USACO 3.4.1 closed fence

       不得不承認這道題着實是一道好題，可惜當年我還在用PASCAL的時候壓根沒做這道題……具體詳情我想我是需要追究matt和s.p.willam（原skyprophet）兩位神牛的責任的……

      這個東西比較困難，我也不知道完美算法是什麼（或者壓根沒有完美算法？？？），於是我祭出了近似算法。這道題目的第一問就是簡單的判斷線段是否相交，非常簡單。由於n最大是200，所以就不用考慮O(nlogn)的掃除線法了——否則我就不會啦！第二問很有意思，問你能看到哪些線段。我們想：如果要看到某條線度，一定是通過某兩個頂點之間的夾縫看到的。當然對於直接看到的線段，目光經過的這個夾縫可以說是很大很大，但是我們可以抽象地確定它的存在。這樣我們只需要搞出來這些“夾縫”！我的想法是近似的讓目光遊離於各個頂點的四周，也就是將各個頂點想四周移動後引射線作爲目光，之後尋找具光源最近的交點所在線段，這條線段就是能被看到的之一！

 

/* ID: wangqia6 TASK: fence4 LANG: C++ */ #include <fstream> #include <cstring> #include <cmath> #include <algorithm> using namespace std; const double da = 0.0000123456; const double db = 0.0000456789; const double zero = 1e-6; const double inf = 20000000; const long NMAX = 205; struct point { double x,y; }; ifstream fin ("fence4.in"); ofstream fout ("fence4.out"); long n,tot = 0; point o,p[NMAX],tmp; bool vis[NMAX]; void initdata() { fin >> n; fin >> o.x >> o.y; for (long i = 1; i <=n; i++) fin >> p[i].x >> p[i].y; p[n + 1] = p[1]; return; } double det(double xa,double ya,double xb,double yb) { return xa * yb - ya * xb; } double cross(point pa,point pb,point pc) { return det(pb.x - pa.x,pb.y - pa.y,pc.x - pa.x,pc.y - pa.y); } bool diff(double da,double db) { bool flag = (da > zero && db < -zero) || (da < -zero && db > zero); return flag; } bool eql_zero(double x) { return x <zero && x > -zero; } bool on_seg(point pa,point pb,point pc) { return min(pa.x,pb.x) <= pc.x && max(pa.x,pb.x) >= pc.x && min(pa.y,pb.y) <= pc.y && max(pa.y,pb.y) >= pc.y; } bool intersect(point pa,point pb,point pc,point pd) { double da = cross(pa,pb,pc), db = cross(pa,pb,pd), dc = cross(pc,pd,pa), dd = cross(pc,pd,pb); if (diff(da,db) && diff(dc,dd)) return true; else return (eql_zero(da) && on_seg(pa,pb,pc)) || (eql_zero(db) && on_seg(pa,pb,pd)) || (eql_zero(dc) && on_seg(pc,pd,pa)) || (eql_zero(dd) && on_seg(pc,pd,pb)); } bool worka() { long i,j; for (i = 1; i < n - 1; i++) for (j = i + 2; j <= n; j++) if (intersect(p[i],p[i + 1],p[j],p[j + 1]) && !((i == 1) && (j == n))) return true; return false; } point find_point(point pa,point pb,point pc,point pd) { point k; double da = cross(pa,pb,pc),db = cross(pa,pb,pd); k.x = (da * pd.x - db * pc.x) / (da - db); k.y = (da * pd.y - db * pc.y) / (da - db); return k; } double sqr(double x) { return x * x; } double dist(point a,point b) { return sqr(a.x - b.x) + sqr(a.y - b.y); } void lookup() { point k; double min_tmp = inf,dist_tmp; long min_vex = 0; for (long i = 1; i <= n; i++) if (intersect(o,tmp,p[i],p[i + 1])) { k = find_point(o,tmp,p[i],p[i + 1]); dist_tmp = dist(o,k); if (dist_tmp + zero < min_tmp) { min_tmp = dist_tmp; min_vex = i; } } if ((min_vex > 0) && (! vis[min_vex])) { tot++; vis[min_vex] = true; } } void workb() { memset(vis,0,sizeof(vis)); for (long i = 1; i <= n; i++) { tmp.x = (p[i].x + da - o.x) * inf; tmp.y = (p[i].y + db - o.y) * inf; lookup(); tmp.x = (p[i].x - da - o.x) * inf; tmp.y = (p[i].y - db - o.y) * inf; lookup(); tmp.x = (p[i].x + da - o.x) * inf; tmp.y = (p[i].y - db - o.y) * inf; lookup(); tmp.x = (p[i].x - da - o.x) * inf; tmp.y = (p[i].y + db - o.y) * inf; lookup(); } } void write(point pa,point pb) { fout << pa.x << ' ' << pa.y << ' ' << pb.x << ' ' << pb.y << endl; } void outitdata() { fout << tot << endl; for (long i = 1; i < n - 1; i++) if (vis[i]) write(p[i],p[i + 1]); if (vis[n]) write(p[1],p[n]); if (vis[n - 1]) write(p[n - 1],p[n]); return; } int main() { initdata(); if (worka()) { fout << "NOFENCE" << endl; fin.close(); fout.close(); return 0; } workb(); outitdata(); fin.close(); fout.close(); return 0; }