hdu 1392(求凸包周长)

/*
*  题目要求：求凸包的周长 
*/

#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <iostream>

using namespace std;

const int N = 105;
const double eps = 1e-8;

struct point {
    int x;
    int y;
}p[N], stack[N];

bool isZero(double x) {
    return (x > 0 ? x : -x) < eps;
}

double dis(point A, point B) {
    return sqrt((A.x-B.x)*(A.x-B.x)+(A.y-B.y)*(A.y-B.y));
}

double crossProd(point A, point B, point C) {
    return (B.x-A.x)*(C.y-A.y) - (B.y-A.y)*(C.x-A.x);
}

//以最左下的点为基准点，其他各点（逆时针方向）以极角从小到大的排序规则
int cmp(const void *a, const void *b) {
    point *c = (point *)a;
    point *d = (point *)b;
    double k = crossProd(p[0], *c, *d);//极角大小转化为求叉乘
    if (k<eps || isZero(k) && dis(p[0], *c)>dis(p[0], *d)) return 1;
    return -1;
}

double Graham(int n) {
    int x = p[0].x;
    int y = p[0].y;
    int mi = 0;
    for (int i=1; i<n; ++i) {//找到最左下的一个点
        if (p[i].x<x || (p[i].x==x && p[i].y<y)) {
            x = p[i].x;
            y = p[i].y;
            mi = i;
        }
    }
    point tmp = p[mi];
    p[mi] = p[0];
    p[0] = tmp;
    qsort(p+1, n-1, sizeof(point), cmp);
    p[n] = p[0];
    stack[0] = p[0];
    stack[1] = p[1];
    stack[2] = p[2];
    int top = 2;
    for (int i=3; i<=n; ++i) {//加入一个点后,向右偏拐或共线，则上一个点不在凸包内，则--top，该过程直到不向右偏拐或没有三点共线的点 
        while (crossProd(stack[top-1], stack[top], p[i])<=eps && top>=2) --top;
        stack[++top] = p[i];//在当前情况下符合凸包的点，入栈
    }
    double len = 0;
    for (int i=0; i<top; ++i) len += dis(stack[i], stack[i+1]);
    return len;
}

int main() {
    int n;
    while (scanf("%d", &n), n) {
        for (int i=0; i<n; ++i) scanf ("%d%d", &p[i].x, &p[i].y);
        if (n == 1) printf ("0.00\n");
        else if (n == 2) printf ("%.2lf\n", dis(p[0], p[1]));
        else {
            double len = Graham(n);
            printf ("%.2lf\n", len);
        }
    }
    return 0;
}