poj 2826 An Easy Problem?!(线段交,细节题)
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【题目大意】:给出两条线段,问这两条线段能够接住多少水。
【解题思路】:先大概估算了一下,这道题一共wa了不下20次。题目的大意不难,难在下面几个注意点上:
1)线段不能平行或者重合
2)不能够出现斜率为0的线段(10+wa以上才发现)
3)线段相交后开口应该向上
4)处于高位的线段的在x轴上的投影不能遮住地位线段的投影(两个方向)
5)求面积的时候,利用叉积/2来求,注意要以地位点的纵坐标为主
【代码】:
#include <iostream>#include <cstdio>#include <cmath>#include <cstring>#include <string>#include <algorithm>using namespace std;#define eps 1e-8double p,q;int cnt;struct Point{ double x, y; Point() {} Point(double a, double b) { x = a, y = b; }}point[4];struct Line{ Point a, b; Line() {} Line(Point x, Point y) { a = x, b = y; }}line[2];inline int sig(double k){ return k < -eps ? -1 : k > eps;}inline double det(double x1, double y1, double x2, double y2){ return x1 * y2 - x2 * y1;}inline double dotdet(double x1, double y1, double x2, double y2){ return x1 * x2 + y1 * y2;}inline double dot(Point o, Point a, Point b){ return dotdet(a.x - o.x, a.y - o.y, b.x - o.x, b.y - o.y);}inline double xmult(Point o, Point a, Point b){ return det(a.x - o.x, a.y - o.y, b.x - o.x, b.y - o.y);}inline int between(Point o, Point a, Point b){ return sig(dot(o, a, b));}inline bool sameline(Line u, Line v){ if (sig(xmult(u.a, v.a, v.b)) == 0 && sig(xmult(u.b, v.a, v.b)) == 0) return true; return false;}inline bool parallel(Line u, Line v){//利用斜率判平行,返回true表示平行 return sig((u.a.x - u.b.x) * (v.a.y - v.b.y) - (v.a.x - v.b.x) * (u.a.y - u.b.y)) == 0;}inline int intersectt(Point a, Point b, Point c, Point d, Point &p){ double s1, s2, s3, s4; int d1 = sig(s1 = xmult(a, b, c)); int d2 = sig(s2 = xmult(a, b, d)); int d3 = sig(s3 = xmult(c, d, a)); int d4 = sig(s4 = xmult(c, d, b)); if ((d1^d2) == -2 && (d3^d4) == -2) { p.x = (c.x * s2 - d.x * s1) / (s2 - s1); p.y = (c.y * s2 - d.y * s1) / (s2 - s1); return 1; } if((d1==0&&d2==0)||(d3==0&&d4==0)) return 0; if (d1 == 0 && between(c, a, b) <= 0) {p=c; return 2;} if (d2 == 0 && between(d, a, b) <= 0) {p=d; return 2;} if (d3 == 0 && between(a, c, d) <= 0) {p=a; return 2;} if (d4 == 0 && between(b, c, d) <= 0) {p=b; return 2;} return 0;}inline int intersect(Line u, Line v, Point &p){ return intersectt(u.a, u.b, v.a, v.b, p);}inline double get_area(Point a,Point b,Point c){ return fabs((a.x*b.y-a.y*b.x+b.x*c.y-c.x*b.y+c.x*a.y-a.x*c.y)/2);}double solve(Line a,Line b){ if ((point[0].y==point[1].y) ||(point[2].y==point[3].y)) return 0; if (sameline(a,b)==true) return 0; //判重合 if (parallel(a,b)==true) return 0; //判平行 Point tmp; int k; k=intersect(a,b,tmp); //判相交,顺便求交点 if (k==0) return 0; else { //判断开口向上 cnt=0; for (int i=0; i<4; i++) if (point[i].y>tmp.y) cnt++; if (cnt<=1) return 0; //判断线段的覆盖 if (point[1].x==point[3].x) return 0; if ((point[1].x<tmp.x&&point[3].x<point[1].x&&xmult(tmp,point[3],point[1])>0)|| (point[1].x>tmp.x&&point[3].x>point[1].x&&xmult(tmp,point[3],point[1])<0)) return 0; /* if (point[1].x<=tmp.x && point[3].x<=tmp.x) { if (point[1].x>=point[3].x) return 0; } //右侧线段的覆盖 if (point[1].x>=tmp.x && point[3].x>=tmp.x) { if (point[3].x>=point[1].x) return 0; }*/ //求面积,以低的木板作为标准 double anss; Point tmp1; tmp1=Point((point[1].y-tmp.y)*(point[3].x-tmp.x)/(point[3].y-tmp.y)+tmp.x,point[1].y); anss=get_area(tmp,point[1],tmp1); return anss; }}int main(){ int T; scanf("%d",&T); while (T--) { scanf("%lf%lf",&p,&q); point[0]=Point(p,q); scanf("%lf%lf",&p,&q); point[1]=Point(p,q); scanf("%lf%lf",&p,&q); point[2]=Point(p,q); scanf("%lf%lf",&p,&q); point[3]=Point(p,q); if (point[0].y>point[1].y) swap(point[0],point[1]); if (point[2].y>point[3].y) swap(point[2],point[3]); if (point[1].y>point[3].y) {swap(point[0],point[2]); swap(point[1],point[3]); } line[0]=Line(point[0],point[1]); line[1]=Line(point[2],point[3]); printf("%.2lf\n",solve(line[0],line[1])); } return 0;}
【运行结果】wa的太多一个版都放不下。。。。
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