[POJ 1385] Lifting the Stone (computational geometry)

Title Link: http://poj.org/problem?id=1385

Title: Give you a polygon point, to seek the center of gravity.

First, the center of gravity of the triangle: ((X1+X2+X3)/3, (Y1+Y2+Y3)/3)

Then the center of mass of the polygon is divided into a number of triangles, the triangle area is the weight, the center of gravity of each triangle weighted average.

Attention:

Pair<double,double> will be mle.

Fabs will lose precision? (This I do not know), so in the use of vector cross-product to find the triangular area is the best way to directly let the area is positive. Otherwise the fabs will be WA ...

Code:

1#include <cstdio>2#include <cstring>3#include <algorithm>4#include <cmath>5 using namespacestd;6typedefLong LongLL;7 #defineEPS 1e-88 #defineX First9 #defineY SecondTen  Onetypedefstruct_point{//with Pair<double,double> will mle!!  A     DoubleFirst ; -     Doublesecond; - }point; the  - typedef point VECTOR; - Double operator*(VECTOR x,vector y) { -     DoubleRes; +res = x.x*y.y-x.y*y.x; -     returnRes; + } AVECTORoperator-(point X,point y) { at VECTOR Res; -Res. X = x.x-y.x; -Res. Y = x.y-y.y; -     returnRes; - } -  in Const intMax_n =1000001; - intT,n; to Point pt[max_n]; +  -Point Getcenter [Point points[],intN) { the Point Res; *     Doublearea,areamulx,areamuly; $Area =0.0; Areamulx =0.0; Areamuly =0.0;Panax Notoginseng      for(intI=1; i<n-1; i++){ -VECTOR V1 = points[i]-points[0]; theVECTOR v2 = points[i+1]-points[i];//if Fabs will lose precision after  +         DoubleTarea = V1 * V2/2.0; AArea + =Tarea; theAreamulx + = (points[0]. X+points[i]. x+points[i+1]. X) *Tarea; +Areamuly + = (points[0]. Y+points[i]. y+points[i+1]. Y) *Tarea; -     } $Res. X = Areamulx/(3.0*Area ); $Res. Y = Areamuly/(3.0*Area ); -     returnRes; - } the  - intMain () {Wuyiscanf"%d",&T); the      while(t-- ){ -scanf"%d",&N); Wu          for(intI=0; i<n;i++){ -scanf"%LF%LF", &pt[i]. x,&Pt[i]. Y); About         } $Point ans =Getcenter (pt,n); -printf"%.2LF%.2lf\n", ans. X+eps,ans. y+EPS); -     } -     return 0; A}

[POJ 1385] Lifting the Stone (computational geometry)