Simple geometry (relative motion distance max) UVA 11796 Dog Distance

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Test instructions: Two dogs running on a polyline, the speed is unknown, at the same time to go, at the same time. The difference between the maximum distance and the minimum distance between two dogs during a run

Analysis: Training Guide P261, consider the relative motion, set a stationary, B relative a motion, the relative motion vector: vb-va (can be understood as the speed vector), then is the PA to the line segment Pb-pb+vb-va distance maximum

/************************************************* author:running_time* Created time:2015/10/22 Thursday 10:21:19* Fi Le Name:UVA_11796.cpp ************************************************/#include <cstdio> #include < algorithm> #include <iostream> #include <sstream> #include <cstring> #include <cmath># Include <string> #include <vector> #include <queue> #include <deque> #include <stack># Include <list> #include <map> #include <set> #include <bitset> #include <cstdlib> #include <ctime>using namespace std; #define Lson L, Mid, RT << 1#define Rson mid + 1, R, RT << 1 | 1typedef long Ll;const int N = + 10;const int INF = 0x3f3f3f3f;const int MOD = 1e9 + 7;const Double EPS = 1e-10;st    Ruct point {double x, y; Point (Double x=0, double y=0): X (x), Y (y) {}};typedef point vector;double dot (vector A, vector b) {return a.x * b . x + a.y * B.Y;} Double Cross (Vector A, VecTor B) {return a.x * b.y-a.y * b.x;}    int dcmp (double x) {if (Fabs (x) < EPS) return 0; else return x < 0? -1:1;} 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);} BOOL operator = = (Const point &a, const point &b) {return dcmp (a.x-b.x) = = 0 && dcmp (a.y-b.y) = = 0;} Double Length (Vector a) {return sqrt (dot (A, a));}    Double dis_to_seg (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 A[n], b[n];d ouble mx, mn;void updata (point P, point A, point B) {mn = min (mn, dis_to_seg (P, A, B)); mx = max (mx, max (Length (p-a), Length (p-b)));}    int main (void) {int T, cas = 0; scanf ("%d", &t);   while (t--) {int na, NB;        scanf ("%d%d", &na, &AMP;NB);        for (int i=0; i<na; ++i) scanf ("%lf%lf", &a[i].x, &AMP;A[I].Y);        for (int i=0; i<nb; ++i) scanf ("%lf%lf", &b[i].x, &AMP;B[I].Y);        Double Lena = 0, LenB = 0;        for (int i=0; i<na-1; ++i) Lena + = Length (a[i+1]-a[i]);        for (int i=0; i<nb-1; ++i) LenB + = Length (b[i+1]-b[i]);        int sa = 0, sb = 0;   mx = -1e9;        MN = 1e9;        Point pa = a[0], PB = B[0];            while (SA < na-1 && SB < nb-1) {double la = length (a[sa+1]-PA);            Double lb = length (b[sb+1]-Pb); Double tim = min (LA/Lena, LB/LENB);            Vector Va = (a[sa+1]-PA)/La * Tim * LENA;            Vector Vb = (b[sb+1]-Pb)/lb * Tim * LENB;            Updata (PA, Pb, Pb + Vb-va);            PA = pa + Va;            PB = Pb + Vb;            if (PA = = a[sa+1]) sa++;        if (Pb = = b[sb+1]) sb++;    } printf ("Case%d:%.0f\n", ++cas, MX-MN); } return 0;}

　　

Simple geometry (relative motion distance max) UVA 11796 Dog Distance