【LA 3263】That Nice Euler Circuits (Shanghai 2004)（计算几何）

Description

Solution

Dot(Vector A, Vector B

Source

/**********************************************************
* Happy Spring Festival !
* Au: Hany01
* Prob: [LA3263] That Nice Euler Circuits, Shanghai 2004
* Date: Feb 9th, 2018
* Email: hany01@foxmail.com
**********************************************************/

#include<bits/stdc++.h>

using namespace std;

typedef long long LL;
typedef pair<int, int> PII;
typedef vector<int> VI;
#define rep(i , j) for (int i = 0 , i##_end_ = j; i < i##_end_ ; ++ i)
#define For(i , j , k) for (int i = (j) , i##_end_ = (k) ; i <= i##_end_ ; ++ i)
#define Fordown(i , j , k) for (int i = (j) , i##_end_ = (k) ; i >= i##_end_ ; -- i)
#define Set(a , b) memset(a , b , sizeof(a))
#define SZ(a) ((int)(a.size()))
#define ALL(a) a.begin(), a.end()
#define pb(a) push_back(a)
#define mp(a, b) make_pair(a, b)
#define INF (0x3f3f3f3f)
#define INF1 (2139062143)
#define Mod (1000000007)
#define y1 wozenmezhemecaia
#ifdef hany01
#define debug(...) fprintf(stderr , __VA_ARGS__)
#else
#define debug(...)
#endif

inline void File() {
#ifdef hany01
freopen("LA3263.in" , "r" , stdin);
freopen("LA3263.out" , "w" , stdout);
#endif
}

template<typename T> inline bool chkmax(T &a, T b) { return a < b ? a = b, 1 : 0; }
template<typename T> inline bool chkmin(T &a, T b) { return b < a ? a = b, 1 : 0; }

inline int read() {
register char c_; register int _ , __;
for (_ = 0 , __ = 1 , c_ = getchar() ; !isdigit(c_) ; c_ = getchar()) if (c_ == '-')  __ = -1;
for ( ; isdigit(c_) ; c_ = getchar()) _ = (_ << 1) + (_ << 3) + (c_ ^ 48);
return _ * __;
}

const double eps = 1e-10;

const int maxn = 305, maxv = 90005;

struct Point
{
double x, y;
Point(double x = 0, double y = 0): x(x), y(y) {}
};
typedef Point Vector;

int dcmp(double x) { if (fabs(x) < eps) return 0; return x < 0 ? -1 : 1; }
Vector operator + (Vector A, Vector B) { return Point(A.x + B.x, A.y + B.y); }
Vector operator - (Vector A, Vector B) { return Point(A.x - B.x, A.y - B.y); }
Vector operator * (Vector A, double p) { return Point(A.x * p, A.y * p); }
Vector operator / (Vector A, double p) { return Point(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) && !dcmp(a.y - b.y); }
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; }
bool SegmentProperIntersection(Point A1, Point A2, Point B1, Point B2) {
double c1 = Cross(A2 - A1, B1 - A1), c2 = Cross(A2 - A1, B2 - A1),
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 A, Point B) { return !dcmp(Cross(A - P, B - P)) && dcmp(Dot(A - P, B - P)) < 0; }
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; }

int n, e, cnt, Case;
Point p[maxn], v[maxv];

int main()
{
File();
while (scanf("%d", &n) != EOF && n) {
For(i, 1, n) scanf("%lf%lf", &p[i].x, &p[i].y), v[i] = p[i];
cnt = e = n - 1;
For(i, 1, n - 1) For(j, i + 1, n - 1) if (SegmentProperIntersection(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 + 1, v + 1 + cnt);
cnt = unique(v + 1, v + 1 + cnt) - v - 1;
For(i, 1, cnt) For(j, 1, n - 1) if (OnSegment(v[i], p[j], p[j + 1])) ++ e;
printf("Case %d: There are %d pieces.\n", ++ Case, e - cnt + 2);
}
return 0;
}