Submission #120329

#	Time	Username	Problem	Language	Result	Execution time	Memory
120329		Adhyyan1252	Cities (BOI16_cities)	C++11	100 / 100	3863 ms	51208 KiB

cities

#include<bits/stdc++.h>
//12 48
using namespace std;

#define int long long
#define INF 1e17
typedef pair<int, int> ii;
template <typename T>
using vv = vector<vector<T> >;

struct edge{
	int u, v, c;
};

int n, k, m;
vector<int> h;
vv<int> g;
vector<edge> e;
vector<vector<int> > dh;
void dijkstra1(int val){ //val is the index of the impp array
	int source = h[val];
	dh[val] = vector<int>(n, INF);
	priority_queue<ii> q;
	q.push({0, source});
	while(!q.empty()){
		pair<int, int> t = q.top();
		q.pop();
		if(dh[val][t.second] != INF){
			assert(dh[val][t.second] <= -t.first);
			continue;
		}
		dh[val][t.second] = -t.first;
		for(int eid: g[t.second]){
			int next = e[eid].u + e[eid].v - t.second;
			if(dh[val][next] == INF){
				q.push({t.first - e[eid].c, next});
			}else{
				assert(dh[val][next] <= (-t.first + e[eid].c));
			}
		}
	}
}

vector<vector<vector<int> > > dab;

signed main(){
	ios::sync_with_stdio(false); cin.tie(0);
	cin>>n>>k>>m;
	h.resize(k);
	for(int i = 0; i < k; i++){
		cin>>h[i]; h[i]--;
	}
	g.resize(n);
	for(int i = 0; i < m; i++){
		int a, b, c; cin>>a>>b>>c;
		a--, b--;
		e.push_back({a, b, c});
		g[a].push_back(i);
		g[b].push_back(i);
	}
	
	//find shortest path from all important to all others
	dh.resize(k);
	for(int i = 0; i < k; i++){
		dijkstra1(i);
	}
	//d[a][b][i] short distance from i to a and i to b
	dab = vector<vector<vector<int> > > (k, vector<vector<int> > (k, vector<int>(n, INF)));
	for(int a = 0; a < k; a++){
		for(int b = 0; b < k; b++){
			if(a == b){
				dab[a][a] = dh[a];
			}else{
				for(int i = 0; i < n; i++){
					dab[a][b][i] = dh[a][i] + dh[b][i];
				}
			}
		}
	}
	
	//do multisource dijkstra from 
	for(int a = 0; a < k; a++){
		for(int b = 0; b < k; b++){
			//make dab[a][b][i] the best value for i
			vector<int> vis(n, 0);
			priority_queue<ii> q;
			for(int i = 0; i < n; i++){
				q.push({-dab[a][b][i], i});
			}
			while(!q.empty()){
				ii t = q.top(); q.pop();
				if(vis[t.second]) {
					assert(-t.first >= dab[a][b][t.second]);
					continue;
				}
				vis[t.second] = 1;
				assert(dab[a][b][t.second] >= -t.first);
				dab[a][b][t.second] = -t.first;
				
				for(int eid: g[t.second]){
					int next = e[eid].u + e[eid].v - t.second;
					if(dab[a][b][next] > (-t.first + e[eid].c)){
						q.push({t.first - e[eid].c, next});
						assert(vis[next] == 0);
					}
				}
			}
		}
	}
	
	int bestAns = LONG_LONG_MAX;
	//find answer
	for(int i = 0; i < n; i++){
		vector<int> perm(k);
		for(int j = 0; j < k; j++) perm[j] = j;
		
		do{
			int curAns = 0;
			for(int j = 0; j < k; j += 2){
				if(j == k-1){
					curAns += dab[perm[j]][perm[j]][i];
				}else{
					curAns += dab[perm[j]][perm[j+1]][i];
				}
			}
			bestAns = min(bestAns, curAns);
		}while(next_permutation(perm.begin(), perm.end()));
	}
	cout<<bestAns<<endl;
}	

• Subtask 1: 22 / 22
• Subtask 2: 14 / 14
• Subtask 3: 15 / 15
• Subtask 4: 23 / 23
• Subtask 5: 26 / 26