This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#pragma GCC optimize("O2")
#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2,fma")
#include <iostream>
#include <vector>
#include <set>
using namespace std;
#define int long long
const int N = 1.1e5;
vector<pair<int,int>> nei[N];
int dp[N][33];
int sp[10],n,m,k;
void dijkstra(int ind){
for (int i=1;i<N;i++)
dp[i][1<<ind] = 1e17;
dp[sp[ind]][1<<ind] = 0;
set<pair<int,int>> st;
st.insert({0,sp[ind]});
while (st.size() > 0){
int u = (*begin(st)).second;
st.erase(begin(st));
for (auto [i,c] : nei[u]){
if (dp[i][1<<ind] > dp[u][1<<ind] + c){
dp[i][1<<ind] = dp[u][1<<ind] + c;
st.insert({dp[i][1<<ind],i});
}
}
}
}
void calc(int msk){
for (int smsk = 0;smsk <= msk;smsk ++){
if ((msk | smsk) != msk)
continue;
for (int u=1;u<=n;u++){
dp[u][msk] = min(dp[u][msk],dp[u][msk - smsk] + dp[u][smsk]);
for (auto [i,c] : nei[u]){
dp[u][msk] = min(dp[u][msk],dp[u][smsk] + dp[i][msk - smsk] + c);
dp[u][msk] = min(dp[u][msk],dp[i][smsk] + dp[i][msk - smsk] + c);
}
}
}
}
signed main(){
// ios_base::sync_with_stdio(false);
// cin.tie(NULL);
// cout.tie(NULL);
cin>>n>>k>>m;
for (int i=1;i<=k;i++)
cin>>sp[i-1];
for (int i=1;i<=m;i++){
int a,b,c;
cin>>a>>b>>c;
nei[a].push_back({b,c});
nei[b].push_back({a,c});
}
for (int i=1;i<=n;i++)
for (int j=1;j<32;j++)
dp[i][j] = 1e17;
for (int i=1;i<=k;i++)
dijkstra(i-1);
for (int i=0;i<32;i++){
if (__builtin_popcount(i) == 2)
calc(i);
}
for (int i=0;i<32;i++){
if (__builtin_popcount(i) == 3)
calc(i);
}
for (int i=0;i<32;i++){
if (__builtin_popcount(i) == 4)
calc(i);
}
for (int i=0;i<32;i++){
if (__builtin_popcount(i) == 5)
calc(i);
}
int Ans = 1e17;
for (int i=1;i<=n;i++)
Ans = min(Ans,dp[i][(1<<k) - 1]);
cout<<Ans<<endl;
}
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