最大空凸包

Posted 2022-12-14 nublity

#pragma GCC optimize(2)
#pragma GCC optimize(3, "Ofast", "inline")

#include<bits/stdc++.h>

#define ll long long
#define met(a, x) memset(a,x,sizeof(a))

using namespace std;
const double pi = acos(-1.0);
typedef struct Point 
    int x, y;

    Point() 

    Point(int x, int y) : x(x), y(y) 

    Point operator+(const Point &b) const  return Point(x + b.x, y + b.y); 

    Point operator-(const Point &b) const  return Point(x - b.x, y - b.y); 

    int operator*(const Point &b) const  return x * b.y - y * b.x; 

    int len() const  return x * x + y * y; 

    int operator<(const Point &a) const 
        if ((*this) * a > 0 || (*this) * a == 0 && len() < a.len())
            return 1;
        return 0;
    
 Point;
int n;
Point s[122], p[122];
int dp[122][122];

int Jud(int m) 
    int ans, i, j, now, k, flag, S;
    memset(dp, 0, sizeof(dp));
    ans = 0;
    for (i = 2; i <= m; i++) 
        now = i - 1;
        while (now >= 1 && p[i] * p[now] == 0)
            now--;
        flag = 0;
        if (now == i - 1)
            flag = 1;
        while (now >= 1) 
            S = p[now] * p[i];
            k = now - 1;
            while (k >= 1 && (p[now] - p[i]) * (p[k] - p[now]) > 0)
                k--;
            if (k >= 1)
                S += dp[now][k];
            if (flag)
                dp[i][now] = S;
            ans = max(ans, S);
            now = k;
        
        if (flag == 0)
            continue;
        for (j = 1; j <= i - 1; j++)
            dp[i][j] = max(dp[i][j], dp[i][j - 1]);
    
    return ans;


int main() 
    ios::sync_with_stdio(false);
    cin.tie(0);
    int _, i, j, m, ans;
    cin >> _;
    while (_--) 
        cin >> n;
        for (i = 1; i <= n; i++)
            cin >> s[i].x >> s[i].y;
        ans = 0;
        for (i = 1; i <= n; i++) 
            m = 0;
            for (j = 1; j <= n; j++) 
                if (s[j].y > s[i].y || s[j].y == s[i].y && s[j].x >= s[i].x)
                    p[++m] = s[j] - s[i];
            
            sort(p + 1, p + m + 1);
            ans = max(ans, Jud(m));
        
        cout << fixed << setprecision(1) << (ans/2.0) << endl;
    
    return 0;