j].n;k++)

        printf("%lf %lf\n",p[j].data[k].x,p[j].data[k].y);

    printf("0 0\n");

    return 0;

}

代码

// poj3608

#include<algorithm>

#include<iostream>

#include<cstring>

#include<cstdlib>

#include<cstdio>

#include<cmath>

#include<map>

#define esp 1e-8

#define inf 2147483640

#define LL long long

#define Pi acos(-1.0)

#define free(a) freopen(a".in","r",stdin);freopen(a".out","w",stdout);

using namespace std;

inline LL getint() {

    LL x=0,f=1;char ch=getchar();

    while (ch>'9' || ch<'0') {if (ch=='-') f=-1;ch=getchar();}

    while (ch>='0' && ch<='9') {x=x*10+ch-'0';ch=getchar();}

    return x*f;

}

const int maxn=10010;

struct point {

    double x,y;

    point() {};

    point (double _x,double _y):x(_x),y(_y){}

    friend point operator - (const point &a,const point &b) {

        point x;

        x.x=a.x-b.x;x.y=a.y-b.y;

        return x;

    }

}p1[maxn],p2[maxn],p0;

int sn[maxn],sm[maxn],n,m;

double cross(point p0,point p1,point p2) { //叉乘

    return (p1.x-p0.x)*(p2.y-p0.y)-(p2.x-p0.x)*(p1.y-p0.y);

}

double dis(point a,point b) { //点a与点b之间的距离

    return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));

}

bool cmp(point a,point b) { //极角排序

    double t=cross(p0,a,b);

    if (t<0) return 0;

    if (t>0) return 1;

    return dis(p0,a)<dis(p0,b);

}

int dcmp(double x) { //double比较

    return fabs(x)<esp ? 0 : (x>0 ? 1 : -1);

}

int Graham(int n,point *p) { //求凸包

    int k=1,top=2;

    for (int i=2;i<=n;i++)

        if (p[i].x==p[k].x ? p[i].y<p[k].y : p[i].x<p[k].x) k=i;

    p0=p[k];p[k]=p[1];p[1]=p0;

    sort(p+2,p+1+n,cmp);

    for (int i=3;i<=n;i++) {

        while (top>1 && cross(p[top-1],p[top],p[i])<=0) top--;

        p[++top]=p[i];

    }

    return top;

}

double pldis(point a,point b,point c) { //点a到线段bc的最短距离

    point s(a-b),t(c-b);

    if (s.x*t.x+s.y*t.y<0) return dis(a,b);

    s=(a-c);t=(b-c);

    if (s.x*t.x+s.y*t.y<0) return dis(a,c);

    return fabs(cross(a,b,c))/dis(b,c);

}

double lldis(point a,point b,point c,point d) { //线段ab与线段cd的最短距离

    return min(min(pldis(a,c,d),pldis(b,c,d)),min(pldis(c,a,b),pldis(d,a,b)));

}

double RC(point *pl,point *pr,int p,int q,int n,int m) { //旋转卡壳

    double tmp,minl=1e90;

    pl[n+1]=pl[1];pr[m+1]=pr[1];

    for (int i=1;i<=n;i++) {

        while ((tmp=cross(pl[p+1],pr[q+1],pl[p])-cross(pl[p+1],pr[q],pl[p]))>esp) q=q%m+1;

        if (tmp<-esp) minl=min(minl,pldis(pr[q],pl[p],pl[p+1]));

        else minl=min(minl,lldis(pl[p],pl[p+1],pr[q],pr[q+1]));

        p=p%n+1;

    }

    return minl;

}

void clocksort() { //逆时针排序

    p0.x=0;p0.y=0;

    for (int i=1;i<=n;i++) {p0.x+=p1[i].x;p0.y+=p1[i].y;}

    p0.x/=n;p0.y/=n;

    sort(p1+1,p1+1+n,cmp);

    p0.x=0;p0.y=0;

    for (int i=1;i<=m;i++) {p0.x+=p2[i].x;p0.y+=p2[i].y;}

    p0.x/=m;p0.y/=m;

    sort(p2+1,p2+1+m,cmp);

}

int main() {

    while (scanf("%d%d",&n,&m)!=EOF && n && m) {

        for (int i=1;i<=n;i++) scanf("%lf%lf",&p1[i].x,&p1[i].y);

        for (int i=1;i<=m;i++) scanf("%lf%lf",&p2[i].x,&p2[i].y);

        n=Graham(n,p1);

        m=Graham(m,p2);

        //clocksort();

        int l=1,r=1;

        for (int i=1;i<=n;i++) if (dcmp(p1[i].y-p1[l].y)<0) l=i; //最下点

        for (int i=1;i<=m;i++) if (dcmp(p2[i].y-p2[r].y)>0) r=i; //最上点

        printf("%.5lf\n",min(RC(p1,p2,l,r,n,m),RC(p2,p1,r,l,m,n)));

    }

    return 0;

}

　　

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