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;

}