상어의 저녁식사

• maximum flow solution

#include <bits/stdc++.h>

#pragma optimization_level 3
#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math,O3")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx")
#pragma GCC optimize("Ofast")//Comment optimisations for interactive problems (use endl)
#pragma GCC target("avx,avx2,fma")
#pragma GCC optimization ("unroll-loops")

#define MAX_N 202
#define ll long long
#define pll pair<ll, ll>
#define vpll vector<pll>
#define vall3 vector<array<ll,3>>
#define vll vector<ll>
#define vs vector<string>
#define vvs vector<vs>
#define vvll vector<vll>
#define all(a) begin(a), end(a)
using namespace std;

ll n;
vll adj[MAX_N];
ll cap[MAX_N][MAX_N], path[MAX_N], flo[MAX_N][MAX_N];

bool eat(array<ll,3>& a, array<ll,3>& b) {
    return a[0] >= b[0] and a[1] >= b[1] and a[2] >= b[2];
}

bool eq(array<ll,3>& a, array<ll,3>& b) {
    return a[0] == b[0] and a[1] == b[1] and a[2] == b[2];
}

bool bfs(ll u, ll v) {
    memset(path, -1, sizeof path);
    queue<ll> q;
    q.push(u);
    while(!q.empty() and path[v] == -1) {
        auto n = q.front(); q.pop();
        for(auto& m : adj[n]) {
            if(flo[n][m] > 0 and path[m] == -1) {
                path[m] = n;
                q.push(m);
            }
        }
    }
    return path[v] != -1;
}

ll solve(vall3& spec) {
    ll u = 52, v = 53, gap = 100;
    for(ll i = 0; i < n; i++) {
        for(ll j = 0; j < n; j++) {
            if((eq(spec[i], spec[j]) and i < j) or (!eq(spec[i], spec[j]) and eat(spec[i], spec[j]))) {
                adj[i].push_back(j + gap);
                adj[j+gap].push_back(i);
                flo[i][j + gap] = 1;
            }
        }
        adj[u].push_back(i);
        adj[i].push_back(u);
        flo[u][i] = 2;
        adj[i+gap].push_back(v);
        adj[v].push_back(i+gap);
        flo[i + gap][v] = 1;
    }
    ll res = 0;
    while(bfs(u,v)) {
        ll vv = v, mi = INT_MAX;
        while(vv != u) {
            auto uu = path[vv];
            mi = min(mi, flo[uu][vv]);
            vv = uu;
        }
        vv = v;
        while(vv != u) {
            auto uu = path[vv];
            flo[vv][uu] += mi;
            flo[uu][vv] -= mi;
            vv = uu;
        }
        res++;
    }

    return n - res;
}

int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.setf(ios::fixed);
    cout.precision(6);
    cin>>n;
    vall3 sh;
    for(ll i = 0, s, p, c; i < n; i++) {
        cin>>s>>p>>c;
        sh.push_back({s,p,c});
    }

    cout<<solve(sh);

    return 0;
}

• bipartited matching solution

#include <bits/stdc++.h>

#pragma optimization_level 3
#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math,O3")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx")
#pragma GCC optimize("Ofast")//Comment optimisations for interactive problems (use endl)
#pragma GCC target("avx,avx2,fma")
#pragma GCC optimization ("unroll-loops")

#define MAX_N 202
#define ll long long
#define pll pair<ll, ll>
#define vpll vector<pll>
#define vall3 vector<array<ll,3>>
#define vll vector<ll>
#define vs vector<string>
#define vvs vector<vs>
#define vvll vector<vll>
#define all(a) begin(a), end(a)
using namespace std;

ll n;
vll adj[MAX_N];
ll seen[MAX_N], match[MAX_N];

bool eat(array<ll,3>& a, array<ll,3>& b) {
    return a[0] >= b[0] and a[1] >= b[1] and a[2] >= b[2];
}

bool eq(array<ll,3>& a, array<ll,3>& b) {
    return a[0] == b[0] and a[1] == b[1] and a[2] == b[2];
}

bool dfs(ll u, ll s) {
    seen[u] = s;
    for(auto& v : adj[u]) {
        if(match[v] == -1 or (seen[match[v]] != s and dfs(match[v], s))) {
            match[v] = u;
            return true;
        }
    }
    return false;
}

ll solve(vall3& spec) {
    ll u = 52, v = 53, gap = 100;
    for(ll i = 0; i < n; i++) {
        for(ll j = 0; j < n; j++) {
            if((eq(spec[i], spec[j]) and i < j) or (!eq(spec[i], spec[j]) and eat(spec[i], spec[j]))) {
                adj[i].push_back(j + gap);
            }
        }
    }
    ll res = 0;
    memset(seen, -1, sizeof seen);
    memset(match, -1, sizeof match);
    for(ll i = 0; i < n; i++) {
        dfs(i, i * 2);
        dfs(i, i * 2 + 1);
    }

    for(ll i = 0; i < n; i++) {
        res += match[i + gap] == -1;
    }

    return res;
}

int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.setf(ios::fixed);
    cout.precision(6);
    cin>>n;
    vall3 sh;
    for(ll i = 0, s, p, c; i < n; i++) {
        cin>>s>>p>>c;
        sh.push_back({s,p,c});
    }

    cout<<solve(sh);

    return 0;
}