北京G，计算几何，线段相交

bfs肯定没问题了，

不过中间的判断非常恶心

关键是三角形

出题人：这题很容易怀疑人生

提供几组数据(from zm)

2
0 0
0 2
2 0
..
..
2
1 1
0 1
1 0
..
..
2
0.5 0.5
0.5 1.5
1.5 0.5
..
..

计算几何的边界好搞啊

#include <set>
#include <cmath>
#include <queue>
#include <cstdio>
#include <vector>
#include <cstring>
#include <iostream>
#include <algorithm>
typedef long long LL;
using namespace std;
const int N = 22;
const int dx[] = {-1, -1, -1,  0,  0,  1,  1,  1};
const int dy[] = {-1,  0,  1, -1,  1, -1,  0,  1};

struct point{
    double x, y;

    point():x(0), y(0){}
    point(double _x, double _y): x(_x),y(_y){}
    inline void read(){
        scanf("%lf%lf", &x, &y);
    }
    point operator + (const point &a) const {
        return point(x+a.x, y+a.y);
    }
    point operator - (const point &a) const {
        return point(x-a.x, y-a.y);
    }
    point operator * (const double &k) const {
        return point(x * k, y * k);
    }
    double operator ^ (const point &a) const {  // det
        return x*a.y - y*a.x;
    }
    double dis(const point &b) {
        return (x-b.x)*(x-b.x) + (y-b.y)*(y-b.y);
    }
    inline void print(){
        printf("point: (%.2lf, %.2lf)\n", x, y);
    }
    bool onSeg(point P1, point P2){
        point Q = point(x, y);
        if (min(P1.x,P2.x) > Q.x || Q.x > max(P1.x,P2.x)) return false;
        if (min(P1.y,P2.y) > Q.y || Q.y > max(P1.y,P2.y)) return false;
        double ans = fabs((Q - P1) ^ (Q - P2));
        //printf("??? = %.4lf\n", ans);
        if (fabs((Q - P1) ^ (Q - P2)) > 0) return false;
        return true;
    }
} A, B, C;

double s(point p, point a, point b){
    return fabs((p - a) ^ (p - b));
}
bool inTra(point P, point A, point B, point C){
    double s1 = s(P, A, B), s2 = s(P, B, C), s3 = s(P, C, A);
    if (s1 == 0 || s2 == 0 || s3 == 0) return false;
    double a =  s1 + s2 + s3;
    double b = s(A, B, C);
    //printf("%.2lf\n", a-b);
    return fabs(a - b) == 0.;
}

bool segXseg(point p1, point p2, point p3, point p4){
    if (p1.onSeg(p3, p4) || p2.onSeg(p3, p4)) return false;
    if (p3.onSeg(p1, p2) || p4.onSeg(p1, p2)) return false;
    //---------------------------------------------
    if (max(p1.x, p2.x) < min(p3.x, p4.x)) return 0;
    if (max(p1.y, p2.y) < min(p3.y, p4.y)) return 0;
    if (max(p3.x, p4.x) < min(p1.x, p2.x)) return 0;
    if (max(p3.y, p4.y) < min(p1.y, p2.y)) return 0;//ju xin shi yan

    double x = (p3 - p1) ^ (p2 - p1);
    double y = (p4 - p1) ^ (p2 - p1);
    double z = (p1 - p3) ^ (p4 - p3);
    double w = (p2 - p3) ^ (p4 - p3); //KuaLi
    return x*y <= 0 && z*w <= 0;
}

bool xj(point p1, point p2, point A, point B, point C){  //xiangjiao
    //for (double k = 0.01; k < 1; k += 0.01)
        //if (inTra((p1*k + p2*(1-k)), A, B, C)) return true;
    if (inTra(p1*0.01 + p2*0.99, A, B, C)) return true;
    if (inTra(p1*0.99 + p2*0.01, A, B, C)) return true;
    if (segXseg(p1, p2, A, B)) return true;
    if (segXseg(p1, p2, A, C)) return true;
    if (segXseg(p1, p2, C, B)) return true;
    return false;
}

bool wea[N][N];  // weather
bool vis[N][N];
int step[N][N];

int bfs(const int &n, int sx, int sy){
    if (!wea[sx][sy]) return -1;
    memset(vis, false, sizeof vis);
    vis[sx][sy] = true;
    step[sx][sy] = 0;
    queue <point> Q;
    for (Q.push(point(sx, sy)); !Q.empty();){
        point p = Q.front(); Q.pop();
        if (p.x == n-1 && p.y == n-1) return step[n-1][n-1]; 
        for (int i = 0; i < 8; i++){
            int cx = (int)p.x + dx[i];
            int cy = (int)p.y + dy[i];
            if (cx < 0 || cx >= n|| cy < 0 || cy >= n) continue;
            if (!wea[cx][cy] || vis[cx][cy]) continue;  //weather
            if (xj(p, point(cx, cy), A, B, C)) continue;
            step[cx][cy] = step[(int)p.x][(int)p.y] + 1;
            vis[cx][cy] = true;
            //printf("-----------(%d, %d)->(%d, %d), %d\n", (int)p.x, (int)p.y, cx, cy, step[cx][cy]);
            Q.push(point(cx, cy));
        }
    }
    return -1;
}

int main(){
    //freopen("in.txt", "r", stdin);
    char ch;
    for (int n; ~scanf("%d", &n);){
        A.read(); B.read(); C.read();
        memset(wea, true, sizeof wea);
        for (int i = 0; i < n; i ++)
            for (int j = 0; j < n; j++) if (inTra(point(i, j), A, B, C)) {
                //printf("%d, %d\n", i, j);
                wea[i][j] = false;
            }
        scanf("\n");
        for (int j = n-1; j >= 0; j--){
            for (int i = 0; i < n; i++){ 
                scanf("%c", &ch);
                if (ch == '#') wea[i][j] = false;
            }
            scanf("\n");
        }
        int ans = bfs(n, 0, 0);
        printf("%d\n", ans);
    }
    return 0;
}