mmrz's library

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:heavy_check_mark: verify/aoj/id/2828.test.cpp

Depends on

Code

#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/challenges/sources/JAG/Prelim/2828"
#include "./../../../template/template.hpp"
#include "./../../../graph/hungarian.hpp"

using namespace mmrz;

void mmrz::solve(){
	int n;
	while(cin >> n && n){
		vector<vector<int>> mat(n, vector<int>(3));
		rep(i, n){
			rep(j, 3)cin >> mat[i][j];
			sort(all(mat[i]));
		}
		vector a(n, vector(n, 0LL));
		rep(i, n)rep(j, n){
			if(i == j)continue;
			bool flg = true;
			rep(k, 3)if(mat[i][k] <= mat[j][k])flg = false;
			if(not flg)continue;

			a[i][j] = mat[j][0]*mat[j][1]*mat[j][2];
		}

		vector<int> h = hungarian<false, ll>(a);

		ll ans = 0;
		rep(i, n){
			ans += mat[i][0]*mat[i][1]*mat[i][2];
		}
		rep(i, n){
			ans -= a[i][h[i]];
		}

		cout << ans << '\n';

	}
}
#line 1 "verify/aoj/id/2828.test.cpp"
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/challenges/sources/JAG/Prelim/2828"
#line 1 "template/template.hpp"
# include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
const double pi = acos(-1);
template<class T>constexpr T inf() { return ::std::numeric_limits<T>::max(); }
template<class T>constexpr T hinf() { return inf<T>() / 2; }
template <typename T_char>T_char TL(T_char cX) { return tolower(cX); }
template <typename T_char>T_char TU(T_char cX) { return toupper(cX); }
template<class T> bool chmin(T& a,T b) { if(a > b){a = b; return true;} return false; }
template<class T> bool chmax(T& a,T b) { if(a < b){a = b; return true;} return false; }
int popcnt(unsigned long long n) { int cnt = 0; for (int i = 0; i < 64; i++)if ((n >> i) & 1)cnt++; return cnt; }
int d_sum(ll n) { int ret = 0; while (n > 0) { ret += n % 10; n /= 10; }return ret; }
int d_cnt(ll n) { int ret = 0; while (n > 0) { ret++; n /= 10; }return ret; }
ll gcd(ll a, ll b) { if (b == 0)return a; return gcd(b, a%b); };
ll lcm(ll a, ll b) { ll g = gcd(a, b); return a / g*b; };
ll MOD(ll x, ll m){return (x%m+m)%m; }
ll FLOOR(ll x, ll m) {ll r = (x%m+m)%m; return (x-r)/m; }
template<class T> using dijk = priority_queue<T, vector<T>, greater<T>>;
# define all(qpqpq)           (qpqpq).begin(),(qpqpq).end()
# define UNIQUE(wpwpw)        (wpwpw).erase(unique(all((wpwpw))),(wpwpw).end())
# define LOWER(epepe)         transform(all((epepe)),(epepe).begin(),TL<char>)
# define UPPER(rprpr)         transform(all((rprpr)),(rprpr).begin(),TU<char>)
# define rep(i,upupu)         for(ll i = 0, i##_len = (upupu);(i) < (i##_len);(i)++)
# define reps(i,opopo)        for(ll i = 1, i##_len = (opopo);(i) <= (i##_len);(i)++)
# define len(x)                ((ll)(x).size())
# define bit(n)               (1LL << (n))
# define pb push_back
# define eb emplace_back
# define exists(c, e)         ((c).find(e) != (c).end())

struct INIT{
	INIT(){
		std::ios::sync_with_stdio(false);
		std::cin.tie(0);
		cout << fixed << setprecision(20);
	}
}INIT;

namespace mmrz {
	void solve();
}

int main(){
	mmrz::solve();
}
#line 2 "graph/hungarian.hpp"

#line 6 "graph/hungarian.hpp"

template<bool is_min, typename T>
std::vector<int> hungarian(std::vector<std::vector<T>> a) {
	T infty = std::numeric_limits<T>::max()/T(2);
	int n = (int)a.size();
	
	if(not is_min){
		for(int i = 0;i < n;i++){
			for(int j = 0; j < n;j++){
				a[i][j] = -a[i][j];
			}
		}
	}

	std::vector<int> p(n);
	std::iota(p.begin(), p.end(), 0);

	std::vector<T> h = {0};
	h.reserve(n);
	for(int i = 1;i < n;i++){
		h.push_back(0);
		std::vector<T> d(i+1, infty);
		std::vector<int> pre(i+1, -1);
		std::vector<bool> used(i+1, false);

		d[i] = 0;
		pre[i] = i;

		for(int _ = 0;_ <= i;_++){
			T min_d = infty;
			int v = -1;
			for(int j = 0;j <= i;j++){
				if(not used[j] && min_d > d[j]-h[j]){
					min_d = d[j]-h[j];
					v = j;
				}
			}
				
			used[v] = true;

			for(int j = 0;j <= i;j++){
				if(not used[j] || j == i){
					T nd = d[v] - a[v][p[v]] + a[j][p[v]];
					if(d[j] > nd){
						d[j] = nd;
						pre[j] = v;
					}
				}
			}
		}

		int cur = i;
		while(pre[cur] != i){
			std::swap(p[cur], p[pre[cur]]);
			cur = pre[cur];
		}
		h = d;
	}
	return p;
}
#line 4 "verify/aoj/id/2828.test.cpp"

using namespace mmrz;

void mmrz::solve(){
	int n;
	while(cin >> n && n){
		vector<vector<int>> mat(n, vector<int>(3));
		rep(i, n){
			rep(j, 3)cin >> mat[i][j];
			sort(all(mat[i]));
		}
		vector a(n, vector(n, 0LL));
		rep(i, n)rep(j, n){
			if(i == j)continue;
			bool flg = true;
			rep(k, 3)if(mat[i][k] <= mat[j][k])flg = false;
			if(not flg)continue;

			a[i][j] = mat[j][0]*mat[j][1]*mat[j][2];
		}

		vector<int> h = hungarian<false, ll>(a);

		ll ans = 0;
		rep(i, n){
			ans += mat[i][0]*mat[i][1]*mat[i][2];
		}
		rep(i, n){
			ans -= a[i][h[i]];
		}

		cout << ans << '\n';

	}
}
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