POJ 2187 旋转卡壳 + 水平序 Graham 扫描算法

//#pragma comment(linker, "/STACK:16777216") //for c++ Compiler
#include <stdio.h>
#include <iostream>
#include <cstring>
#include <cmath>
#include <stack>
#include <queue>
#include <vector>
#include <algorithm>
#define ll long long
#define Max(a,b) (((a) > (b)) ? (a) : (b))
#define Min(a,b) (((a) < (b)) ? (a) : (b))
#define Abs(x) (((x) > 0) ? (x) : (-(x)))
using namespace std;

const int INF = 0x3f3f3f3f;
const int MAXN = 50001;
const double eps = 1e-8;

struct POINT{
    int x;
    int y;
    POINT() : x(0), y(0) {};
    POINT(double _x_, double _y_) : x(_x_), y(_y_) {};
};

bool Mult(const POINT & sp, const POINT & ep, const POINT & op){
    return (sp.x - op.x) * (ep. y - op.y) >= (ep.x - op.x) * (sp.y - op.y);
}

bool operator < (const POINT & l, const POINT & r){
    return l.y < r. y || (l.y == r.y && l.x < r.x);
}

int Cross(const POINT & a, const POINT & b, const POINT & o){
    return (a.x - o.x) * (b.y - o.y) - (b.x - o.x) * (a.y - o.y);
}

int SquareDis(POINT a, POINT b){
    return (a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y);
}

int Graham(POINT *pnt, POINT *res, int n){
    int i, len, top =1;
    sort(pnt, pnt + n);
    if (n == 0)
        return 0;
    res[0] = pnt[0];
    if (n == 1)
        return 1;
    res[1] = pnt[1];
    if (n == 2)
        return 2;
    res[2] = pnt[2];
    for (i =2; i < n; i++){
        while (top && Mult(pnt[i], res[top], res[top -1]))
            top--;
        res[++top] = pnt[i];
    }
    len = top;
    res[++top] = pnt[n -2];
    for (i = n -3; i >=0; i--){
        while (top != len &&  Mult(pnt[i], res[top], res[top -1]))
            top--;
        res[++top] = pnt[i];
    }
    return top;
}

int rotating_calipers(POINT *ch, int n){
    int q =1, ans =0;
    ch[n] = ch[0];
    for (int i = 0; i < n; ++i){
        while (Cross(ch[i + 1], ch[q + 1], ch[i]) > Cross(ch[i + 1], ch[q], ch[i]))
            q = (q +1) % n;
        ans = max(ans, max(SquareDis(ch[i], ch[q]), SquareDis(ch[i + 1], ch[q + 1])));
    }
    return ans;
}

int main(){
    POINT pnt[MAXN], res[MAXN];
    int n;
    while(EOF != scanf("%d",&n)){
        for (int i = 0; i < n; i++)
            scanf("%d%d", &pnt[i].x, &pnt[i].y);
        int count = Graham(pnt, res,  n);
        int ans = rotating_calipers(res, count);
        printf("%d\n", ans);
    }
    return 0;
}