hdu 2202(凸包+枚举凸包上的点)

/*
*  题目要求：求三角形的最大面积 
*  方法：凸包+枚举凸包上的点 
*/

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

using namespace std;

const int N = 50005;
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));
}

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

int cmp(const void *a, const void *b) {
    point *c = (point *)a;
    point *d = (point *)b;
    double k = crossProd(p[0], *c, *d);
    if (k<eps || (isZero(k)&&dis(p[0], *c)>dis(p[0], *d))) return 1;
    return -1;
}

int Graham(int n) {
    int x = p[0].x;
    int y = p[0].y;
    int mi = 0;
    for (int i=1; i<n; ++i) {
        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];
    for (int i=0; i<3; ++i) stack[i] = p[i];
    int top = 2;
    for (int i=3; i<n; ++i) {
        while (crossProd(stack[top-1], stack[top], p[i])<=eps && top>=2) --top;
        stack[++top] = p[i];
    }
    return top;    
}

double maxTrangle(int n) {
    int top = Graham(n);
    double area, maxArea = 0;
    for (int i=0; i<top; ++i) {
        for (int j=i+1; j<top; ++j) {
            for (int k=j+1; k<=top; ++k) {
                area = crossProd(stack[i], stack[j], stack[k]);
                if (maxArea < area) maxArea = area; 
            }
        }
    }
    return maxArea * 0.5;
}

int main() {
    int n;
    while (scanf("%d", &n) != EOF) {
        for (int i=0; i<n; ++i) scanf ("%d%d", &p[i].x, &p[i].y);
        double ans = maxTrangle(n);
        printf ("%.2lf\n", ans);
    }
    return 0;
}