题意:两只狗在折线上跑,速度未知,同时出发,同时达到。问跑的过程中,两狗的最大距离和最小距离的差
分析:训练指南P261,考虑相对运动,设A静止不动,B相对A运动,相对的运动向量:Vb - Va(可以理解为速度矢量),那么就是pa到线段pb-pb+Vb-Va的距离最值
/************************************************ * Author :Running_Time * Created Time :2015/10/22 星期四 10:21:19 * File 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 | 1 typedef long long ll; const int N = 55 + 10; const int INF = 0x3f3f3f3f; const int MOD = 1e9 + 7; const double EPS = 1e-10; struct 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]; double 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, &nb); for (int i=0; i<na; ++i) scanf ("%lf%lf", &A[i].x, &A[i].y); for (int i=0; i<nb; ++i) scanf ("%lf%lf", &B[i].x, &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; }
时间: 2024-10-20 15:00:52