hoj2036

求多边形面积，选定（0,0）点，用三角形法求，求三角形面积时用叉积，把式子展开并合并同类项可得模板中的公式。

View Code

   
     

    
      #include 
    
      <
    
      iostream
    
      >
    
      
#include 
    
      <
    
      cstdio
    
      >
    
      
#include 
    
      <
    
      cstdlib
    
      >
    
      
#include 
    
      <
    
      cstring
    
      >
    
      

    
      using
    
       
    
      namespace
    
       std;


    
      #define
    
       maxn 101
    
      


    
      struct
    
       XPoint
{
 
    
      double
    
       x, y;
}point[maxn];


    
      int
    
       n;


    
      void
    
       input()
{
 
    
      for
    
       (
    
      int
    
       i 
    
      =
    
       
    
      0
    
      ; i 
    
      <
    
       n; i
    
      ++
    
      )
 {
 scanf(
    
      "
    
      %lf%lf
    
      "
    
      , 
    
      &
    
      point[i].x, 
    
      &
    
      point[i].y);
 }
}


    
      double
    
       areaofp(
    
      int
    
       vcount, XPoint plg[])
{
 
    
      int
    
       i;
 
    
      double
    
       s;
 
    
      if
    
       (vcount
    
      <
    
      3
    
      ) 
    
      return
    
       
    
      0
    
      ;
 s
    
      =
    
      plg[
    
      0
    
      ].y
    
      *
    
      (plg[vcount
    
      -
    
      1
    
      ].x
    
      -
    
      plg[
    
      1
    
      ].x);
 
    
      for
    
       (i
    
      =
    
      1
    
      ;i
    
      <
    
      vcount;i
    
      ++
    
      )
 s
    
      +=
    
      plg[i].y
    
      *
    
      (plg[(i
    
      -
    
      1
    
      )].x
    
      -
    
      plg[(i
    
      +
    
      1
    
      )
    
      %
    
      vcount].x);
 
    
      return
    
       s
    
      /
    
      2
    
      ;
}


    
      int
    
       main()
{
 
    
      //
    
      freopen("D:\\t.txt", "r", stdin);
    
      

    
       
    
      while
    
       (scanf(
    
      "
    
      %d
    
      "
    
      , 
    
      &
    
      n) 
    
      !=
    
       EOF 
    
      &&
    
       n 
    
      !=
    
       
    
      0
    
      )
 {
 input();
 printf(
    
      "
    
      %.1f\n
    
      "
    
      , areaofp(n, point));
 }
 
    
      return
    
       
    
      0
    
      ;
}