标签:顶点 push 老师 poi cas main cti c++ gif
此题是刘汝佳老师书里的例题,P260
欧拉定理: 设平面图的顶点数为V,边数为E,面数为F,则 V + F - E = 2;
注意这里的面数包括了外面那个面。 例如
这个图的面数 为 2, 因为包括了封闭面外面那个面。
#include <bits/stdc++.h> #define LL long long #define mem(i, j) memset(i, j, sizeof(i)) #define rep(i, j, k) for(int i = j; i <= k; i++) #define dep(i, j, k) for(int i = k; i >= j; i--) #define pb push_back #define make make_pair #define INF INT_MAX #define inf LLONG_MAX #define PI acos(-1) using namespace std; const int N = 310; struct Point { double x, y; Point(double x = 0, double y = 0) : x(x), y(y) { } /// 构造函数 }; typedef Point Vector; /// 向量+向量=向量, 点+向量=向量 Vector operator + (Vector A, Vector B) { return Vector(A.x + B.x, A.y + B.y); } ///点-点=向量 Vector operator - (Point A, Point B) { return Vector(A.x - B.x, A.y - B.y); } ///向量*数=向量 Vector operator * (Vector A, double p) { return Vector(A.x * p, A.y * p); } ///向量/数=向量 Vector operator / (Vector A, double p) { return Vector(A.x / p, A.y / p); } const double eps = 1e-10; 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 a.x == b.x ? a.y < b.y : a.x < b.x; } 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; } Vector Rotate(Vector A, double rad) { return Vector(A.x*cos(rad) - A.y*sin(rad), A.x*sin(rad) + A.y*cos(rad)); } 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; } bool SegmentProperInsection(Point a1, Point a2, Point b1, Point b2) { double c1 = Cross(a2 - a1, b1 - a1), c2 = Cross(a2 - a1, b2 - a1); double 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; } Point P[N], v[N * N]; int main() { int n, Case = 0; while(scanf("%d", &n) == 1 && n ) { rep(i, 0, n - 1) { scanf("%lf %lf", &P[i].x, &P[i].y); v[i] = P[i]; } n--; int cnt = n, tot = n; rep(i, 0, n - 1) rep(j, i + 1, n - 1) if(SegmentProperInsection(P[i], P[i + 1], P[j], P[j + 1])) v[cnt++] = GetLineIntersection(P[i], P[i + 1] - P[i], P[j], P[j + 1] - P[j]); sort(v, v + cnt); cnt = unique(v, v + cnt) - v; rep(i, 0, cnt - 1) rep(j, 0, n - 1) if(OnSegment(v[i], P[j], P[j + 1])) tot++; printf("Case %d: There are %d pieces.\n", ++Case, tot + 2 - cnt); } return 0; }
LA 3263 (欧拉定理 + 判断线段相交 + 求线段交点)
标签:顶点 push 老师 poi cas main cti c++ gif
原文地址:https://www.cnblogs.com/Willems/p/12321848.html