ZOJ - 1453 —— Surround the Trees （求凸包长度）

#include <cstdio>
#include <iostream>
#include <cmath>
#include <algorithm>
using namespace std;

struct Point {
    int x, y;
    Point(int x=0, int y=0):x(x),y(y) {}
} p[105];

typedef Point Vector;

Vector operator - (Point a, Point b)
{
    return Vector(a.x-b.x, a.y-b.y);
}

// 叉乘 
double Cross(Vector a, Vector b)
{
    return a.x*b.y - a.y*b.x;
}

// 确定浮点数的符号性质(+, -, 0) 
const double EPS = 1e-10;
int dcmp(double x)
{
    if(fabs(x) < EPS)    return 0;
    return x < 0 ? -1 : 1;    
}

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

bool cmp(Point a, Point b) // 用于极角排序 
{
    Vector u = a-p[0], v = b-p[0];
    int sign = dcmp(Cross(u, v));
    if(sign == 0)    return Dist(a, p[0]) < Dist(b, p[0]);
    return sign > 0;
}

double grahamscan(Point *a, int n)
{
    if(n == 1)    return 0;
    // 这里zoj和hdu有不同，zoj认为要乘2，hdu认为不乘，有点坑 
    if(n == 2)    return 2*Dist(a[0], a[1]); 
    
    int *st = new int[n];
    int j=0;
    st[j++] = 0;
    st[j++] = 1;
    st[j++] = 2;
    for(int i=3; i<n; i++) {
        // 这里可以取到 等于，减少不必要的距离计算 
        while(dcmp(Cross(a[st[j-1]]-a[st[j-2]], a[i]-a[st[j-2]])) <= 0) --j; 
        st[j++] = i;
    }
    
    double ret = 0.0;
    for(int i=1; i<j; i++) {
        ret += Dist(a[st[i-1]], a[st[i]]);
    }
    return ret + Dist(a[st[0]], a[st[j-1]]);
}

int main ()
{
    int n;
    while(scanf("%d", &n) != EOF && n) {
        int mini, miny=32767+10;
        for(int i=0; i<n; i++) {
            scanf("%d%d", &p[i].x, &p[i].y);
            if(miny > p[i].y) {
                miny = p[i].y;
                mini = i;
            }
        }
        swap(p[0], p[mini]);
        
        sort(p+1, p+n, cmp);
    
        printf("%.2lf\n", grahamscan(p, n));
    }
    
    return 0;
}