結果

問題 No.108 トリプルカードコンプ
ユーザー T101010101
提出日時 2023-06-12 16:44:02
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
AC  
実行時間 46 ms / 5,000 ms
コード長 9,580 bytes
コンパイル時間 14,554 ms
コンパイル使用メモリ 363,632 KB
最終ジャッジ日時 2025-02-14 02:04:44
ジャッジサーバーID
(参考情報)
judge2 / judge2
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

#pragma region Macros
#pragma GCC target("avx,avx2,fma")
#pragma GCC optimize("O3,unroll-loops")
#include <bits/extc++.h>
// #include <atcoder/all>
// using namespace atcoder;
using namespace std;
using namespace __gnu_pbds;
// #include <boost/multiprecision/cpp_dec_float.hpp>
// #include <boost/multiprecision/cpp_int.hpp>
// namespace mp = boost::multiprecision;
// using Bint = mp::cpp_int;
// using Bdouble = mp::number<mp::cpp_dec_float<128>>;
#define TO_STRING(var) # var
#define pb emplace_back
#define int ll
#define endl '\n'
#define sqrt __builtin_sqrt
using ll = long long;
using ld = long double;
const ld PI = acos(-1);
const ld EPS = 1e-10;
const int INF = 1 << 30;
const ll INFL = 1LL << 61;
// const int MOD = 998244353;
const int MOD = 1000000007;
const vector<int> dx = {0, 1, -1, 0, 1, 1, -1, -1}; // → ↓ ← ↑ ↘ ↙ ↖ ↗
const vector<int> dy = {1, 0, 0, -1, 1, -1, -1, 1};
struct Edge {
int from, to;
int cost;
Edge(int to, int cost) : from(-1), to(to), cost(cost) {}
Edge(int from, int to, int cost) : from(from), to(to), cost(cost) {}
Edge &operator=(const int &x) {
to = x;
return *this;
}
operator int() const { return to; }
};
__attribute__((constructor))
void constructor() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
cout << fixed << setprecision(12);
}
int POW(int x, int n) {
__int128_t ret = 1;
if (n < 0) { cout << "error" << endl; return 0; }
else if (x == 1 or n == 0) ret = 1;
else if (x == -1 && n % 2 == 0) ret = 1;
else if (x == -1) ret = -1;
else if (n % 2 == 0) ret = POW(x * x, n / 2);
else ret = x * POW(x, n - 1);
if (ret > 8e18) ret = 0;
return ret;
}
int floor(int x, int y) { return (x > 0 ? x / y : (x - y + 1) / y); }
int ceil(int x, int y) { return (x > 0 ? (x + y - 1) / y : x / y); }
ll per(int x, int y) {
if (y == 0) {
cout << "error" << endl;
return INFL;
}
if (x >= 0 && y > 0) return x / y;
if (x >= 0 && y < 0) return x / y - (x % y < 0);
if (x < 0 && y < 0) return x / y + (x % y < 0);
// if (x < 0 && y > 0)
return x / y - (x % y < 0);
}
ll mod(int x, int y) {
if (y == 0) {
cout << "error" << endl;
return INFL;
}
if (x >= 0 && y > 0) return x % y;
if (x >= 0 && y < 0) return x % y;
if (x < 0 && y < 0) {
__int128_t ret = x % y;
ret += (__int128_t)abs(y) * INFL;
ret %= abs(y);
return ret;
}
// if (x < 0 && y > 0) {
__int128_t ret = x % y;
ret += (__int128_t)abs(y) * INFL;
ret %= abs(y);
return ret;
// }
}
template <class T> bool chmax(T &a, const T& b) {
if (a < b) { a = b; return true; }
return false;
}
template <class T> bool chmin(T &a, const T& b) {
if (a > b) { a = b; return true; }
return false;
}
int countl_zero(int N) { return __builtin_clzll(N); }
int countl_one(int N) {
int ret = 0; while (N % 2) { N /= 2; ret++; }
return ret;
}
int countr_zero(int N) { return __builtin_ctzll(N); }
int countr_one(int N) {
int ret = 0, k = 63 - __builtin_clzll(N);
while (k != -1 && (N & (1LL << k))) { k--; ret++; }
return ret;
}
int popcount(int N) { return __builtin_popcountll(N); }
int unpopcount(int N) { return 64 - __builtin_clzll(N) - __builtin_popcountll(N); }
int top_bit(int N) { return 63 - __builtin_clzll(N);} // 2^k
int bot_bit(int N) { return __builtin_ctz(N);} // 2^k
int MSB(int N) { return 1 << (63 - __builtin_clzll(N)); } // mask
int bit_width(int N) { return 64 - __builtin_clzll(N); } //
int ceil_log2(int N) { return 63 - __builtin_clzll(N); }
int bit_floor(int N) { return 1 << (63 - __builtin_clzll(N)); }
int floor_log2(int N) { return 64 - __builtin_clzll(N-1); }
int bit_ceil(int N) { return 1 << (64 - __builtin_clzll(N-1)) - (N==1); }
class UnionFind {
public:
UnionFind() = default;
UnionFind(int N) : par(N), sz(N, 1) {
iota(par.begin(), par.end(), 0);
}
int root(int x) {
if (par[x] == x) return x;
return (par[x] = root(par[x]));
}
bool unite(int x, int y) {
int rx = root(x);
int ry = root(y);
if (rx == ry) return false;
if (sz[rx] < sz[ry]) swap(rx, ry);
sz[rx] += sz[ry];
par[ry] = rx;
return true;
}
bool issame(int x, int y) { return (root(x) == root(y)); }
int size(int x) { return sz[root(x)]; }
vector<vector<int>> groups(int N) {
vector<vector<int>> G(N);
for (int x = 0; x < N; x++) {
G[root(x)].push_back(x);
}
G.erase(
remove_if(G.begin(), G.end(),
[&](const vector<int>& V) { return V.empty(); }),
G.end());
return G;
}
private:
vector<int> par;
vector<int> sz;
};
template<int mod> class Modint{
public:
int val = 0;
Modint(int x = 0) { while (x < 0) x += mod; val = x % mod; }
Modint(const Modint &r) { val = r.val; }
Modint operator -() { return Modint(-val); } //
Modint operator +(const Modint &r) { return Modint(*this) += r; }
Modint operator +(const int &q) { Modint r(q); return Modint(*this) += r; }
Modint operator -(const Modint &r) { return Modint(*this) -= r; }
Modint operator -(const int &q) { Modint r(q); return Modint(*this) -= r; }
Modint operator *(const Modint &r) { return Modint(*this) *= r; }
Modint operator *(const int &q) { Modint r(q); return Modint(*this) *= r; }
Modint operator /(const Modint &r) { return Modint(*this) /= r; }
Modint operator /(const int &q) { Modint r(q); return Modint(*this) /= r; }
Modint& operator ++() { val++; if (val >= mod) val -= mod; return *this; } //
Modint operator ++(signed) { ++*this; return *this; } //
Modint& operator --() { val--; if (val < 0) val += mod; return *this; }
Modint operator --(signed) { --*this; return *this; }
Modint &operator +=(const Modint &r) { val += r.val; if (val >= mod) val -= mod; return *this; }
Modint &operator +=(const int &q) { Modint r(q); val += r.val; if (val >= mod) val -= mod; return *this; }
Modint &operator -=(const Modint &r) { if (val < r.val) val += mod; val -= r.val; return *this; }
Modint &operator -=(const int &q) { Modint r(q); if (val < r.val) val += mod; val -= r.val; return *this; }
Modint &operator *=(const Modint &r) { val = val * r.val % mod; return *this; }
Modint &operator *=(const int &q) { Modint r(q); val = val * r.val % mod; return *this; }
Modint &operator /=(const Modint &r) {
int a = r.val, b = mod, u = 1, v = 0;
while (b) {int t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v);}
val = val * u % mod; if (val < 0) val += mod;
return *this;
}
Modint &operator /=(const int &q) {
Modint r(q); int a = r.val, b = mod, u = 1, v = 0;
while (b) {int t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v);}
val = val * u % mod; if (val < 0) val += mod;
return *this;
}
bool operator ==(const Modint& r) { return this -> val == r.val; }
bool operator <(const Modint& r) { return this -> val < r.val; }
bool operator !=(const Modint& r) { return this -> val != r.val; }
};
using mint = Modint<MOD>;
// using mint = modint<MOD>;
istream &operator >>(istream &is, mint& x) {
int t; is >> t;
x = t;
return (is);
}
ostream &operator <<(ostream &os, const mint& x) {
return os << x.val;
}
mint modpow(const mint &x, int n) {
if (n == 0) return 1;
mint t = modpow(x, n / 2);
t = t * t;
if (n & 1) t = t * x;
return t;
}
int modpow(__int128_t x, int n, int mod) {
__int128_t ret = 1;
while (n > 0) {
if (n % 2 == 1) ret = ret * x % mod;
x = x * x % mod;
n /= 2;
}
return ret;
}
vector<mint> fac, finv, Inv;
void COMinit(int N) {
fac.resize(N + 1);
finv.resize(N + 1);
Inv.resize(N + 1);
fac[0] = fac[1] = 1;
finv[0] = finv[1] = 1;
Inv[1] = 1;
for (int i = 2; i <= N; i++) {
fac[i] = fac[i-1] * mint(i);
Inv[i] = -Inv[MOD % i] * mint(MOD / i);
finv[i] = finv[i - 1] * Inv[i];
}
}
mint COM(int N, int K) {
if (N < K) return 0;
if (N < 0 || K < 0) return 0;
return fac[N] * finv[K] * finv[N - K];
}
#pragma endregion
int N;
// dp[i][j][k] := 1i2j3k
//
ld dp[301][301][301];
ld rec(int i, int j, int k) {
if (dp[i][j][k] != -1) return dp[i][j][k];
dp[i][j][k] = 1;
if (i - 1 >= 0) {
dp[i][j][k] += rec(i - 1, j, k) * i / (ld)N; //
}
if (i + 1 <= N && j - 1 >= 0) {
dp[i][j][k] += rec(i + 1, j - 1, k) * j / (ld)N;
}
if (j + 1 <= N && k - 1 >= 0) {
dp[i][j][k] += rec(i, j + 1, k - 1) * k / (ld)N;
}
dp[i][j][k] /= (1. - (ld)(N - i - j - k) / N); // ->
return dp[i][j][k];
}
signed main() {
cin >> N;
int a = 0, b = 0, c = 0; // 1 / 2 / 3
vector<int> A(N);
for (int i = 0; i < N; i++) {
cin >> A[i];
if (A[i] == 2) a++;
if (A[i] == 1) b++;
if (A[i] == 0) c++;
}
for (int i = 0; i <= N; i++) {
for (int j = 0; j <= N; j++) {
for (int k = 0; k <= N; k++) {
dp[i][j][k] = -1;
}
}
}
dp[0][0][0] = 0;
cout << rec(a, b, c) << endl;
}
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