POJ 3449 （给正方形的对角线两点求另外两点坐标 + 判断线段是否相交）

题目：传送门

题意：给许多多边形， 判断多边形是否相交。

 

思路：输入输出挺恶心的，得模拟着做。

 

  给正方形的对角线两点，求另外两点坐标可由下列四条式子推导得到：

　　　x1 + x3 = x0 + x2

　　　y1 + y3 = y0 + y2;

　　   y1 - y3 =  x0 - x2;

　　   x1 - x3  =  y2 - y0;

　

　　  x1 = ( (x0 + x2) + (y2 - y0) ) / 2

　　  y1 = ( (y0 + y2) + (x0 - x2) ) / 2

　　  x3 = ( (x0 + x2) - (y2 - y0) ) / 2

　　  y3 = ( (y0 + y2) - (x0 - x2) ) / 2

 

　然你矩形的 3 个顶点，让你求第4个，直接算：

　　 x3 = x2 + (x0 - x1)

　　 y3 = y2 + (y0 - y1)

 

剩下的模拟即可，挺麻烦的。

 

代码大部分参考了  kuangbin

#include <iostream>
#include <stdio.h>
#include <string.h>
#include <algorithm>
#include <queue>
#include <map>
#include <vector>
#include <set>
#include <string>
#include <math.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;

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

const double eps = 1e-10;

int dcmp(double x) {
    if(fabs(x) < eps) return 0; else return x < 0 ? -1 : 1;
}

Point operator + (Point A, Point B) { return Point(A.x + B.x, A.y + B.y); }
Point operator - (Point A, Point B) { return Point(A.x - B.x, A.y - B.y); }
Point operator * (Point A, double p) { return Point(A.x * p, A.y * p); }
Point operator / (Point A, double p) { return Point(A.x / p, A.y / p); }

double Cross(Point A, Point B) { /// 叉积
    return A.x * B.y - A.y * B.x;
}
double Dot(Point A, Point B) {
    return A.x * B.x + A.y * B.y; /// 点积
}

struct note {
    char id;
    int n;
    Point p[30];
} a[30];

bool cmp(note A, note B) {
    return A.id < B.id;
}

bool SPI(Point a1, Point a2, Point b1, Point b2) { /// 判断线段a1a2与线段b1b2是否相交
    return
    max(a1.x,a2.x) >= min(b1.x,b2.x) &&
    max(b1.x,b2.x) >= min(a1.x,a2.x) &&
    max(a1.y,a2.y) >= min(b1.y,b2.y) &&
    max(b1.y,b2.y) >= min(a1.y,a2.y) &&
    dcmp(Cross(b1 - a2, a1 - a2)) * dcmp(Cross(b2 - a2, a1 - a2)) <= 0 &&
    dcmp(Cross(a1 - b2, b1 - b2)) * dcmp(Cross(a2 - b2, b1 - b2)) <= 0;
}

bool judge(note A, note B) {
    rep(i, 0, A.n - 1) rep(j, 0, B.n - 1)
        if(SPI(A.p[i], A.p[(i + 1) % A.n], B.p[j], B.p[(j + 1) % B.n]))
            return true;
    return false;
}

char s[105];
bool vis[105];

int main() {

    int n;
    while(scanf("%s", s) == 1) {
        if(s[0] == '.') break;
        a[0].id = s[0];
        scanf("%s", s);
        if(strcmp(s,"square")==0) {
            a[0].n = 4;
            scanf(" (%lf,%lf)",&a[0].p[0].x,&a[0].p[0].y);
            scanf(" (%lf,%lf)",&a[0].p[2].x,&a[0].p[2].y);
            a[0].p[1].x = ((a[0].p[0].x+a[0].p[2].x)+(a[0].p[2].y-a[0].p[0].y))/2;
            a[0].p[1].y = ((a[0].p[0].y+a[0].p[2].y)+(a[0].p[0].x-a[0].p[2].x))/2;
            a[0].p[3].x = ((a[0].p[0].x+a[0].p[2].x)-(a[0].p[2].y-a[0].p[0].y))/2;
            a[0].p[3].y = ((a[0].p[0].y+a[0].p[2].y)-(a[0].p[0].x-a[0].p[2].x))/2;
        }
        else if(strcmp(s,"line")==0) {
            a[0].n = 2;
            scanf(" (%lf,%lf)",&a[0].p[0].x,&a[0].p[0].y);
            scanf(" (%lf,%lf)",&a[0].p[1].x,&a[0].p[1].y);
        }
        else if(strcmp(s,"triangle")==0) {
            a[0].n = 3;
            scanf(" (%lf,%lf)",&a[0].p[0].x,&a[0].p[0].y);
            scanf(" (%lf,%lf)",&a[0].p[1].x,&a[0].p[1].y);
            scanf(" (%lf,%lf)",&a[0].p[2].x,&a[0].p[2].y);
        }
        else if(strcmp(s,"rectangle")==0) {
            a[0].n = 4;
            scanf(" (%lf,%lf)",&a[0].p[0].x,&a[0].p[0].y);
            scanf(" (%lf,%lf)",&a[0].p[1].x,&a[0].p[1].y);
            scanf(" (%lf,%lf)",&a[0].p[2].x,&a[0].p[2].y);
            a[0].p[3].x = a[0].p[2].x + (a[0].p[0].x - a[0].p[1].x);
            a[0].p[3].y = a[0].p[2].y + (a[0].p[0].y - a[0].p[1].y);
        }
        else if(strcmp(s,"polygon")==0) {
            scanf("%d",&a[0].n);
            rep(i, 0, a[0].n - 1) {
                scanf(" (%lf,%lf)",&a[0].p[i].x,&a[0].p[i].y);
            }
        }

        n = 1;
        while(scanf("%s", s) == 1) {
            if(s[0] == '-')break;
            a[n].id = s[0];
            scanf("%s", s);
            if(strcmp(s,"square")==0) {
                a[n].n = 4;
                scanf(" (%lf,%lf)",&a[n].p[0].x,&a[n].p[0].y);
                scanf(" (%lf,%lf)",&a[n].p[2].x,&a[n].p[2].y);
                a[n].p[1].x = ((a[n].p[0].x+a[n].p[2].x)+(a[n].p[2].y-a[n].p[0].y))/2;
                a[n].p[1].y = ((a[n].p[0].y+a[n].p[2].y)+(a[n].p[0].x-a[n].p[2].x))/2;
                a[n].p[3].x = ((a[n].p[0].x+a[n].p[2].x)-(a[n].p[2].y-a[n].p[0].y))/2;
                a[n].p[3].y = ((a[n].p[0].y+a[n].p[2].y)-(a[n].p[0].x-a[n].p[2].x))/2;
            }
            else if(strcmp(s,"line")==0) {
                a[n].n = 2;
                scanf(" (%lf,%lf)",&a[n].p[0].x,&a[n].p[0].y);
                scanf(" (%lf,%lf)",&a[n].p[1].x,&a[n].p[1].y);
            }
            else if(strcmp(s,"triangle")==0) {
                a[n].n = 3;
                scanf(" (%lf,%lf)",&a[n].p[0].x,&a[n].p[0].y);
                scanf(" (%lf,%lf)",&a[n].p[1].x,&a[n].p[1].y);
                scanf(" (%lf,%lf)",&a[n].p[2].x,&a[n].p[2].y);
            }
            else if(strcmp(s,"rectangle")==0) {
                a[n].n = 4;
                scanf(" (%lf,%lf)",&a[n].p[0].x,&a[n].p[0].y);
                scanf(" (%lf,%lf)",&a[n].p[1].x,&a[n].p[1].y);
                scanf(" (%lf,%lf)",&a[n].p[2].x,&a[n].p[2].y);
                a[n].p[3].x = a[n].p[2].x + (a[n].p[0].x - a[n].p[1].x);
                a[n].p[3].y = a[n].p[2].y + (a[n].p[0].y - a[n].p[1].y);
            }
            else if(strcmp(s,"polygon")==0) {
                scanf("%d",&a[n].n);
                rep(i, 0, a[n].n - 1) {
                    scanf(" (%lf,%lf)",&a[n].p[i].x,&a[n].p[i].y);
                }
            }
            n++;
        }

        sort(a, a + n, cmp);

        rep(i, 0, n - 1) {
            printf("%c ", a[i].id);
            mem(vis, 0);
            int cnt = 0;
            rep(j, 0, n - 1) {
                if(i == j) continue;
                if(judge(a[i], a[j])) {
                    cnt++;
                    vis[j] = 1;
                }
            }

            if(cnt == 0) puts("has no intersections");
            else if(cnt == 1) {
                printf("intersects with ");
                rep(j, 0, n - 1) {
                    if(vis[j]) {
                        printf("%c\n",a[j].id);
                        break;
                    }
                }
            }
            else if(cnt == 2) {
                printf("intersects with ");
                rep(j, 0, n - 1) {
                    if(vis[j]) {
                        if(cnt == 2) printf("%c ", a[j].id);
                        if(cnt == 1) printf("and %c\n", a[j].id);
                        cnt--;
                    }
                }
            }
            else {
                printf("intersects with ");
                rep(j, 0, n - 1) {
                    if(vis[j]) {
                        if(cnt > 1) printf("%c, ", a[j].id);
                        if(cnt == 1) printf("and %c\n", a[j].id);
                        cnt--;
                    }
                }
            }
        }
        puts("");
    }
    return 0;
}