結果

問題 No.108 トリプルカードコンプ
ユーザー にしろ
提出日時 2024-11-29 14:31:37
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 226 ms / 5,000 ms
コード長 8,260 bytes
コンパイル時間 7,070 ms
コンパイル使用メモリ 335,264 KB
実行使用メモリ 20,480 KB
最終ジャッジ日時 2024-11-29 14:31:46
合計ジャッジ時間 8,208 ms
ジャッジサーバーID
(参考情報)
judge4 / judge3
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 3
other AC * 20
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#include <bits/stdc++.h>
#include <atcoder/all>
using namespace std;
using ll = long long;
using ul = unsigned long;
using ld = long double;
using st = string;
using mint = atcoder::modint998244353;
using Mint = atcoder::modint1000000007;
#define vl vector<ll>
#define vvl vector<vector<ll>>
#define vvvl vector<vector<vector<ll>>>
#define vvvvl vector<vector<vector<vector<ll>>>>
#define vd vector<ld>
#define vvd vector<vector<ld>>
#define vvvd vector<vector<vector<ld>>>
#define vb vector<bool>
#define vvb vector<vector<bool>>
#define vvvb vector<vector<vector<bool>>>
#define vs vector<string>
#define vvs vector<vector<string>>
#define vvvs vector<vector<vector<string>>>
#define vp vector<pair<ll,ll>>
#define vvp vector<vector<pair<ll,ll>>>
#define vvvp vector<vector<vector<pair<ll,ll>>>>
#define vm vector<mint>
#define vvm vector<vector<mint>>
#define vM vector<Mint>
#define vvM vector<vector<Mint>>
#define cmx(n,v) n=n<v?v:n
#define cmn(n,v) n=n>v?v:n
#define all(n) begin(n),end(n)
#define nxp(a) next_permutation(all(a))
#define rev(n) reverse(all(n))
#define sor(n) stable_sort(all(n))
#define rep(i,n) for(ll i=0;i<(n);++i)
#define reprev(i,n) for(ll i=n-1;0<=i;--i)
#define rrep(i,a,n) for(ll i=a;i<(n);++i)
#define sz(n) n.size()
#define bit(j,i) (i&(1<<j))
#define yn(x) cout << (x?"Yes":"No") << endl;
#define lb(vec,src) lower_bound(vec.begin(),vec.end(),src)-vec.begin()
#define ub(vec,src) upper_bound(vec.begin(),vec.end(),src)-vec.begin()
#define lb2(vec,src) *lower_bound(vec.begin(),vec.end(),src)
#define ub2(vec,src) *upper_bound(vec.begin(),vec.end(),src)
#define mne1(a) min_element(all(a))
#define mxe1(a) max_element(all(a))
#define mne2(a) *min_element(all(a))
#define mxe2(a) *max_element(all(a))
#define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());}
const ll inf = 9e18;
ll calc_digit(ll N){
ll res = 0;
while(N>0){
res++;
N/=10;
}
return res;
}
ll factorial(ll n, ll mod = 1e18) {
ll ans = 1;
for(ll i = n; i >= 2; i--) ans = (ans * i) % mod;
return ans;
}
ll round_up(ll x,ll y){
return (x+y-1)/y;
}
ll floor_int(ll x,ll m){
ll r=(x%m+m)%m; //
return (x-r)/m; //return
}
ll rmd(ll x,ll m){
ll r=(x%m+m)%m; //
return r;
}
ll rmd_2(ll x,ll m){
ll r=(x%m+m)%m; //
return (m-r)%m; //return
}
ll bubble_sort(vl a,ll n){
ll res=0;
rep(i,n-1){
for(ll j=n-1;j>i;j--){
if(a[j-1]>a[j]){
swap(a[j-1],a[j]);
res++;
}
}
}
return res;
}
ll sum_v(vl a){
ll res=0;
ll n=sz(a);
rep(i,n) res+=a[i];
return res;
}
ll stair_sum(ll from,ll to){
return (from+to)*(to-from+1)/2;
}
ll Power(ll var, ll p) {
if (p == 1) return var;
ll ans = Power(var * var, p / 2);
if (p & 1) ans *= var;;
return ans;
}
ll cnt_01(ll n,ll now){
ll res=0;
res+=(n/now)*(now/2);
if(n%now>=now/2) res+=n%now-(now/2)+1;
return res;
}
ll sum_pop(ll n){
ll res=0;
for(ll b=0;b<60;b++){
res+=(n/(1ll<<(b+1)))*(1ll<<b);
res+=max(0ll,n%(1ll<<(b+1))-(1ll<<b)+1);
}
return res;
}
ll Tree_Diameter(vvl& g){
ll n=sz(g);
ll start=0;
ll ans=0;
for(ll i=0;i<2;i++){
queue<ll> q;
q.push(start);
vl dis(n,inf);
dis[start]=0;
while(!q.empty()){
ll u=q.front();
q.pop();
start=u;
ans=dis[u];
for(ll v:g[u]){
if(dis[v]!=inf) continue;
dis[v]=dis[u]+1;
q.push(v);
}
}
}
return ans;
}
mint m_Power(mint var,ll p) {
if (p == 1) return var;
mint ans = m_Power(var * var, p / 2);
if (p & 1) ans *= var;;
return ans;
}
Mint M_Power(Mint var,ll p) {
if (p == 1) return var;
Mint ans = M_Power(var * var, p / 2);
if (p & 1) ans *= var;;
return ans;
}
bool is_prime(ll N){
if(N==1) return false;
if(N==2) return true;
if(N%2==0) return false;
for(ll p=3;p*p<=N;p+=2) if(N%p==0) return false;
return true;
}
bool in_out(ll x,ll y,ll h,ll w){
return 0<=x and x<h and 0<=y and y<w;
}
bool dis_solve1(ll x1,ll x2,ll y1,ll y2,ll r){
ll xx=(x1-x2),yy=(y1-y2);
ll dis=xx*xx+yy*yy;
return (r*r==dis);
}
bool dis_solve2(ll x1,ll x2,ll y1,ll y2,ll d1,ll d2){
ll xx=(x1-x2),yy=(y1-y2),r1=(d1+d2),r2=(d1-d2);
ll dis=xx*xx+yy*yy;
return (r2*r2<=dis&&dis<=r1*r1);
}
void printl(vl v,ll len=0){
ll vsz=min(len,ll(v.size()));
for(ll i=0;i<vsz;i++){
cout << v[i] << endl;
}
}
void prints(vs v){
ll vsz=v.size();
for(ll i=0;i<vsz;i++){
cout << v[i] << endl;
}
}
vl p_list(ll n){
vl res;
vb check(n+1);
for(ll i=2;i<=n;i++){
if(check[i]) continue;
res.push_back(i);
ll ii=i;
while(ii<=n){
check[ii]=true;
ii+=i;
}
}
return res;
}
vl cumulative_sum(vl a){
ll s=sz(a);
vl b(s+1,0);
for(ll i=0;i<s;i++){
b[i+1]=a[i]+b[i];
}
return b;
}
vl n_num(ll a,ll n){
vl res;
while(a){
res.push_back(a%n);
a/=n;
}
rev(res);
return res;
}
vl c_press(vl a){
ll n=sz(a);
vl res=a,c=a;
sor(c);
uniq(c);
rep(i,n) res[i]=lb(c,res[i]);
return res;
}
vl min_fact(ll n){
vl pl;
vl res(n+1,-1);
for(ll d=2;d<=n;d++){
if(res[d]==-1){
res[d]=d;
pl.push_back(d);
}
for(ll p:pl){
if(p*d>n||p>res[d]) break;
res[p*d]=p;
}
}
return res;
}
vvl to_grid(vl &a,ll k){
ll n=sz(a);
ll m=(n+k-1)/k;
vvl b(k,vl(m,inf));
rep(i,n) b[i%k][i/k]=a[i];
return b;
}
vvl rotate_ll(vvl& V2d,ll wise){
vvl a=V2d;
ll h=sz(a),w=sz(a[0]);
vvl res(w,vl(h));
if(wise) {rep(i,h)rep(j,w) res[j][h-i-1]=a[i][j];}
else {rep(i,h)rep(j,w) res[w-j-1][i]=a[i][j];}
return res;
}
vs rotate_st(vs s,ll wise){
vs a=s;
ll h=sz(a),w=sz(a[0]);
vs res(w);
rep(i,w) res[i].append(h,'.');
if(wise) {rep(i,h)rep(j,w) res[j][h-i-1]=a[i][j];}
else {rep(i,h)rep(j,w) res[w-j-1][i]=a[i][j];}
return res;
}
vp prime_factorize(ll N){
vp res;
for (ll a = 2; a * a <= N; ++a) {
if (N % a != 0) continue;
ll ex = 0;
while (N % a == 0) {
ex++;
N /= a;
}
res.push_back({a, ex});
}
if (N != 1) res.push_back({N, 1});
return res;
}
template <typename T> void input(T &a) { cin >> a; };
template <typename T1, typename... T2> void input(T1&a, T2 &...b) { cin >> a; input(b...); };
template<typename T = ll>
vector<T> rd(size_t n) {
vector<T> ts(n);
for (size_t i = 0; i < n; i++) cin >> ts[i];
return ts;
}
template<typename TV, const ll N> void read_tuple_impl(TV&) {}
template<typename TV, const ll N, typename Head, typename... Tail>
void read_tuple_impl(TV& ts) {
get<N>(ts).emplace_back(*(istream_iterator<Head>(cin)));
read_tuple_impl<TV, N + 1, Tail...>(ts);
}
template<typename... Ts> decltype(auto) read_tuple(size_t n) {
tuple<vector<Ts>...> ts;
for (size_t i = 0; i < n; i++) read_tuple_impl<decltype(ts), 0, Ts...>(ts);
return ts;
}
ll di[8]={1,-1,0,0,1,1,-1,-1};
ll dj[8]={0,0,1,-1,1,-1,-1,1};
//abcdefghijklmnopqrstuvwxyz
//std::setprecision(15);
//2^29<10^9
int main(){
ios::sync_with_stdio(0);
cin.tie(0);
ll n;
cin >> n;
vl a=rd(n);
vl cnt(3);
rep(i,n){
if(a[i]>=3) continue;
cnt[a[i]]++;
}
map<array<ll,3>,ld> dp;
dp[{0,0,0}]=0.0;
auto e = [&] (auto f,ll i,ll j,ll k) -> ld {
if(dp.count({i,j,k})) return dp[{i,j,k}];
ll sum=i+j+k;
ld p=ld(n-sum)/ld(n);
ld res=p/(1.0-p);
if(i>0) res+=f(f,i-1,j+1,k)*(ld(i)/ld(i+j+k));
if(j>0) res+=f(f,i,j-1,k+1)*(ld(j)/ld(i+j+k));
if(k>0) res+=f(f,i,j,k-1)*(ld(k)/ld(i+j+k));
res+=1.0;
return dp[{i,j,k}]=res;
};
ld ans=e(e,cnt[0],cnt[1],cnt[2]);
cout << setprecision(15) << ans << endl;
return 0;
}
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