Brush (IV) (LOJ 1018)

#include<bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;


#define debug(x) cerr << '[' << (#x) << "] = " << x << '\n'

template<class T> using ordered_set = tree<T, null_type , less<T> , rb_tree_tag , tree_order_statistics_node_update> ;

int N;
vector<pair<int,int>>dust;
int dp[1<<16];
vector<int>slope(300);
int solve(int mask) {
    if(mask == (1<<N)-1) return 0;
    int &ret = dp[mask];
    if(ret!=-1) return ret;
    ret = INT_MAX;
    int i;
    for(i=0; i<N; ++i) if(~mask >> i & 1) break;
    for(int j=0; j<N; ++j) if((i!=j) && ~mask >> j & 1) {
        ret = min(ret, 1+solve(mask | slope[i*N + j]));
    }
    if(ret==INT_MAX) ret = 1;
    return ret;
}
void PlayGround(int T) {
    cin >> N;
    for(int i=0; i<(1<<N); ++i) dp[i] = -1;
    for(int i=0; i<N; ++i) {
        int x, y; cin >> x >> y;
        dust.push_back(make_pair(x, y));
    }
    for(int i=0; i<N; ++i) {
        for(int j=0; j<N; ++j) if(i!=j) {
            int gapx = dust[i].first - dust[j].first;
            int gapy = dust[i].second - dust[j].second;
            int mask = (1<<i) | (1<<j);
            for(int k=0; k<N; ++k) if(i!=k && j!=k) {
                if(gapx * (dust[i].second - dust[k].second) == gapy * (dust[i].first - dust[k].first))
                    mask |= (1<<k);
            }
            slope[i*N + j] = mask;
        }
    }
    cout << "Case " << T << ": " << solve(0) << '\n';
    dust.clear();
    #ifndef ONLINE_JUDGE
        cerr << "Time elapsed: " << 1.0 * clock() / CLOCKS_PER_SEC << " s.\n";
    #endif
}
int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    #ifndef ONLINE_JUDGE
        freopen("input.txt", "r", stdin);
    #endif
    int T;
    cin >> T;
    for(int i=1; i<=T; ++i)
    PlayGround(i);

    return 0;
}