凸包旋转卡壳 模板

原文链接
求一个凸包内最远两个点的距离。

#include <iostream>
#include <algorithm>
#include <vector>
#include <cmath>
#include <iomanip>
#include <cstring>
#include <cstdio>
using namespace std;
const int MAXN = 50010;
struct Point
{
    double x;
    double y;
}p[MAXN];

//计算叉积，小于0说明p1在p2的逆时针方向(右边)，即p0p1的极角大于p0p2的极角
double cross_product(Point p0, Point p1, Point p2)
{
    return (p1.x - p0.x)*(p2.y - p0.y) - (p2.x - p0.x)*(p1.y - p0.y);
}

//计算距离
double dis(Point p1, Point p2)
{
    return sqrt((p1.x - p2.x)*(p1.x - p2.x) + (p1.y - p2.y)*(p1.y - p2.y));
}

bool com(const Point &p1, const Point &p2)
{
    double temp = cross_product(p[0], p1, p2);
    if (fabs(temp) < 1e-6)//极角相等按照距离从小到大排序
    {
        return dis(p[0], p1) < dis(p[0], p2);
    }
    else
    {
        return temp > 0;
    }
}

vector<Point> graham_scan(int n)
{
    vector<Point> ch;
    int top = 2;
    int index = 0;
    for (int i = 1; i < n; ++i)//选出Y坐标最小的点，若Y坐标相等，选择X坐标小的点
    {
        if (p[i].y < p[index].y || (p[i].y == p[index].y && p[i].x < p[index].x))
        {
            index = i;
        }
    }
    swap(p[0], p[index]);
    ch.push_back(p[0]);
    //按极角排序
    sort(p + 1, p + n, com);
    ch.push_back(p[1]);
    ch.push_back(p[2]);
    for (int i = 3; i < n; ++i)
    {
        while (top > 0 && cross_product(ch[top - 1], p[i], ch[top]) >= 0)
        {
            --top;
            ch.pop_back();
        }
        ch.push_back(p[i]);
        ++top;
    }
    return ch;
}

//旋转卡壳法
double rotating_caliper(vector<Point> v)
{
    double max_dis = 0.0;
    int n = v.size();
    if (n == 2)
    {
        max_dis = dis(v[0], v[1]);
    }
    else
    {
        v.push_back(v[0]);
        int j = 2;
        for (int i = 0; i < n; ++i)
        {
            while (cross_product(v[i], v[i + 1], v[j]) < cross_product(v[i], v[i + 1], v[j + 1]))
            {
                j = (j + 1) % n;
            }
            max_dis = max(max_dis, max(dis(v[j], v[i]), dis(v[j], v[i + 1])));
        }
    }
    return max_dis;
}
int main()
{
    int n;
    while(~scanf("%d", &n))
    {
        for(int i=0;i<n;++i)
            scanf("%lf %lf", &p[i].x, &p[i].y);
        printf("%f\n", rotating_caliper(graham_scan(n)));
    }
}