G. 8 Game

#include <bits/stdc++.h>

using namespace std;

#define cin_2d(vec, n, m) for(int i = 0; i < n; i++) for(int j = 0; j < m && cin >> vec[i][j]; j++);
#define cout_2d(vec, n, m) for(int i = 0; i < n; i++, cout << "\n") for(int j = 0; j < m && cout << vec[i][j] << " "; j++);
#define cout_map(mp) for(auto& [f, s] : mp) cout << f << "  " << s << "\n";
#define Time cerr << "Time Taken: " << (float)clock() / CLOCKS_PER_SEC << " Secs" << "\n";
#define fixed(n) fixed << setprecision(n)
#define ceil(n, m) (((n) / (m)) + ((n) % (m) ? 1 : 0))
#define fill(vec, value) memset(vec, value, sizeof(vec));
#define Num_of_Digits(n) ((int)log10(n) + 1)
#define mod_combine(a, b, m) (((a % m) * (b % m)) % m)
#define all(vec) vec.begin(), vec.end()
#define rall(vec) vec.rbegin(), vec.rend()
#define sz(x) int(x.size())
#define debug(x) cout << #x << ": " << (x) << "\n";
#define fi first
#define se second
#define Pair pair < int, int >
#define ll long long
#define ull unsigned long long
#define Mod  1'000'000'007
#define OO 2'000'000'000
#define EPS 1e-9
#define PI acos(-1)

template < typename T = int > istream& operator >> (istream &in, vector < T > &v) {
    for (auto &x: v) in >> x;
    return in;
}

template < typename T = int > ostream& operator << (ostream &out, const vector < T > &v) {
    for (const T &x: v) out << x << ' ';
    return out;
}

void AhMeD_HoSSaM(){
    ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
    #ifndef ONLINE_JUDGE
        freopen("input.txt", "r", stdin), freopen("output.txt", "w", stdout);
    #endif
}

vector < vector < ll > > adj(10);
vector < ll > puzzle(10), cost(10);

bool check(vector < ll >& p){
    for(int i = 1; i <= 8; i++)
        if(p[i] != i)
         return false;
    return true;
}

ll BFS(ll start){
    if(check(puzzle)) return 0;
    queue < pair < pair < ll, ll > , vector < ll > > > bfs;
    map < vector < ll >, ll > path;
    bfs.push({{start, 0ll}, puzzle});
    path.insert({puzzle, 0ll});
    while(!bfs.empty()){
        int sz = sz(bfs);
        while(sz--){
            auto [node, curr_vec] = bfs.front();
            ll curr_node = node.first, curr_cost = node.second;
            bfs.pop();
            for(auto& new_node : adj[curr_node]){
                swap(curr_vec[curr_node], curr_vec[new_node]);
                if(!path.count(curr_vec) || path[curr_vec] > curr_cost + cost[curr_vec[curr_node]]){
                    path[curr_vec] = curr_cost + cost[curr_vec[curr_node]];
                    bfs.push({{new_node, curr_cost + cost[curr_vec[curr_node]]}, curr_vec});
                }
                swap(curr_vec[new_node], curr_vec[curr_node]);
            }
        }
    }
    if(!path.count({0, 1, 2, 3, 4, 5, 6, 7 ,8 ,0})) return -1;
    return path[{0, 1, 2, 3, 4, 5, 6, 7 ,8 ,0}];
}

void Solve(){
    adj = {{0}, {2, 4}, {1, 3, 5}, {2, 6}, {1, 7, 5}, {2, 4, 6, 8}, {3, 5, 9}, {4, 8}, {5, 7, 9}, {6, 8}};
    for(int i = 0, sq; i < 3; i++)
        for(int j = 1; j <= 3 && cin >> sq; j++)
            puzzle[i * 3 + j] = sq;
    for(ll i = 1; i <= 8 && cin >> cost[i]; i++);
    ll beg = -1;
    for(int i = 1; i <= 9; i++)
        if(puzzle[i] == 0)
            beg = i;
    ll ans =  BFS(beg);
    cout << ans << "\n";
}

int main(){
    AhMeD_HoSSaM();
    int t = 1;
    //cin >> t;
    while(t--)
        Solve();
    return 0;
}