hdu 2036 - 改革春风吹满地(计算几何)

题意：求解多边形面积

解法：

先了解数学上“叉积”的含义与性质：

三角形ΔABC的面积为：

我们可以依次计算每个三角形的面积，ΔABC，ΔACE，ΔEF … …

所有三角形的面积之和为整个多边形的面积.

每次计算由A0,Ai,Ai+1组成的三角形

代码：

   1:  #include<stdlib.h>

   2:  #include<string.h>

   3:  #include<stdio.h>

   4:  #include<math.h>

   5:  #define N 101

   6:  struct point{

   7:      int x;

   8:      int y;

   9:  }array[N];

  10:  int main(){

  11:      int n,i;

  12:      while(scanf("%d",&n)!=EOF && n){

  13:          double sum=0;

  14:          for(i=0;i<n;i++){

  15:              scanf("%d %d",&array[i].x,&array[i].y);

  16:          }

  17:          for(i=1;i<n-1;i++){

  18:              int ax=array[i].x-array[0].x;

  19:              int ay=array[i].y-array[0].y;

  20:              int bx=array[i+1].x-array[0].x;

  21:              int by=array[i+1].y-array[0].y;

  22:              

  23:              //很奇怪，加上ABS，就WA了

  24:              sum+=ax*by-bx*ay;                    //计算叉积，再求和

  25:          }

  26:          printf("%.1lf\n",sum/2);

  27:      }

  28:  }

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