POJ 3449 Geometric Shapes (多邊形相交)

這題主要是給正方形對角線兩個點求另外兩個點：不用旋轉什麼的，可以由點之間的關係推得。比較好推，具體見代碼。

剩下的思路比較簡單，輸入輸出有點麻煩，尤其是 A and C 和 A, B, and C 這種的區別。。。

#include <iostream>
#include <stdio.h>
#include <string.h>
#include <algorithm>
#include <queue>
#include <map>
#include <vector>
#include <set>
#include <string>
#include <math.h>
#include <cstdio>
#include <cstring>
#include <cctype>

using namespace std;

const double eps = 1e-8;
int sgn(double x)
{
    if (fabs(x) < eps) return 0;
    if (x < 0) return -1;
    else return 1;
}
struct Point
{
    double x,y;
    Point(){}
    Point(double _x,double _y)
    {
        x = _x;y = _y;
    }
    //向量
    Point operator -(const Point &b)const
    {
        return Point(x - b.x,y - b.y);
    }
    //叉積
    double operator ^(const Point &b)const
    {
        return x*b.y - y*b.x;
    }
    //點積
    double operator *(const Point &b)const
    {
        return x*b.x + y*b.y;
    }
    void input()
    {
        scanf("%lf%lf",&x,&y);
    }
};
struct Line
{
    Point s,e;
    Line(){}
    Line(Point _s,Point _e)
    {
        s = _s;e = _e;
    }
    //兩直線相交求交點
    //第一個值爲0表示直線重合，爲1表示平行，爲0表示相交,爲2是相交
    //只有第一個值爲2時，交點纔有意義
    pair<int,Point> operator &(const Line &b)const
    {
        Point res = s;
        if (sgn((s-e)^(b.s-b.e)) == 0)
        {
            if(sgn((s-b.e)^(b.s-b.e)) == 0)
                return make_pair(0,res);//重合
            else return make_pair(1,res);//平行
        }
        double t = ((s-b.s)^(b.s-b.e))/((s-e)^(b.s-b.e));
        res.x += (e.x-s.x)*t;
        res.y += (e.y-s.y)*t;
        return make_pair(2,res);
    }
};

bool inter(Line l1,Line l2)//判斷線段相交
{
    return
    max(l1.s.x,l1.e.x) >= min(l2.s.x,l2.e.x) &&
    max(l2.s.x,l2.e.x) >= min(l1.s.x,l1.e.x) &&
    max(l1.s.y,l1.e.y) >= min(l2.s.y,l2.e.y) &&
    max(l2.s.y,l2.e.y) >= min(l1.s.y,l1.e.y) &&
    sgn((l2.s-l1.e)^(l1.s-l1.e))*sgn((l2.e-l1.e)^(l1.s-l1.e)) <= 0 &&
    sgn((l1.s-l2.e)^(l2.s-l2.e))*sgn((l1.e-l2.e)^(l2.s-l2.e)) <= 0;
}

typedef struct Shape {
    string name, type;
    int pnum, snum;
    Point pts[27];
    Line segs[27];
}Shape;

Shape shape[32];

Point getp()
{
    Point ret;
    string str;
    cin >> str;
    ret.x = ret.y = 0;
    int pos = 0;
    double sign = 1;
    if(str[pos+1] == '-') {
        sign = -1;
        pos++;
    }
    while (isdigit(str[++pos]))
        ret.x = ret.x * 10 + double(str[pos] - '0');
    ret.x *= sign;
    sign = 1;
    if(str[pos+1] == '-') {
        sign = -1;
        pos++;
    }
    while (isdigit(str[++pos]))
        ret.y = ret.y * 10 + double(str[pos] - '0');
    ret.y *= sign;
    return ret;
}

bool cmp(Shape a, Shape b)
{
    return a.name < b.name;
}

int main()
{
    int scnt = 0;
    string str1, str2;

    while (cin >> str1) {
        Shape & curs = shape[scnt];
        if (str1 == "-") {
            sort(shape, shape+scnt, cmp);
            for (int i = 0; i < scnt; i++) {
                cout << shape[i].name;
                int ccnt = 0;
                string buf[100];
                for (int j = 0; j < scnt; j++) {
                    if (i == j) continue;
                    bool cro = false;
                    for (int i0 = 0; !cro && i0 < shape[i].snum; i0++) {
                        for (int j0 = 0; j0 < shape[j].snum; j0++) {
                            if (inter(shape[i].segs[i0], shape[j].segs[j0])) {
                                cro = true;
                                break;
                            }
                        }
                    }
                    if (cro)
                        buf[ccnt++] = shape[j].name;
                }
                if (ccnt == 0)
                    cout << " has no intersections" << endl;
                else {
                    cout << " intersects with ";
                    for (int j = 0; j < ccnt; j++) {
                        if (j == 0)
                            cout << buf[j];
                        else if (j == ccnt - 1) {
                            if(ccnt != 2) cout << ",";
                            cout << " and " << buf[j] << endl;
                        }
                        else
                            cout << ", " << buf[j];
                    }
                    if (ccnt == 1)
                        cout << endl;
                }
            }
            scnt = 0;
            cout << endl;
            continue;
        } else if (str1 == ".")
            break;
        else
            cin >> str2;
        curs.name = str1;
        curs.type = str2;
        if (curs.type == "square") {
            Point p[4];
            p[0] = getp(), p[2] = getp();
            curs.pnum = curs.snum = 4;
            double x0 = p[0].x, y0 = p[0].y;
            double x2 = p[2].x, y2 = p[2].y;
            double a = x0 + x2, b = y2 - y0, c = y0 +y2, d = x0 - x2;
            p[1].x = (a + b) / 2.0, p[1].y = (c + d) / 2.0;
            p[3].x = (a - b) / 2.0, p[3].y = (c - d) / 2.0;
            for (int i = 0; i < 4; i++) {
                curs.pts[i] = p[i];
                curs.segs[i].s = p[i];
                curs.segs[i].e = p[(i+1) % 4];
            }
        } else if (curs.type == "rectangle") {
            Point p[4];
            for(int i = 0; i < 3; i++) p[i] = getp();
            p[3].x = p[2].x + p[0].x - p[1].x;
            p[3].y = p[2].y + p[0].y - p[1].y;
            curs.pnum = curs.snum = 4;
            for (int i = 0; i < 4; i++) {
                curs.pts[i] = p[i];
                curs.segs[i].s = p[i];
                curs.segs[i].e = p[(i+1) % 4];
            }
        } else if (curs.type == "line") {
            curs.pnum = 2;
            curs.snum = 1;
            curs.segs[0].s = curs.pts[0] = getp();
            curs.segs[0].e = curs.pts[1] = getp();
        } else if (curs.type == "triangle") {
            curs.pnum = curs.snum = 3;
            for (int i = 0; i < 3; i++)
                curs.segs[i].s = curs.segs[(i+2) % 3].e = curs.pts[i] = getp();
        } else if (curs.type == "polygon") {
            cin >> curs.pnum;
            curs.snum = curs.pnum;
            for (int i = 0; i < curs.pnum; i++)
                curs.segs[i].s = curs.segs[(i+curs.pnum-1) % curs.pnum].e = curs.pts[i] = getp();
        }
        scnt++;
    }

    return 0;
}