結果

問題 No.1821 LEQ-GEQ Permutations
ユーザー oteraotera
提出日時 2022-01-22 07:20:05
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 297 ms / 2,500 ms
コード長 6,428 bytes
コンパイル時間 2,008 ms
コンパイル使用メモリ 209,520 KB
実行使用メモリ 103,272 KB
最終ジャッジ日時 2024-05-05 03:09:15
合計ジャッジ時間 6,075 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge1
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 41 ms
103,040 KB
testcase_01 AC 40 ms
103,168 KB
testcase_02 AC 41 ms
103,040 KB
testcase_03 AC 40 ms
103,040 KB
testcase_04 AC 42 ms
103,168 KB
testcase_05 AC 41 ms
103,168 KB
testcase_06 AC 42 ms
103,072 KB
testcase_07 AC 43 ms
103,164 KB
testcase_08 AC 52 ms
103,156 KB
testcase_09 AC 222 ms
103,040 KB
testcase_10 AC 42 ms
103,168 KB
testcase_11 AC 55 ms
103,168 KB
testcase_12 AC 54 ms
103,168 KB
testcase_13 AC 72 ms
103,040 KB
testcase_14 AC 111 ms
103,100 KB
testcase_15 AC 191 ms
103,168 KB
testcase_16 AC 188 ms
103,184 KB
testcase_17 AC 108 ms
103,232 KB
testcase_18 AC 283 ms
103,168 KB
testcase_19 AC 287 ms
103,248 KB
testcase_20 AC 283 ms
103,056 KB
testcase_21 AC 297 ms
103,064 KB
testcase_22 AC 285 ms
103,040 KB
testcase_23 AC 113 ms
103,272 KB
testcase_24 AC 113 ms
103,168 KB
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 # 

/**
 *    author:  otera
 *    created: 22.01.2022 06:22:39 
**/
#include<bits/stdc++.h>
#include<atcoder/modint>
using namespace std;

using ll = long long;
using ld = long double;
using ull = unsigned long long;
using uint = unsigned;
#define repa(i, n) for(int i = 0; i < n; ++ i)
#define repb(i, a, b) for(int i = a; i < b; ++ i)
#define repc(i, a, b, c) for(int i = a; i < b; i += c)
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, repc, repb, repa)(__VA_ARGS__)
#define rep1a(i, n) for(int i = 0; i <= n; ++ i)
#define rep1b(i, a, b) for(int i = a; i <= b; ++ i)
#define rep1c(i, a, b, c) for(int i = a; i <= b; i += c)
#define rep1(...) overload4(__VA_ARGS__, rep1c, rep1b, rep1a)(__VA_ARGS__)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define per1(i,n) for(int i=n;i>=1;i--)
typedef pair<int, int> P;
typedef pair<ll, ll> LP;
#define pb push_back
#define eb emplace_back
#define fr first
#define sc second
#define all(c) c.begin(),c.end()
#define lb(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define ub(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define Sort(a) sort(all(a))
#define Rev(a) reverse(all(a))
#define Uniq(a) sort(all(a));a.erase(unique(all(a)),end(a))
#define si(c) (int)(c).size()
inline ll popcnt(ull a){ return __builtin_popcountll(a); }
#define tpow(n) (1LL<<(n))
#define unless(A) if(!(A))
ll intpow(ll a, ll b){ ll ans = 1; while(b){ if(b & 1) ans *= a; a *= a; b /= 2; } return ans; }
ll intpow(ll a, ll b, ll m) {ll ans = 1; while(b){ if(b & 1) (ans *= a) %= m; (a *= a) %= m; b /= 2; } return ans; }
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; }
#define INT(...) int __VA_ARGS__;in(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__;in(__VA_ARGS__)
#define ULL(...) ull __VA_ARGS__;in(__VA_ARGS__)
#define STR(...) string __VA_ARGS__;in(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__;in(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__;in(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__;in(__VA_ARGS__)
#define vec(type,name,...) vector<type>name(__VA_ARGS__)
#define VEC(type,name,size) vector<type>name(size);in(name)
#define vv(type,name,h,...) vector<vector<type>>name(h,vector<type>(__VA_ARGS__))
#define VV(type,name,h,w) vector<vector<type>>name(h,vector<type>(w));in(name)
#define vvv(type,name,h,w,...) vector<vector<vector<type>>>name(h,vector<vector<type>>(w,vector<type>(__VA_ARGS__)))
template <class T> using vc = vector<T>;
template <class T> using vvc = vector<vc<T>>;
template <class T> using vvvc = vector<vvc<T>>;
template <class T> using vvvvc = vector<vvvc<T>>;
template <class T> using pq = priority_queue<T>;
template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>;
template<class T> void scan(T& a){ cin >> a; }
template<class T> void scan(vector<T>& a){ for(auto&& i : a) scan(i); }
void in(){}
template <class Head, class... Tail> void in(Head& head, Tail&... tail){ scan(head); in(tail...); }
void print(){ cout << ' '; }
template<class T> void print(const T& a){ cout << a; }
template<class T> void print(const vector<T>& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ cout << ' '; print(*i); } }
int out(){ cout << '\n'; return 0; }
template<class T> int out(const T& t){ print(t); cout << '\n'; return 0; }
template<class Head, class... Tail> int out(const Head& head, const Tail&... tail){ print(head); cout << ' '; out(tail...); return 0; }
#define CHOOSE(a) CHOOSE2 a
#define CHOOSE2(a0,a1,a2,a3,a4,x,...) x
#define debug_1(x1) cout<<#x1<<": "<<x1<<endl
#define debug_2(x1,x2) cout<<#x1<<": "<<x1<<", "#x2<<": "<<x2<<endl
#define debug_3(x1,x2,x3) cout<<#x1<<": "<<x1<<", "#x2<<": "<<x2<<", "#x3<<": "<<x3<<endl
#define debug_4(x1,x2,x3,x4) cout<<#x1<<": "<<x1<<", "#x2<<": "<<x2<<", "#x3<<": "<<x3<<", "#x4<<": "<<x4<<endl
#define debug_5(x1,x2,x3,x4,x5) cout<<#x1<<": "<<x1<<", "#x2<<": "<<x2<<", "#x3<<": "<<x3<<", "#x4<<": "<<x4<<", "#x5<<": "<<x5<<endl
#ifdef DEBUG
#define debug(...) CHOOSE((__VA_ARGS__,debug_5,debug_4,debug_3,debug_2,debug_1,~))(__VA_ARGS__)
#define dump(...) { print(#__VA_ARGS__); print(":"); out(__VA_ARGS__); }
#else
#define debug(...)
#define dump(...)
#endif

using mint = atcoder::modint998244353;

template<class T> struct BiCoef {
    vector<T> fact_, inv_, finv_;
    int MOD = T::mod();
    constexpr BiCoef() {}
    constexpr BiCoef(int n) noexcept : fact_(n, 1), inv_(n, 1), finv_(n, 1) {
        init(n);
    }
    constexpr void init(int n) noexcept {
        fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1);
        for(int i = 2; i < n; i++){
            fact_[i] = fact_[i-1] * i;
            inv_[i] = -inv_[MOD%i] * (MOD/i);
            finv_[i] = finv_[i-1] * inv_[i];
        }
    }
    constexpr T com(int n, int k) const noexcept {
        if(n == k) return 1;
        if (n < k || n < 0 || k < 0) return 0;
        return fact_[n] * finv_[k] * finv_[n-k];
    }
    constexpr T fact(int n) const noexcept {
        if (n < 0) return 0;
        return fact_[n];
    }
    constexpr T inv(int n) const noexcept {
        if (n < 0) return 0;
        return inv_[n];
    }
    constexpr T finv(int n) const noexcept {
        if (n < 0) return 0;
        return finv_[n];
    }
};

BiCoef<mint> bc;

mint dp[5050][5050];

void solve() {
    bc.init(10010);
    rep(i, 5050) rep(j, 5050) dp[i][j] = 0;
    INT(n);
    STR(s);
    int a = 0, b = 0;
    rep(i, n) {
        if(s[i] == '0') ++ a; 
        else ++ b;
    }
    assert(a + b == n);
    dp[0][0] = 1;
    rep1(i, 1, n) {
        rep1(j, 0, i) {
            dp[i][j] += dp[i - 1][j] * j;
            if(j >= 1) dp[i][j] += dp[i - 1][j - 1] * (i - j);
            if(i >= 2 and j >= 1) dp[i][j] += dp[i - 2][j - 1] * (i - 1);
        }
    }
    mint ans = 0;
    rep1(x, 0, a) {
        rep1(y, 0, b) {
            int res = (a - x) + (b - y);
            ans += bc.com(n, res) * bc.com(a, x) * bc.com(b, y) * dp[x + y][x] * bc.fact(res) * bc.fact(x) * bc.fact(y);
            // mint now = bc.com(n, res) * bc.com(a, x) * bc.com(b, y) * dp[x + y][x] * bc.fact(res);
            // debug(x, y, now.val());
        }
    }
    out(ans.val());
}

signed main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    // cout << fixed << setprecision(20);
    // INT(t); rep(i, t)solve();
    solve();
    return 0;
}
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