判断凸多边形

        以HDU2108为例，去AC吧。

//点逆序输入
import java.util.Scanner;
//1s
public class HDU2108 {
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    while(true) {
      int x,y;
      int n = sc.nextInt();
      if(0==n) {
        break;
      }
      Point[] p = new Point[n];
      for(int i=0; i<n; i++) {
        p[i] = new Point();
      }
      for(int i=0; i<n; i++) {
        x = sc.nextInt();
        y = sc.nextInt();
        p[i] = new Point(x,y);
      }
      //凸多边形
      boolean tag = true;
      int j,k,t;
      for(int i=0; i<n; i++) {
        //k,t直接对n求余就行了
        j = i;
        k = i+1;
        t = i+2;
        //以三角形为例看看
        if(k==n) {
          k = 0;
        }
        if(t==n+1) {
          t = 1;
        }
        if(t==n) {
          t = 0;
        }
        //注意是后面减去前面的
        Point p1 = new Point(p[k].x - p[j].x,
            p[k].y - p[j].y);
        Point p2 = new Point(p[t].x - p[k].x,
            p[t].y - p[k].y);
        //叉积
        int ans = p1.x*p2.y - p1.y*p2.x;
        if(ans<0) {
          tag = false;
          break;
        }
      }
      if(tag) {
        System.out.println("convex");
      }else {
        System.out.println("concave");
      }
    }
  }
}
class Point {
  int x;
  int y;
  public Point() {
    this.x = 0;
    this.y = 0;
  }
  public Point(int x, int y) {
    this.x = x;
    this.y = y;
  }
}