nyoj-253-LK的旅行（Graham算法和旋转卡壳）

题目链接

 /*
     Name:nyoj-253-LK的旅行
     Copyright:
     Author:
     Date: 2018/4/27 15:01:36
     Description:
     zyj的模板
 */
 #include <iostream>
 #include <cstdio>
 #include <algorithm>
 #include <cstring>
 using namespace std;
 const int MAXN = ;
 struct Point
 {
     int x, y;
     Point(int _x = , int _y = )
     {
         x = _x;
         y = _y;
     }
     Point operator - (const Point &b)const
     {
         return Point(x - b.x, y - b.y);
     }
     int operator ^(const Point &b)const
     {
         return x * b.y - y * b.x;
     }
     int operator *(const Point &b)const
     {
         return x * b.x + y * b.y;
     }
     void input()
     {
         scanf("%d%d", &x, &y);
         return ;
     }
 };
 // 距离的平方
 int dist2(Point a, Point b)
 {
     return (a - b) * (a - b);
 }

 // 二维凸包
 Point list[MAXN];
 int Stack[MAXN], top;
 bool _cmp(Point p1, Point p2)
 {
     int tmp = (p1 - list[]) ^ (p2 - list[]);
     if (tmp > )
     {
         return true;
     }
     else if (tmp ==  && dist2(p1, list[]) <= dist2(p2, list[]))
     {
         return true;
     }
     else
     {
         return false;
     }
 }
 void Graham(int n)
 {
     Point p0;
     int k = ;
     p0 = list[];
     for (int i = ; i < n; i++)
     {
         if (p0.y > list[i].y || (p0.y == list[i].y && p0.x > list[i].x))
         {
             p0 = list[i];
             k = i;
         }
     }
     swap(list[k], list[]);
     sort(list + , list + n, _cmp);
     if (n == )
     {
         top = ;
         Stack[] = ;
         return ;
     }
     if (n == )
     {
         top = ;
         Stack[] = ;
         Stack[] = ;
         return ;
     }
     Stack[] = ;
     Stack[] = ;
     top = ;
     for (int i = ; i < n; i++)
     {
         while (top >  && ((list[Stack[top - ]] - list[Stack[top - ]]) ^ (list[i] - list[Stack[top - ]])) <= )
         {
             top--;
         }
         Stack[top++] = i;
     }
     return ;
 }
 // 旋转卡壳,求两点间距离平方的最大值
 int rotating_calipers(Point p[],int n)
 {
     int ans = ;
     Point v;
     int cur = ;
     for (int i = ; i < n; i++)
     {
         v = p[i] - p[(i + ) % n];
         while ((v ^ (p[(cur + ) % n] - p[cur])) < )
         {
             cur = (cur + ) % n;
         }
         ans = max(ans, max(dist2(p[i], p[cur]), dist2(p[(i + ) % n], p[(cur + ) % n])));
     }
     return ans;
 }
 Point p[MAXN];
 int main()
 {
     int n;
     cin>>n;
     while (n--)
     {
         int m;
         cin>>m;
         for (int i = ; i < m; i++)
         {
             list[i].input();
         }
         Graham(m);
         for (int i = ; i < top; i++)
         {
             p[i] = list[Stack[i]];
         }
         printf("%d\n", rotating_calipers(p, top));
     }
     return ;
 }