Submission #1291001

#	Time	Username	Problem	Language	Result	Execution time	Memory
1291001		yf_yusuf	Toll (APIO13_toll)	C++20	0 / 100	5 ms	332 KiB

toll

//```//    YF YUSUF
// #include <bits/stdc++.h>
#include <iostream>
#include <vector>
#include <set>
#include <map>
#include <algorithm>
#include <cmath>
#include <numeric>
#include <queue>
#include <stack>
#include <cassert>
#include <climits>
#include <string>
#include <cstdlib>
#include <random>
#include <iomanip>
#include <ctime>
using namespace std;
#ifdef YF_CHECK
	bool LOCAL = 1;
#else
	#pragma GCC optimize ("unroll-loops")
	#pragma GCC optimize ("inline")
	#pragma GCC optimize ("Ofast")
	#pragma GCC optimize ("O3")
	bool LOCAL = 0;
#endif
using ll   = long long;
using ld   = long double;
using vll  = vector <ll>;
using mll  = map <ll,ll>;
using pll  = pair <ll,ll>;
using vvl  = vector <vll>;
using vpll = vector <pll>;
template<class T>T MIN(T&a,T b){a=min(a,b);return a;}
template<class T>T MAX(T&a,T b){a=max(a,b);return a;}
#define all(a) a.begin(),a.end()
#define rall(a) a.rbegin(),a.rend()
#define sgr v+v+1,(tl+tr)/2+1,tr
#define sgl v+v,tl,(tl+tr)/2
#define pb push_back
#define ins insert
#define S second
#define F first
mt19937_64 MT(time(0));
ll BP(ll a,ll b,ll mod=1e9+7){
	if(b==0)return 1;
	ll q=BP(a,b/2,mod);
	return ((q*q)%mod*(b%2?a:1ll))%mod;
}
ll f(ll x){return x*(x+1)/2;}
ll dup(ll a,ll b){return (a+b-1)/b;}
ll lcm(ll a,ll b){return a/__gcd(a,b)*b;}
ll invf(ll x){return (-1+sqrt(1+8*x))/2;}
ll lg(ll x){return (x ? 63 - __builtin_clzll(x) : -1);}
const ll  mod=998244353;
const ll  INF=1e18;
const ll  inf=1e9+7;
const ll  N  =1e6+7;
ll a[N];
vpll K,g[N];
ll n,m,k;
struct DSU{
	vll p,sz;
	vector<pair<ll*, ll>>rb;
	ll n;
	DSU(ll n):n(n){
		build(n);
	}
	DSU();
	void build(ll n){
		p.resize(n+1, 0);
		sz.resize(n+1, 1);
		for(int i=1;i<=n;i++){
			p[i] = i;
			sz[i] = 1;
		}
	}
	ll get(ll x){
		if(p[x]==x)return x;
		else return get(p[x]);
	}
	bool check(ll a,ll b){
		a = get(a);
		b = get(b);
		return (a!=b);
	}
	bool up(ll a,ll b){
		a = get(a);
		b = get(b);
		if(a==b)return 0;
		if(sz[a] < sz[b])swap(a,b);
		rb.pb({ &p[b],  p[b]});
		rb.pb({&sz[a], sz[a]});
		p[b] = a;
		sz[a] += sz[b];
		return 1;
	}
	void rollback(int last){
		while(rb.size() > last){
			*rb.back().F = rb.back().S;
			rb.pop_back();
		}
	}
};
ll up[5][N];
void YF_MAIN(ll TEST){
	cin>>n>>m>>k;
	vvl E, A, B;
	{
		vvl e;
		DSU graph(n);
		for(int i=1;i<=m;i++){
			ll v,u,w;
			cin>>v>>u>>w;
			e.pb({w,v,u});
		}
		sort(all(e));
		for(auto V : e){
			if(graph.up(V[1], V[2]))E.pb(V);
		}
	}
	DSU dsu(n);
	{
		DSU graph(n);
		for(int i=1;i<=k;i++){
			ll v,u;
			cin>>v>>u;
			graph.up(v, u);
			K.pb({v,u});
		}
		for(auto V : E){
			if(graph.up(V[1], V[2])){
				A.pb(V);
				dsu.up(V[1], V[2]);
			} else{
				B.pb(V);
			}
		}
	}
	ll color[n+1]{}, suma[n+1]{}, b[n+1]{};
	ll sz=0;
	{
		set<ll>st;
		mll mp;
		for(int i=1;i<=n;i++){
			cin>>a[i];
			color[i] = dsu.p[i];
			st.insert(color[i]);
		}
		for(auto i : st)
			mp[i] = ++sz;
		for(int i=1;i<=n;i++)
			color[i] = mp[color[i]];
		for(int i=1;i<=n;i++){
			suma[color[i]] += a[i];
		}
	}
	for(auto &[v, u] : K){ v = color[v]; u = color[u]; }
	for(auto &V : A){ V[1] = color[V[1]]; V[2] = color[V[2]]; }
	for(auto &V : B){ V[1] = color[V[1]]; V[2] = color[V[2]]; }
	DSU cycle(n), msu(n);
	vpll g[n+1]{};
	vll d(n+1, inf);
	ll W[sz+1][sz+1]{};
	ll ans = 0;
	for(int mask = 1; mask < (1<<k); mask++){
		cycle.rollback(0);
		msu.rollback(0);
		bool can = 1;
		for(int i=0; i<k; i++)if((mask>>i)&1){
			auto [v, u] = K[i];
			W[v][u] = W[u][v] = inf;
			if(!cycle.up(v, u)){
				can = 0;
				break;
			}
			else{
				g[v].pb({1, u});
				g[u].pb({1, v});
			}
		}
		if(!can)continue;
		vvl nd;
		for(auto V : B){
			ll v = V[1], u = V[2];
			if(cycle.check(v, u)){
				g[v].pb({0, u});
				g[u].pb({0, v});
			} else{
				nd.pb(V);
			}
		}
		queue<ll>q;
		q.push(color[1]);
		vvl e;
		d[color[1]] = 0;
		while(q.size()){
			ll v = q.front();
			q.pop();
			for(auto [b, to] : g[v])if(d[to] > d[v] + 1){
				d[to] = d[v] + 1;
				e.pb({b, v, to});
				q.push(to);
				up[0][to] = v;
			}
		}
		// for(int j=1;j<5;j++){
			// for(int v=1; v<=sz; v++){
				// up[j][v] = up[j-1][up[j-1][v]];
			// }
		// }
		reverse(all(e));
		// im so alone, nothink feels like home
		// come fly with me, 
		for(auto V : nd){
			ll w = V[0], v = V[1], u = V[2];
			while(d[v] < d[u]){
				ll p = up[0][u];
				// cout<<u<<" "<<p<<" u\n";
				W[u][p] = W[p][u] = min(W[p][u], V[0]);
				u = p;
			}
			swap(v, u);
			while(d[v] < d[u]){
				ll p = up[0][u];
				// cout<<u<<" "<<p<<" v\n";
				W[u][p] = W[p][u] = min(W[p][u], V[0]);
				u = p;
			}
			while(v != u){
				ll p = up[0][u];
				ll P = up[0][v];
				W[u][p] = W[p][u] = min(W[p][u], V[0]);
				W[v][P] = W[P][v] = min(W[P][v], V[0]);
				v = P;
				u = p;
			}
		}
		for(int i=1;i<=sz;i++){
			b[i] = suma[i];
		}
		ll now = 0;
		for(auto V : e){
			b[V[1]] += b[V[2]];
		}
		for(auto V : e){
			now += W[V[1]][V[2]] * b[V[2]];
		}
		MAX(ans, now);
		for(int i=1;i<=sz;i++){
			g[i].clear();
			b[i] = 0;
		}
	}
	cout<<ans;
}
const bool TECT=0;
const bool FLSH=0;
const ll SN=1e0 + 7; ll SM[SN];
const ll FN=1e0 + 7; ll FACT[FN], inv[FN], FMOD=inf;
ll PNK(ll n,ll k){return FACT[n] *inv[n-k]%FMOD;}
ll CNK(ll n,ll k){return PNK(n,k)*inv[k  ]%FMOD;}
void BEFORE(){
	for(ll i=2;i<SN;i++){
		if(SM[i])continue;
		for(ll j=i;j<SN;j+=i)
			MAX(SM[j],i);
	}
	FACT[0]=inv[0]=1;
	for(int i=1;i<FN;i++){
		FACT[i]=FACT[i-1]*i%FMOD;
		inv[i]=BP(FACT[i],FMOD-2,FMOD);
	}
}
signed main(){
	// freopen(("input.txt"),"r",stdin);freopen(("output.txt"),"w",stdout);
	if(FLSH){
		ios_base::sync_with_stdio(0);
		cout.setf(ios::fixed);
		cout.precision(0);
		cout.tie(0);
		cin.tie(0);
	}
	int TEST=1;
	if(TECT)
		cin>>TEST;
	BEFORE();
	for(int T=1;T<=TEST;T++){
		// cout<<"Case "<<T<<": ";
		YF_MAIN(T);
		cout<<(T==TEST ? "" : "\n");
	}
	return 0;
} 
//   YF YUSUF ```

• Subtask 1: 0 / 16
• Subtask 2: 0 / 18
• Subtask 3: 0 / 22
• Subtask 4: 0 / 22
• Subtask 5: 0 / 22