本文主要是介绍uva 1342 欧拉定理（计算几何模板），希望对大家解决编程问题提供一定的参考价值，需要的开发者们随着小编来一起学习吧！
题意：
给几个点，把这几个点用直线连起来，求这些直线把平面分成了几个。
解析：
欧拉定理：
顶点数 + 面数 - 边数= 2。
代码：
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <cstring>
#include <cmath>
#include <stack>
#include <vector>
#include <queue>
#include <map>
#include <climits>
#include <cassert>
#define LL long longusing namespace std;
const int inf = 0x3f3f3f3f;
const double eps = 1e-8;
const double pi = acos(-1.0);
const double ee = exp(1.0);/
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 - (Point A, Point 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)//µ¥Î»·¨Ïß turn left 90 degrees
{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;
}bool SegmentProperIntersection(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 readPoint()
{double x, y;scanf("%lf %lf", &x, &y);return Point(x, y);
}const int maxn = 300 + 10;
Point P[maxn], V[maxn * maxn];int main()
{#ifdef LOCALfreopen("in.txt", "r", stdin);#endif // LOCALint ca = 1;int n;while (scanf("%d", &n) && n){for (int i = 0; i < n; i++){P[i] = readPoint();V[i] = P[i];}n--;int c = n, e = n;for (int i = 0; i < n; i++){for (int j = i + 1; j < n; j++){if (SegmentProperIntersection(P[i], P[i + 1], P[j], P[j + 1])){V[c++] = GetLineIntersection(P[i], P[i + 1] - P[i], P[j], P[j + 1] - P[j]);}}}sort(V, V + c);c = unique(V, V + c) - V;for (int i = 0; i < c; i++){for (int j = 0; j < n; j++){if (OnSegment(V[i], P[j], P[j + 1]))e++;}}printf("Case %d: There are %d pieces.\n", ca++, e + 2 - c);}return 0;
}
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