Language: C++

#include<bits/stdc++.h>
//using namespace std;
#pragma GCC target("avx")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#define rep(i,j,n) for(ll i=(ll)(j);i<(ll)(n);i++)
#define REP(i,j,n) for(ll i=(ll)(j);i<=(ll)(n);i++)
#define per(i,j,n) for(ll i=(ll)(j);(ll)(n)<=i;i--)
#define ll long long
#define ALL(a) (a).begin(),(a).end()
#define disup(A,key) distance(A.begin(),upper_bound(ALL(A),(ll)(key)))
#define dislow(A,key) distance(A.begin(),lower_bound(ALL(A),(ll)(key)))
#define pb emplace_back
#define mp std::make_pair
//
#define endl "\n"
//using std::endl;
using std::cin;
using std::cout;
using std::vector;
using std::string;
using std::upper_bound;
using std::lower_bound;
using vi=vector<ll>;
using vii=vector<vi>;
using pii=std::pair<ll,ll>;
//
constexpr ll MOD=1e9+7;
//constexpr ll MOD=998244353;
//constexpr ll MOD=10000000;
//constexpr ll MOD=1e5;
constexpr ll MAX=1e7;
constexpr ll INF=(1ll<<62);
template<class T>
class prique :public std::priority_queue<T, std::vector<T>, std::greater<T>> {};
template<typename T>
struct Segment_tree{
    ll N;
    T mem;
    vector<T> node;
    Segment_tree(vector<T> &X,T m):mem(m){
        ll sz=X.size();
        N=1;
        while(N<sz) N*=2;
        node.resize(2*N-1,mem);
        rep(i,0,sz) node[N-1+i]=X[i];
        per(i,N-2,0){
            node[i]=Compare(node[i*2+1],node[i*2+2]);
        }
    }
    T Compare(T &A,T &B){
        return std::max(A,B);
    }
    void update(ll X,T val){
        X+=N-1;
        node[X]=val;
        while(X>0){
            X=(X-1)/2;
            node[X]=Compare(node[X*2+1],node[X*2+2]);
        }
    }
    T Query(ll a,ll b,ll now,ll l,ll r){ //[a,b),[l,r)
        if(r<0) r=N;
        if(r<=a||b<=l) return mem;
        if(a<=l&&r<=b) return node[now];
        auto vl=Query(a,b,now*2+1,l,(l+r)/2),vr=Query(a,b,now*2+2,(l+r)/2,r);
        return Compare(vl,vr);
    }
};
struct Binary_indexed_tree{
    int N;
    vi bit;
    Binary_indexed_tree(int n):N(n){
        bit.resize(N+1,0);
    }
    void add(int x,int a){
        for(x;x<=N;x+=(x&-x)) bit[x]+=a;
    }
    ll sum(int x){
        ll ret=0;
        for(x;x>0;x-=(x&-x)) ret+=bit[x];
        return ret;
    }
    ll lower_bound(ll X){
        if(sum(N)<X) return -1;
        ll ret=0,memo=1,sum=0;
        while(memo*2<=N) memo*=2;
        while(memo>0){
            if(memo+ret<=N&&sum+bit[memo+ret]<X){
                sum+=bit[memo+ret];
                ret+=memo;
            }
            memo/=2;
        }
        return ret+1;
    }
};
struct Union_Find{
    ll N;
    vi par;
    vi siz;
    Union_Find(int n):N(n){
        par.resize(N);
        siz.resize(N,1);
        rep(i,0,N) par[i]=i;
    }
    ll root(ll X){
        if(par[X]==X) return X;
        return par[X]=root(par[X]);
    }
    bool same(ll X,ll Y){
        return root(X)==root(Y);
    }
    void unite(ll X,ll Y){
        X=root(X);
        Y=root(Y);
        if(X==Y) return;
        par[X]=Y;
        siz[Y]+=siz[X];
        siz[X]=0;
    }
    ll size(ll X){
        return siz[root(X)];
    }
};
long long modpow(long long a, long long n, long long mod) {
    long long res = 1;
    while (n > 0) {
        if (n & 1) res = res * a % mod;
        a = a * a % mod;
        n >>= 1;
    }
    return res;
}
vi fac,finv,inv;
void COMinit() {
    fac.resize(MAX);
    finv.resize(MAX);
    inv.resize(MAX);
    fac[0] = fac[1] = 1;
    finv[0] = finv[1] = 1;
    inv[1] = 1;
    for (int i = 2; i < MAX; i++){
        fac[i] = fac[i - 1] * i % MOD;
        inv[i] = MOD - inv[MOD%i] * (MOD / i) % MOD;
        finv[i] = finv[i - 1] * inv[i] % MOD;
    }
}
ll COM(ll n,ll r){
    if(n<r||n<0||r<0) return 0;
    return fac[n]*finv[r]%MOD*finv[n-r]%MOD;
}
long long modinv(long long a, long long m) {
    long long b = m, u = 1, v = 0;
    while (b) {
        long long t = a / b;
        a -= t * b; std::swap(a, b);
        u -= t * v; std::swap(u, v);
    }
    u %= m; 
    if (u < 0) u += m;
    return u;
}
double dfs(ll zero,ll one,ll two,ll three,std::unordered_map<std::tuple<ll,ll,ll>,double> &memo){
    if(memo.count(std::make_tuple(zero,one,two))) return memo[std::make_tuple(zero,one,two)];
    if(one==0&&two==0&&three==0) return 0;
    double ret=0;
    ll sum=one+two+three;
    if(one>0){
        ret+=one*1.0/sum*dfs(zero+1,one-1,two,three,memo);
    }
    if(two>0){
        ret+=two*1.0/sum*dfs(zero,one+1,two-1,three,memo);
    }
    if(three>0){
        ret+=three*1.0/sum*dfs(zero,one,two+1,three-1,memo);
    }
    ret+=zero*1.0/sum;
    ret++;
    return memo[std::make_tuple(zero,one,two)]=ret;
}
int main(){
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    ll N; cin>>N;
    vi cnt(4);
    rep(i,0,N){
        ll X; cin>>X;
        cnt[X]++;
    }
    std::unordered_map<std::tuple<ll,ll,ll>,double> memo;
    double ans=dfs(cnt[0],cnt[1],cnt[2],cnt[3],memo);
    printf("%.15lf\n",ans);
}


Compiler output:
a.cc: In function 'int main()':
a.cc:192:53: error: use of deleted function 'std::unordered_map<_Key, _Tp, _Hash, _Pred, _Alloc>::unordered_map() [with _Key = std::tuple<long long int, long long int, long long int>; _Tp = double; _Hash = std::hash<std::tuple<long long int, long long int, long long int> >; _Pred = std::equal_to<std::tuple<long long int, long long int, long long int> >; _Alloc = std::allocator<std::pair<const std::tuple<long long int, long long int, long long int>, double> >]'
  192 |     std::unordered_map<std::tuple<ll,ll,ll>,double> memo;
      |                                                     ^~~~
In file included from /usr/include/c++/14/unordered_map:41,
                 from /usr/include/c++/14/functional:63,
                 from /usr/include/x86_64-linux-gnu/c++/14/bits/stdc++.h:53,
                 from a.cc:1:
/usr/include/c++/14/bits/unordered_map.h:148:7: note: 'std::unordered_map<_Key, _Tp, _Hash, _Pred, _Alloc>::unordered_map() [with _Key = std::tuple<long long int, long long int, long long int>; _Tp = double; _Hash = std::hash<std::tuple<long long int, long long int, long long int> >; _Pred = std::equal_to<std::tuple<long long int, long long int, long long int> >; _Alloc = std::allocator<std::pair<const std::tuple<long long int, long long int, long long int>, double> >]' is implicitly deleted because the default definition would be ill-formed:
  148 |       unordered_map() = default;
      |       ^~~~~~~~~~~~~
/usr/include/c++/14/bits/unordered_map.h: At global scope:
/usr/include/c++/14/bits/unordered_map.h:148:7: error: use of deleted function 'std::_Hashtable<_Key, _Value, _Alloc, _ExtractKey, _Equal, _Hash, _RangeHash, _Unused, _RehashPolicy, _Traits>::_Hashtable() [with _Key = std::tuple<long long int, long long int, long long int>; _Value = std::pair<const std::tuple<long long int, long long int, long long int>, double>; _Alloc = std::allocator<std::pair<const std::tuple<long long int, long long int, long long int>, double> >; _ExtractKey = std::__detail::_Select1st; _Equal = std::equal_to<std::tuple<long long int, long long int, long long int> >; _Hash = std::hash<std::tuple<long long int, long long int, long long int> >; _RangeHash = std::__detail::_Mod_range_hashing; _Unused = std::__detail::_Default_ranged_hash; _RehashPolicy = std::__detail::_Prime_rehash_policy; _Traits = std::__detail::_Hashtable_traits<true, false, true>]'
In file included from /usr/include/c++/14/bits/unordered_map.h:33:
/usr/include/c++/14/bits/hashtable.h:539:7: note: 'std::_Hashtable<_Key, _Value, _Alloc, _ExtractKey, _Equal, _Hash, _RangeHash, _Unused, _RehashPolicy, _Traits>::_Hashtable() [with _Key = std::tuple<long long int, long long int, long long int>; _Value = std::pair<const std::tuple<long long int, long long int, long long int>, double>; _Alloc = std::allocator<std::pair<const std::tuple<long long int, long long int, long long int>, double> >; _ExtractKey = std::__detail::_Select1st; _Equal = std::equal_to<std::tuple<long long int, long long int, long long int> >; _Hash = std::hash<std::tuple<long long int, long long int, long long int> >; _RangeHash = std::__detail::_Mod_range_hashing; _Unused = std::__detail::_Default_ranged_hash; _RehashPolicy = std::__detail::_Prime_rehash_policy; _Traits = std::__detail::_Hashtable_traits<true, false, true>]' is implicitly deleted because the default definition would be ill-formed:
  539 |       _Hashtable() = default;
      |       ^~~~~~~~~~
/usr/include/c++/14/bits/hashtable.h:539:7: error: use of deleted function 'std::__detail::_Hashtable_base<_Key, _Value, _ExtractKey, _Equal, _Hash, _RangeHash, _Unused, _Traits>::_Hashtable_base() [with _Key = std::tuple<long long int, long long int, long long int>; _Value = std::pair<const std::tuple<long long int, long long int, long long int>, double>; _ExtractKey = std::__detail::_Select1st; _Equal = std::equal_to<std::tuple<long long int, long long int, long long int> >; _Hash = std::hash<std::tuple<long long int, long long int, long long int> >; _RangeHash = std::__detail::_Mod_range_hashing; _Unused = std::__detail::_Default_ranged_hash; _Traits = std::__detail::_Hashtable_traits<true, false, true>]'
In file included from /usr/include/c++/14/bits/hashtable.h:35:
/usr/include/c++/14/bits/hashtable_policy.h:1731:7: note: 'std::__detail::_Hashtable_base<_Key, _Value, _ExtractKey, _Equal, _Hash, _RangeHash, _Unused, _Traits>::_Hashtable_base() [with _Key = std::tuple<long long int, long long int, long long int>; _Value = std::pair<const std::tuple<long long int, long long int, long long int>, double>; _ExtractKey = std::__detail::_Select1st; _Equal = std::equal_to<std::tuple<long long int, long long int, long long int> >; _Hash = std::hash<std::tuple<long long int, long long int, long long int> >; _RangeHash = std::__detail::_Mod_range_hashing; _Unused = std::__detail::_Default_ranged_hash; _Traits = std::__detail::_Hashtable_traits<true, false, true>]' is implicitly deleted because the default definition would be ill-formed:
 1731 |       _Hashtable_base() = default;
      |       ^~~~~~~~~~~~~~~
/usr/include/c++/14/bits/hashtable_policy.h:1731:7: error: use of deleted function 'std::__detail::_Hash_code_base<_Key, _Value, _ExtractKey, _Hash, _RangeHash, _Unused, __cache_hash_code>::_Hash_code_base() [with _Key = std::tuple<long long int, long long int, long long int>; _Value = std::pair<const std::tuple<long long int, long long int, long long int>, double>; _ExtractKey = std::__detail::_Select1st; _Hash = std::hash<std::tuple<long long int, long long int, long long int> >; _RangeHash = std::__detail::_Mod_range_hashing; _Unused = std::__detail::_Default_ranged_hash; bool __cache_hash_code = true]'
/usr/include/c++/14/bits/hashtable_policy.h: In instantiation of 'std::__detail::_Hashtable_ebo_helper<_Nm, _Tp, true>::_Hashtable_ebo_helper() [with int _Nm = 1; _Tp = std::hash<std::tuple<long long int, long long int, long long int> >]':
/usr/include/c++/14/bits/hashtable_policy.h:1328:7:   required from here
 1328 |       _Hash_code_base() = default;
      |       ^~~~~~~~~~~~~~~
/usr/include/c++/14/bits/hashtable_policy.h:1245:49: error: use of deleted function 'std::hash<std::tuple<long long int, long long int, long long int> >::hash()'
 1245 |       _Hashtable_ebo_helper() noexcept(noexcept(_Tp())) : _Tp() { }
      |                                                 ^~~~~
In file included from /usr/include/c++/14/string_view:50,
                 from /usr/include/c++/14/bits/basic_string.h:47,
                 from /usr/include/c++/14/string:54,
                 from /usr/include/c++/14/bitset:52,
                 from /usr/include/x86_64-linux-gnu/c++/14/bits/stdc++.h:52:
/usr/include/c++/14/bits/functional_hash.h:102:12: note: 'std::hash<std::tuple<long long int, long long int, long long int> >::hash()' is implicitly deleted because the default definition would be ill-formed:
  102 |     struct hash : __hash_enum<_Tp>
      |            ^~~~
/usr/include/c++/14/bits/functional_hash.h:102:12: error: no matching function for call to 'std::__hash_enum<std::tuple<long long int, long long int, long long int>, false>::__hash_enum()'
/usr/include/c++/14/bits/functional_hash.h:83:7: note: candidate: 'std::__hash_enum<_Tp, <anonymous> >::__hash_enum(std::__hash_enum<_Tp, <anonymous> >&&) [with _Tp = std::tuple<long long int, long long int, long long int>; bool <anonymous> = false]'
   83 |       __hash_enum(__hash_enum&&);
      |       ^~~~~~~~~~~
/usr/include/c++/14/bits/functional_hash.h:83:7: note:   candidate expects 1 argument, 0 provided
/usr/include/c++/14/bits/functional_hash.h:102:12: error: 'std::__hash_enum<_Tp, <anonymous> >::~__hash_enum() [with _Tp = std::tuple<long long int, long long int, long long int>; bool <anonymous> = false]' is private within this context
  102 |     struct hash : __hash_enum<_Tp>
      |            ^~~~
/usr/include/c++/14/bits/functional_hash.h:84:7: note: declared private here
   84 |       ~__hash_enum();
      |       ^
/usr/include/c++/14/bits/hashtable_policy.h:1245:49: note: use '-fdiagnostics-all-candidates' to display considered candidates
 1245 |       _Hashtable_ebo_helper() noexcept(noexcept(_Tp())) : _Tp() { }
      |                                                 ^~~~~
/usr/include/c++/14/bits/hashtable_policy.h:1328:7: note: 'std::__detail::_Hash_code_base<_Key, _Value, _ExtractKey, _Hash, _RangeHash, _Unused, __cache_hash_code>::_Hash_code_base() [with _Key = std::tuple<long long int, long long int, long long int>; _Value = std::pair<const std::tuple<long long int, long long int, long long int>, double>; _ExtractKey = std::__detail::_Select1st; _Hash = std::hash<std::tuple<long long int, long long int, long long int> >; _RangeHash = std::__detail::_Mod_range_hashing; _Unused = std::__detail::_Default_ranged_hash; bool __cache_hash_code = true]' is implicitly deleted because the default definition would be ill-formed:
 1328 |       _Hash_code_base() = default;
      |       ^~~~~~~~~~~~~~~
/usr/include/c++/14/bits/hashtable_policy.h:1328:7: error: use of deleted function 'std::__detail::_Hashtable_ebo_helper<1, std::hash<std::tuple<long long int, long long int, long long int> >, true>::~_Hashtable_ebo_helper()'
/usr/include/c++/14/bits/hashtable_policy.h:1242:12: note: 'std::__detail::_Hashtable_ebo_helper<1, std::hash<std::tuple<long long int, long long int, long long int> >, true>::~_Hashtable_ebo_helper()' is implicitly deleted because the default definition would be ill-formed:
 1242 |     struct _Hashtable_ebo_helper<_Nm, _Tp, true>
      |            ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/hashtable_policy.h:1242:12: error: use of deleted function 'std::hash<std::tuple<long long int, long long int, long long int> >::~hash()'
/usr/include/c++/14/bits/functional_hash.h:102:12: note: 'std::hash<std::tuple<long long int, long long int, long long int> >::~hash()' is implicitly deleted because the default definition would be ill-formed:
  102 |     struct hash : __hash_enum<_Tp>
      |            ^~~~
/usr/include/c++/14/bits/functional_hash.h:102:12: error: 'std::__hash_enum<_Tp, <anonymous> >::~__hash_enum() [with _Tp = std::tuple<long long int, long long int