Can read about orientation here
Idea comes from the slope comparison.
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#include <iostream> #include <algorithm> #include <cstdio> #include <vector> #include <cmath> using namespace std; struct point{ double x,y; }; vector<point>pp; double area(int n,vector<point> arr) { double ans = 0.0; for(int i=0;i<n;i++) { ans += (arr[i].x*arr[(i+1)%n].y - arr[i].y*arr[(i+1)%n].x); } return fabs(ans/2.0); } int checkCross(point p, point q, point r) { int val = (q.y - p.y) * (r.x - q.x) - (q.x - p.x) * (r.y - q.y); if (val == 0) return 0; // colinear return (val > 0)? 1: 2; // clock or counterclock wise } int convexCalc(int n,vector<point> arr) { point tmp; pp.clear(); int leftMost=0; for(int i=1;i<n;i++) { if(arr[i].x<arr[leftMost].x) leftMost=i; } int left=leftMost,j; do { pp.push_back(arr[left]); j = (left+1)%n; for(int i=0;i<n;i++) { if( checkCross(arr[left],arr[i],arr[j])==2 ) j=i; } left=j; }while(leftMost!=left); return pp.size(); } bool cmp(point a,point b) { if(a.x!=b.x) return a.x<b.x; return a.y<b.y; } int main() { int n,kase=1; vector<point>arr; point tmp; double ans,ans2; while(scanf("%d",&n),n) { arr.clear(); for(int i=0;i<n;i++) { scanf("%lf%lf",&tmp.x,&tmp.y); arr.push_back(tmp); } ans = area(n,arr); int cnt = convexCalc(n,arr); ans2 = area(cnt,pp); printf("Tile #%d\n",kase++); ans = ((ans2-ans)/ans2)*100; printf("Wasted Space = %.2lf %%\n\n",ans); } return 0; } |