Submission #1291609

#	Time	Username	Problem	Language	Result	Execution time	Memory
1291609		yf_yusuf	Toll (APIO13_toll)	C++20	16 / 100	3 ms	572 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  =1e5+7;
ll a[N];
vpll K;
vector<pair<ll, ll>>g[N];
ll n,m,k;
struct DSU{
	vll p,sz; ll n;
	DSU(ll n):n(n){
		p.resize(n+1, 0); sz.resize(n+1, 1);
		build();
	}
	DSU();
	void build(){
		for(int i=1;i<=n;i++){p[i] = i;sz[i] = 1;}
	}
	ll get(ll x){
		return (x == p[x] ? x : p[x] = get(p[x]));
	}
	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);
		p[b] = a;
		sz[a] += sz[b];
		return 1;
	}
};
ll pr[N], d[N];
ll up[5][N], add[5][N];
vvl e;
void dfs(ll v,ll p){
	for(auto [b, to] : g[v])if(to != p){
		up[0][to] = v;
		up[1][to] = up[0][v];
		up[2][to] = up[1][up[1][to]];
		up[3][to] = up[2][up[2][to]];
		up[4][to] = up[3][up[3][to]];
		d[to] = d[v] + 1;
		dfs(to, v);
		e.pb({b, v, to});
	}
}
void YF_MAIN(ll TEST){
	cin>>n>>m>>k;
	vvl E, 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])) dsu.up(V[1], V[2]);
			else B.pb(V);
		}
	}
	ll color[n+1]{};
	long long suma[n+1]{};
	long long b[n+1]{};
	ll sz=0;
	{
		set<ll>st;
		mll mp;
		for(int i=1;i<=n;i++){
			cin>>a[i];
			color[i] = dsu.get(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++) cout<<color[i]<<" ";cout<<"\n";
		for(int i=1;i<=n;i++) suma[color[i]] += a[i];
		n = sz;
		for(auto &[v, u] : K){ v = color[v]; u = color[u]; }
		for(auto &V : B){ V[1] = color[V[1]]; V[2] = color[V[2]]; }
	}
	DSU cycle(n);
	long long ans = 0;
	bool out = 0;
	for(int mask = 1; mask < (1<<k); mask++){
		out = (mask == 858);
		cycle.build();
		for(int i=1;i<=n;i++){ 
			g[i].clear();
			b[i] = suma[i];
			add[0][i] = add[1][i] = add[2][i] = add[3][i] = add[4][i] = inf;
		}
		bool can = 1;
		for(int i=0; i<k; i++)if((mask>>i)&1){
			auto [v, u] = K[i];
			if(!cycle.up(v, u)){
				can = 0;
				break;
			}
			else{
				g[v].pb({1, u});
				g[u].pb({1, v});
				// if(out)cout<<v<<" "<<u<<" g1\n";
			}
		}
		if(!can)continue;
		vvl nd;
		for(auto V : B){
			ll v = V[1], u = V[2];
			if(cycle.up(v, u)){
				g[v].pb({0, u});
				g[u].pb({0, v});
				// if(out)cout<<v<<" "<<u<<" g0\n";
			} else{
				nd.pb(V);
			}
		}
		d[color[1]] = 0;
		dfs(color[1], color[1]);
		// if(out){
			// for(int v=1;v<=n;v++)cout<<d[v]<<" ";cout<<" d\n";
			// for(int i=0;i<5;i++){
				// for(int v=1;v<=n;v++)cout<<up[i][v]<<" ";cout<<" up\n";
			// }
		// }
		// if only u KNEW, that im still here with u
		// im so alone, nothink feels like home
		// come fly with me, 
		for(auto V : nd){//O(n * logn)
			ll w = V[0], v = V[1], u = V[2];
			// if(out)cout<<v<<" "<<u<<" "<<w<<" W\n";
			
			if(d[v] > d[u])swap(v, u);
			// cout<<u<<" "<<v<<" "<<w<<" nd\n";
			for(int i=4;i>=0;i--){
				if(!up[i][u])continue;
				if(d[up[i][u]] >= d[v]){
					MIN(add[i][u], w); 
					u = up[i][u];
				}
			}
			for(int i=4;i>=0;--i){
				// cout<<u<<" "<<v<<" "<<i<<" "<<up[i][u]<<" "<<up[i][v]<<" LAST\n";
				if(!up[i][u])continue;
				if((up[i][v] ^ up[i][u])){
					MIN(add[i][u], w);
					u = up[i][u];
					MIN(add[i][v], w);
					v = up[i][v];
				}
			}
			{
				MIN(add[0][u], w);
				u = up[0][u];
				MIN(add[0][v], w);
				v = up[0][v];
			}
		}
		// if(out){
			// cout<<mask<<" mask\n";
			// for(int i=0;i<5;i++){
				// for(int v=1;v<=n;v++)cout<<(add[i][v] == inf ? -1 : add[i][v])<<" ";cout<<"\n";
			// }
		// }
		for(int i=4;i>0;i--){// O(n log(n))
			for(int u=1;u<=n;u++){
				int v = up[i-1][u];
				MIN(add[i-1][v], add[i][u]);
				MIN(add[i-1][u], add[i][u]);
			}
		}
		
		// cout<<mask<<" mask\n";
		// for(int i=0;i<5;i++){
			// for(int v=1;v<=n;v++)cout<<(add[i][v] == inf ? -1 : add[i][v])<<" ";cout<<"\n";
		// }
		// for(auto V : e) if(V[0])cout<<V[2]<<" ";cout<<" V\n";	
		long long now = 0;
		for(auto V : e) b[V[1]] += b[V[2]]; //O(n)
		for(auto V : e) now += V[0] * 1ll * add[0][V[2]] * b[V[2]]; //O(n)
		// cout<<mask<<" "<<now<<"\n";
		// if(out){
			// cout<<mask<<" "<<now<<" m\n";
			// for(int i=0; i<k; i++)if((mask>>i)&1)cout<<K[i].F<<" "<<K[i].S<<"\n";
			// for(auto V : e){
				// if(!V[0])continue;
				// cout<<b[V[2]]<<" "<<V[2]<<" "<<add[0][V[2]]<<",\n";
			// }
			// cout<<"\n";
		// }
		e.clear();
		MAX(ans, now);
	}
	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: 16 / 16
• Subtask 2: 0 / 18
• Subtask 3: 0 / 22
• Subtask 4: 0 / 22
• Subtask 5: 0 / 22