ソースコード
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pll = pair<long long, long long>;
constexpr char ln = '\n';
constexpr long long MOD = 1000000007;
constexpr long long INF = 1<<30;
constexpr long long LINF = 1LL<<60;
constexpr double EPS = 1e-9;
#define all(v) v.begin(), v.end()
#define rep(i, n) for(int i=0;i<(n);i++)
#define rept(i, j, n) for(int i=(j); i<(n); i++)
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
ll shortest_Hamiltonaian_Path(vector<vector<ll>>& adj, vector<int>& T, bool is_cycle=false, int s=-1){
int k = adj.size();
ll inf = 1LL<<60;
//dp[mask][i]:=通過済みの地点の集合がmaskで、現在地が頂点iである場合の最小コスト
vector<vector<ll>> dp(1 << k, vector<ll>(k, inf));
//init
//複数始点
if(s==-1)for(int i=0; i<k; i++)dp[0][i] = T[i];
//単一始点
else dp[0][s] = 0;
for(int mask=1; mask<(1<<k)-1; mask++){
for(int i=0; i<k; i++){
if(!(mask >> i & 1)){
for(int j=0; j<k; j++){
if(mask >> j & 1){
ll cost = T[i];
rep(l, k){
if(mask>>l&1)cost -= adj[l][i];
}
cost = max(0LL, cost);
chmin(dp[mask][i], dp[mask ^ 1 << j][j] + cost);
}
}
}
}
}
ll res = inf;
rep(i, k)chmin(res, dp[((1<<k)-1) ^ 1 << i][i] + (is_cycle ? adj[i][s] : 0));
return res;
}
int main(){
int N; cin >> N;
vector<int> T(N); rep(i, N)cin >> T[i];
vector<vector<ll>> adj(N, vector<ll>(N));
rep(i, N)rep(j, N)cin >> adj[i][j];
cout << shortest_Hamiltonaian_Path(adj, T) << ln;
}