3
-1 0
0 1
1 1

0.5

思路：计算多边形最低点 -》 将多边形移动到最低点刚好为原点 -》 计算各个顶点和原点连线的cos值，最低点赋特殊值（10）-》所有顶点按照cos值排序-》依次计算相临两点与最低点形成的三角形的面积（公式：s = 1/2*跟号下（p(p-a)(p-b)(p-c)）(其中：abc是三角形三条边)）-》 将所有的这样的三角形面积相加即得到凸多边形的面积

#include <iostream>
#include <vector>
#include <algorithm>
#include <math.h>
#include <stdlib.h>
using namespace std;

struct node {
    double x;
    double y;
    double cos;
};
//移动多边形
void move(vector<node> &org)
{
    double xx = org[0].x;
    double yy = org[0].y;
    for (int i = 0; i < org.size(); ++i) {
        if (org[i].y < yy) {
            yy = org[i].y;
            xx = org[i].x;
        }
    }
    for (int j = 0; j < org.size(); ++j) {
        org[j].x -= xx;
        org[j].y -= yy;
    }
    cout << "move up " << endl;
    for (int j = 0; j < org.size(); ++j) {
        cout << org[j].x << " " << org[j].y << endl;
    }
}
//排序比较规则
bool comp(const node &s1, const node &s2)
{
    return s1.cos < s2.cos;
}
void countCosAndSort(vector<node> &org)
{
    for (int i = 0; i < org.size(); ++i) {
        if ((org[i].y < 0.000001 || org[i].y > -0.000001) &&
             (org[i].x < 0.000001 || org[i].x > -0.000001)) {
            org[i].cos = 10;
            continue;
        }
        double d = sqrt(org[i].x * org[i].x + org[i].y * org[i].y);
        org[i].cos = org[i].x / d;
    }
    sort(org.begin(), org.end(), comp);
    cout << "after sort" << endl;
    for (int i = 0; i < org.size(); ++i) {
        cout << org[i].x << " " << org[i].y << endl;
    }
}
//计算单个三角形面积
double singleArea(node &n1, node &n2)
{
    double len1, len2, len3;
    len1 = sqrt(n1.x * n1.x + n1.y * n1.y);
    len2 = sqrt(n2.x * n2.x + n2.y * n2.y);
    len3 = sqrt((n2.x-n1.x)*(n2.x-n1.x) + (n2.y-n1.y)*(n2.y-n1.y));
    double p = (len1+len2+len3)/2;
    double s = sqrt(p*(p-len1)*(p-len2)*(p-len3));
    return s;
}

//计算多边形面积
double sunArea(vector<node> &org)
{
    move(org);
    countCosAndSort(org);
    double sumA = 0;
    for (int i = 0; i < org.size()-1; ++i) {
        sumA += singleArea(org[i], org[i+1]);
    }
    return sumA;
}

int main()
{
    int t;
    cin >> t;
    vector<node> data;
    node tmp;
    double xx, yy;
    for (int i = 0; i < t; ++i) {
        cin >> xx >> yy;
        tmp.x = xx;
        tmp.y = yy;
        data.push_back(tmp);
    }
    cout << sunArea(data) << endl;

return 0;
}