求凸包。
但是這題有個問題就是需要把在邊界上的點也求出來，那麼在判斷cross的時候應該是<0 而不是 <=0。
還有一個問題是，排序的時候當極角相同的時候，按x從小到大的順序排列的，那麼最後幾個共線的點順序應該倒過來，不然結果只包含一個點。

#include <iostream>
#include <vector>
#include <algorithm>
#include <cstdio>
#include <cstring>
#include <string>
#include <cmath>
 

using namespace std;




struct Point {
    int x;
    int y;
    Point() : x(0), y(0) {}
    Point(int a, int b) : x(a), y(b) {}
};

Point p0;

bool cmp(Point &a, Point &b)  {
    if ((a.x - p0.x) * ( b.y - p0.y) - ( a.y - p0.y) * ( b.x - p0.x) != 0) {
        return (a.x - p0.x) * (b.y - p0.y) - (a.y - p0.y) * (b.x - p0.x) > 0
 
;
    }
    else if (a.x != b.x){
        return a.x < b.x;
    }
    else {
        return a.y < b.y;
    }
}

int cross(Point a, Point b, Point c) {
    return (a.x - c.x) * (b.y - c.y) - (a.y - c.y) * (b.x - c.x);
}

void display(vector<Point> ans) {
    cout << "---" << endl;
    for
 
 (int i = 0; i < ans.size(); i++) {
        cout << ans[i].x << " " << ans[i].y << endl;
    }
    cout << "---" << endl;
}


class Solution {
public:
    vector<Point> outerTrees(vector<Point>& points) {
        if (points.size() < 2) {
            return points;
        }
        Point p(1e10, 1e10);
        int min_index = 0;
        for (int i = 0; i < points.size(); i++) {
            if ((points[i].x <= p.x && points[i].y <= p.y) || points[i].x < p.x) {
                min_index = i;
                p = points[i];
            }
        }
        p0 = p;
        swap(points[0], points[min_index]);
        sort(points.begin() + 1, points.end(), cmp);
        int len = points.size();
        if (cross(points[1], points[len - 1], points[0]) != 0) {
            int temp = len - 2;
            while (cross(points[len - 1], points[temp], points[0]) == 0) {
                temp--;
            }
            reverse(points.begin() + temp + 1, points.end());
        }
      //  display(points);
        vector<Point> ans;
        ans.push_back(points[0]);
        ans.push_back(points[1]);
        for (int i = 2; i < points.size(); i++) {
            int t = ans.size();
            while (ans.size() > 1 && cross(ans[t - 1], points[i], ans[t - 2]) < 0) {
                ans.pop_back();
                t = ans.size();
            }
            ans.push_back(points[i]);
        }
        return ans;
    }
};

int main() {
    Solution a;
    vector<Point> points = {{3, 0}, {4, 0}, {5, 0}, {6, 1}, {7, 2}, {7, 3}, {7, 4}, {6, 5}, {5, 5}, {4, 5}, {3, 5}, {2, 5}, {1, 4}, {1, 3}, {1, 2}, {2, 1}};
    vector<Point> ans = a.outerTrees(points);
    for (int i = 0; i < ans.size(); i++) {
        cout << ans[i].x << " " << ans[i].y << endl;
    }
    return 0;
}
/*
{{1, 1}, {2, 2}, {2, 0}, {2, 4}, {3, 3}, {4, 2}}
{{3, 0}, {4, 0}, {5, 0}, {6, 1}, {7, 2}, {7, 3}, {7, 4}, {6, 5}, {5, 5}, {4, 5}, {3, 5}, {2, 5}, {1, 4}, {1, 3}, {1, 2}, {2, 1}, {4, 2}, {0, 3}}
*/