POJ 2187 求多邊形直徑(凸包+旋轉卡殼)

題目鏈接：http://poj.org/problem?id=2187

方法一：凸包O(nlogn)+枚舉O(n^2) 

#include<cstdio>
#include<cmath>
#include<iostream>
#include<algorithm>
using namespace std;
#define N 51000
struct Point
{
    double x, y;
    Point(double x = 0, double y = 0) : x(x), y(y) {}
};
typedef Point Vector;
Vector operator - (Point A, Point B) {return Vector(A.x-B.x, A.y-B.y);}
Point point[N];
Point convex[N];


double dist(Point a, Point b)
{
    return (a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y);
}

double Cross(Vector A, Vector B)
{
    return A.x*B.y - A.y*B.x;
}

int cmp(Point a, Point b)
{
    if(a.x != b.x) return a.x < b.x;
    return a.y < b.y;
}
int ConvexHull(Point *p, int n, Point *ch)
{
    sort(p, p+n, cmp);
    int m = 0;

    for(int i = 0; i < n; i++)
    {
        while(m > 1 && Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2]) <= 0) m--;
        ch[m++] = p[i];
    }

    int k = m;
    for(int i = n-2; i >= 0; i--)
    {
        while(m > k && Cross(ch[m-1]-ch[m-2], p[i]-ch[m-2]) <= 0) m--;
        ch[m++] = p[i];
    }
    if(n > 1) m--;
    return m;
}
int main()
{
    int n;
    scanf("%d", &n);
    for(int i = 0; i < n; i++)
        scanf("%lf %lf", &point[i].x, &point[i].y);

    int len = ConvexHull(point, n, convex);

    double ans = 0;
    for(int i = 0; i < len; i++)
        for(int j = i+1; j < len; j++)
            ans = max(ans, dist(convex[i],convex[j]));

    printf("%.0lf\n", ans);

    return 0;
}

方法二：凸包O(nlogn)+旋轉卡殼O(n) 

#include<cmath>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
#define N 50000
//定義點
struct Point
{
    double x, y;
    Point(double x = 0, double y = 0) : x(x), y(y) {}
};
typedef Point Vector;
Point p[N+100];
Point ch[N+100];
Vector operator - (Point A, Point B) {return Vector(A.x-B.x, A.y-B.y);}
double Dot(Vector A, Vector B){return A.x*B.x + A.y*B.y;}
double Length(Vector A){return Dot(A, A);}
double Cross(Vector A, Vector B){return A.x*B.y - A.y*B.x;}
bool cmp(Point a, Point b)
{
    if(a.x == b.x) return a.y < b.y;
    else return a.x < b.x;
}

int ConvexHull(Point p[], int n, Point ch[])
{
    sort(p,p+n,cmp);
    int m = 0;
    for(int i = 0; i < n; i++)
    {
        while(m > 1 && Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2]) <= 0) m--;
        ch[m++] = p[i];
    }

    int k = m;
    for(int i = n-2; i >= 0; i--)
    {
        while(m > k && Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2]) <= 0) m--;
        ch[m++] = p[i];
    }
    if(n > 1) m--;
    return m;
}

double slove(Point ch[], int n)
{
    int q = 1;
    double ans = 0;
    for(int i = 0; i < n-1; i++)
    {
        while(Cross(ch[i+1]-ch[i],ch[q]-ch[i]) < Cross(ch[i+1]-ch[i],ch[q+1]-ch[i]))
            q = (q+1)%n;
        ans = max(ans, max(Length(ch[q]-ch[i+1]), Length(ch[q]-ch[i])));
    }
    return ans;
}

int main ()
{
    //freopen("in.txt", "r", stdin);
    int n;
    scanf("%d", &n);
    for(int i = 0; i < n; i++)
        scanf("%lf %lf", &p[i].x, &p[i].y);

    int len = ConvexHull(p, n, ch);
    double ans = slove(ch, len);
    printf("%.0f\n", ans);
    return 0;
}