POJ 1113 凸包
易知先求凸包,然后圆弧部分跟每个内角有关
经过计算发现圆弧总共加起来就是一个圆
#include <iostream> #include <cstdio> #include <cstring> #include <string> #include <algorithm> #include <cstdlib> #include <cmath> #include <map> #include <sstream> #include <queue> #include <vector> #define MAXN 111111 #define MAXM 211111 #define PI acos(-1.0) #define eps 1e-8 #define INF 1000000001 using namespace std; int dblcmp(double d) { if (fabs(d) < eps) return 0; return d > eps ? 1 : -1; } struct point { double x, y; point(){} point(double _x, double _y): x(_x), y(_y){}; void input() { scanf("%lf%lf",&x, &y); } double dot(point p) { return x * p.x + y * p.y; } double distance(point p) { return hypot(x - p.x, y - p.y); } point sub(point p) { return point(x - p.x, y - p.y); } double det(point p) { return x * p.y - y * p.x; } bool operator < (point a)const { return dblcmp(a.x - x) == 0 ? dblcmp(y - a.y) < 0 : x < a.x; } }p[MAXN]; struct line { point a, b; line(){} line(point _a, point _b){ a = _a; b = _b;} }; struct polygon { int n; point p[MAXN]; line l[MAXN]; double area; double circum; void input() { for(int i = 0; i < n; i++) p[i].input(); } void getline() { for(int i = 0; i < n; i++) l[i] = line(p[i], p[(i + 1) % n]); } void getarea() { area = 0; int a = 1, b = 2; while(b <= n - 1) { area += p[a].sub(p[0]).det(p[b].sub(p[0])); a++; b++; } area = fabs(area) / 2; } void getcircum() { circum = 0; for(int i = 0; i < n; i++) circum += l[i].a.distance(l[i].b); } }convex; bool conpoint(point p[],int n) { for (int i = 1; i < n; i++) if (dblcmp(p[i].x - p[0].x) != 0 || dblcmp(p[i].y - p[0].y) != 0) return false; return true; } bool conline(point p[],int n) { for (int i = 2; i < n; i++) if (dblcmp(p[1].sub(p[0]).det(p[i].sub(p[0]))) != 0) return false; return true; } void getconvex(point p[], int n, point res[], int& resn) { resn = 0; if (conpoint(p, n)) { res[resn++] = p[0]; return; } sort(p, p + n); if (conline(p,n)) { res[resn++] = p[0]; res[resn++] = p[n - 1]; return; } for (int i = 0; i < n;) if (resn < 2 || dblcmp(res[resn - 1].sub(res[resn - 2]).det(p[i].sub(res[resn - 1]))) > 0) res[resn++] = p[i++]; else --resn; int top = resn - 1; for (int i = n - 2; i >= 0;) if (resn < top + 2 || dblcmp(res[resn - 1].sub(res[resn - 2]).det(p[i].sub(res[resn - 1]))) > 0) res[resn++] = p[i--]; else --resn; resn--; } double L; int n; int main() { while(scanf("%d%lf", &n, &L) != EOF) { for(int i = 0; i < n; i++) p[i].input(); getconvex(p, n, convex.p, convex.n); convex.getline(); convex.getcircum(); printf("%d\n", (int)(2 * L * PI + convex.circum + 0.5)); } return 0; }
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