UVALive 6859 （凸包）

将每个点分成上下左右四个点加入图中，求出凸包，由于只有长度为sqrt(2.0)和1的边，所以按照横坐标差值和纵坐标差值处理即可，代码如下：

#include <iostream>
#include <cstdio>
#include <cstring>
#include <string>
#include <algorithm>
#include <cmath>
#include <queue>
#include <map>
#include <vector>
using namespace std;
typedef long long LL;
const int maxn = 400007;
double EPS = 1e-10;

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); }
};

bool cmp_x(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* ps, int n) {
    sort(ps, ps+n, cmp_x);
    int k = 0;
    vector<P> qs(n*2);

    for(int i = 0; i < n; ++i) {
        while(k > 1 && (qs[k-1]- qs[k-2]).det(ps[i] - qs[k-1]) <= 0 ) k--;
        qs[k++] = ps[i];
    }

    for(int i = n-2, t = k; i >= 0; --i) {
        while(k > t && (qs[k-1] - qs[k-2]).det(ps[i]-qs[k-1]) <= 0) k--;
        qs[k++] = ps[i];
    }
    qs.resize(k-1);
    return qs;
}

double dist(P p, P q) {
    return (p-q).dot(p-q);
}

int N;
P ps[maxn];

void solve(int n) {
    vector<P> qs = convex_hull(ps, n);
    double res = 0.0;
    int kk = qs.size();
    double two = sqrt(2.0);
    for(int i = 0; i < kk; ++i) {
        int t1 = abs(qs[i].x-qs[(i-1+kk)%kk].x), t2 = abs(qs[i].y-qs[(i-1+kk)%kk].y);
        res += abs(t1-t2);
        res += (double)1.0*min(t1, t2)*two;
    }
    printf("%.5lf\n", res);
}

int main() {
    int n;
    while(~scanf("%d", &n)) {
        int cnt = 0;
        for(int i = 0; i < n; ++i) {
            double x, y; scanf("%lf%lf", &x, &y);
            ps[cnt].x = x+1;
            ps[cnt++].y = y;

            ps[cnt].x = x;
            ps[cnt++].y = y+1;

            ps[cnt].x = x-1;
            ps[cnt++].y = y;

            ps[cnt].x = x;
            ps[cnt++].y = y-1;
        }
        solve(cnt);
    }


}