UVA 11796 Dog Distance 向量+相对运动

题意：训练指南261页

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <vector>
#include <queue>
#include <map>
#include <algorithm>
#include <set>
using namespace std;
#define MM(a) memset(a,0,sizeof(a))
typedef long long ll;
typedef unsigned long long ULL;
const int mod = 1000000007;
const double eps = 1e-10;
const int inf = 0x3f3f3f3f;
const int big=50000;

struct Point {
    double x, y;
    Point(double x = 0, double y = 0) : x(x) , y(y) { }
};

typedef Point Vector;

Vector operator + (Vector A, Vector B) { return Vector(A.x+B.x, A.y+B.y); }
Vector operator - (Vector A, Vector B) { return Vector(A.x-B.x, A.y-B.y); }
Vector operator * (Vector A, double p) { return Vector(A.x*p, A.y*p); }
Vector operator / (Vector A, double p) { return Vector(A.x/p, A.y/p); }

bool operator < (const Point& a, const Point& b) {
    return a.x < b.x || (a.x == b.x && a.y < b.y);
}

int dcmp(double x) {
    if(fabs(x) < eps) return 0; else return x < 0 ? -1 : 1;
}

bool operator == (const Point& a, const Point& b) {
    return dcmp(a.x - b.x) == 0 && dcmp(a.y - b.y) == 0;
}

double Dot(Vector A, Vector B) { return A.x*B.x + A.y*B.y; }
double Length(Vector A) { return sqrt(Dot(A, A)); }
double Angle(Vector A, Vector B) { return acos(Dot(A, B) / Length(A) / Length(B)); }

double Cross(Vector A, Vector B) { return A.x*B.y - A.y*B.x; }
double Area2(Point A, Point B, Point C) { return Cross(B-A, C-A); }

Vector Rotate(Vector A, double rad) {
    return Vector(A.x*cos(rad) - A.y*sin(rad), A.x*sin(rad)+A.y*cos(rad) );
}

Vector Normal(Vector A) {
    double L = Length(A);
    return Vector(-A.y/L, A.x/L);
}

Point GetLineIntersection(Point P, Vector v, Point Q, Vector w) {
    Vector u = P - Q;
    double t = Cross(w, u) / Cross(v, w);
    return P + v * t;
}

double DistanceToLine(Point P, Point A, Point B) {
    Vector v1 = B-A, v2 = P - A;
    return fabs(Cross(v1,v2) / Length(v1));
}

double DistanceToSegment(Point P, Point A, Point B) {
    if(A==B) return Length(P-A);
    Vector v1 = B - A, v2 = P - A, v3 = P - B;
    if(dcmp(Dot(v1, v2)) < 0) return Length(v2);
    else if(dcmp(Dot(v1, v3)) > 0) return Length(v3);
    else return fabs(Cross(v1, v2)) / Length(v1);
}

Point GetLineProjection(Point P, Point A, Point B) {
    Vector v = B - A;
    return A + v * ( Dot(v, P-A) / Dot(v, v) );
}

bool SegmentProperIntersection(Point a1, Point a2, Point b1, Point b2) {
    double c1 = Cross(a2 - a1, b1 - a1), c2 = Cross(a2 - a1, b2 - a1),
            c3 = Cross(b2 - b1, a1 - b1), c4 = Cross(b2 - b1, a2 - b1);
    return dcmp(c1) * dcmp(c2) < 0 && dcmp(c3) * dcmp(c4) < 0;
}

bool OnSegment(Point p, Point a1, Point a2) {
    return dcmp(Cross(a1 - p, a2 - p)) == 0 && dcmp(Dot(a1 - p, a2 - p)) < 0;
}

double ConvexPolygonArea(Point* p, int n) {
    double area = 0;
    for(int i = 1; i < n-1; i++)
        area += Cross(p[i] - p[0], p[i + 1] - p[0]);
    return area / 2;
}

int numa,numb;
Point a[55],b[55];
void input()
{
    scanf("%d",&numa);
    scanf("%d",&numb);
    for(int i=1;i<=numa;i++)
        {
            scanf("%lf %lf",&a[i].x,&a[i].y);
           // printf("|||ai:%f  %f\n",a[i].x,a[i].y);
        }
    for(int i=1;i<=numb;i++)
        {
            scanf("%lf %lf",&b[i].x,&b[i].y);
           // printf("|||ai:%f  %f\n",b[i].x,b[i].y);
        }
}

void solve(int i)
{
   double lena=0,lenb=0;
   for(int i=2;i<=numa;i++)
        lena+=Length(a[i]-a[i-1]);
   for(int i=2;i<=numb;i++)
        lenb+=Length(b[i]-b[i-1]);
   //printf("|||lena:%f  lenb:%f\n",lena,lenb);
   Point sa=a[1],sb=b[1];
   int pa=1,pb=1;
   double minn=inf,maxn=0;
   while(pa<numa&&pb<numb)
   {
       Vector a1=a[pa+1]-sa;
       Vector b1=b[pb+1]-sb;
       double disa=Length(a1);
       double disb=Length(b1);
       //printf("|||disa:%f  disb:%f\n",disa,disb);
       double t=min(disa/lena,disb/lenb);
       a1=a1*t/(disa/lena);
       b1=b1*t/(disb/lenb);

       Point c=b1-a1;
       minn=min(minn,DistanceToSegment(sa,sb,sb+c));
       maxn=max(maxn,Length(sb-sa));
       maxn=max(maxn,Length(sb+c-sa));
       sa=sa+a1;
       //printf("sa:%f %f\n",sa.x,sa.y);
       if(sa==a[pa+1]) pa++;
       sb=sb+b1;
       //printf("sb:%f %f\n",sb.x,sb.y);
       if(sb==b[pb+1]) pb++;
   }
   printf("Case %d: %d\n",i,(int)(maxn-minn+0.5));
}

int main()
{
    int cas;
    scanf("%d",&cas);
    for(int i=1;i<=cas;i++)
    {
        input();
        solve(i);
    }
}

分析：向量的运用，训练指南上讲的也很详细