poj 2187 凸包上的直径 - 旋转卡壳

//poj 2187 凸包上的直径 - 旋转卡壳////解题思路:////裸地凸包 +　旋转卡壳的对踵点////感悟:////对于凸包倒是很好理解,就是判断走的方向在当前方向的左侧或右侧,//左侧表示是凸包上的点,右侧就退栈,直到是为止.////对于旋转卡壳,挑战上的转到法线方向不是很明白.倒是网上说的用的//三角形的面积这种算法倒是更好理解一些~~~受教了~~~#include <cstring>#include <algorithm>#include <iostream>#include <cstdio>#include <cmath>#include <string>#include <vector>#include <queue>#define For(x,a,b,c) for (int x = a; x <= b; x += c)#define Ffor(x,a,b,c) for (int x = a; x >= b; x -= c)#define cls(x,a) memset(x,a,sizeof(x))using namespace std;typedef long long ll;const double PI = acos(-1.0);const double EPS = 1e-10;const int MAX_N = 50000 + 8;const double INF = 1e9;int N,M;double add(double a,double b){if (abs(a+b) < EPS*(abs(a) + abs(b)))return 0;return a + b;}struct P{double x,y;P() {}P(double x,double y) : x(x), y(y) {}P operator + (P p){return P(add(x,p.x),add(y,p.y));}P operator - (P p){return P(add(x,-p.x),add(y,-p.y));}P operator * (double d){return P(x * d,y * d);}double dot(P p){return add(x * p.x,y * p.y);}double det(P p){return add(x * p.y, - y * p.x);}}p[MAX_N];bool on_seg(P p1, P p2, P q){return (p1 - q).det(p2 - q) == 0 && (p1 - q).dot(p2 - q) <= 0;}P intersection(P p1, P p2, P q1, P q2){return p1 + (p2 - p1) * ((q2 - q1).det(q1 - p1) / (q2 - q1).det(p2 - p1));}double dist(P p, P q){return (p - q).dot(p - q);}bool cmp(const P& p, const P& q){if (p.x != q.x)return p.x < q.x;return p.y < q.y;}vector<P> convex_hull(P* p,int n){sort(p + 1, p + N + 1, cmp);int k = 0;vector<P> qs(2 * n + 1);for (int i = 1 ;i <= n; i++){while(k > 1 && (qs[k - 1] - qs[k - 2]).det(p[i] - qs[k - 1]) <= 0) k -- ;qs[k++] = p[i];}for (int i = n - 1,t = k;i >= 1; i--){while( k > t && (qs[k - 1] - qs[k - 2]).det(p[i] - qs[k - 1]) <= 0) k--;qs[k++] = p[i];}qs.resize(k - 1);return qs;}void input(){for (int i = 1 ;i <= N;i ++)scanf("%lf%lf",&p[i].x,&p[i].y);}//void solve(){//vector<P> q = convex_hull(p,N);//double res = 0;//for (int i = 0 ;i < q.size();i ++){//for (int j = 0 ; j < i; j++){//res = max(res,dist(q[i],q[j]));//}//}//printf("%.0lf\n",res);//}//void solve(){//vector<P> q = convex_hull(p,N);////int n = q.size();////if (n == 2){//printf("%.0lf\n",dist(q[0],q[1]));//return ;//}////int i = 0,j = 0;////for (int k = 0 ; k < q.size(); k ++){//if (!cmp(q[i],q[k]))i = k;//if (cmp(q[j],q[k]))j = k;//}////double res = 0;////int si = i, sj = j;////while(i != sj || j != si){//res = max(res,dist(q[i],q[j]));////if ((q[(i + 1) % n] - q[i]).det(q[(j + 1) % n] - q[j]) < 0){//i = (i + 1) % n;//}else {//j = (j + 1) % n;//}//}//printf("%.0lf\n",res);//}void solve(){vector<P> q = convex_hull(p,N);int n = q.size();double res = 0;for (int i = 0 , j = 1; i < n; i++){while((q[i+1] - q[i]).det(q[j] - q[i]) < (q[i+1] - q[i]).det(q[j+1] - q[i]))j = (j + 1) % n;res = max(res,max(dist(q[i],q[j]),dist(q[i+1],q[j+1])));}printf("%.0lf\n",res);}int main(){//freopen("1.in","r",stdin);while(scanf("%d",&N)!=EOF){input();solve();}return 0;}