結果

問題 No.1710 Minimum OR is X
ユーザー gazellegazelle
提出日時 2021-10-15 22:38:39
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 1,774 ms / 2,000 ms
コード長 6,434 bytes
コンパイル時間 2,420 ms
コンパイル使用メモリ 211,372 KB
実行使用メモリ 36,248 KB
最終ジャッジ日時 2023-10-17 20:36:54
合計ジャッジ時間 21,664 ms
ジャッジサーバーID
（参考情報） 		judge12 / judge15
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 44 ms
36,100 KB
testcase_01 AC 45 ms
36,104 KB
testcase_02 AC 295 ms
36,168 KB
testcase_03 AC 44 ms
36,100 KB
testcase_04 AC 45 ms
36,104 KB
testcase_05 AC 44 ms
36,104 KB
testcase_06 AC 45 ms
36,104 KB
testcase_07 AC 45 ms
36,100 KB
testcase_08 AC 711 ms
36,240 KB
testcase_09 AC 566 ms
36,240 KB
testcase_10 AC 1,283 ms
36,240 KB
testcase_11 AC 1,186 ms
36,240 KB
testcase_12 AC 822 ms
36,240 KB
testcase_13 AC 696 ms
36,244 KB
testcase_14 AC 759 ms
36,240 KB
testcase_15 AC 373 ms
36,236 KB
testcase_16 AC 644 ms
36,244 KB
testcase_17 AC 740 ms
36,236 KB
testcase_18 AC 1,702 ms
36,248 KB
testcase_19 AC 1,772 ms
36,248 KB
testcase_20 AC 1,668 ms
36,248 KB
testcase_21 AC 1,761 ms
36,248 KB
testcase_22 AC 1,774 ms
36,248 KB
testcase_23 AC 44 ms
36,112 KB
testcase_24 AC 44 ms
36,104 KB
testcase_25 AC 45 ms
36,196 KB
testcase_26 AC 282 ms
36,204 KB
testcase_27 AC 45 ms
36,232 KB
testcase_28 AC 122 ms
36,176 KB
testcase_29 AC 44 ms
36,148 KB
testcase_30 AC 139 ms
36,124 KB
testcase_31 AC 45 ms
36,208 KB
testcase_32 AC 117 ms
36,176 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 # 

#include <bits/stdc++.h>
#define FOR(i, n, m) for(ll i = (n); i < (ll)(m); i++)
#define REP(i, n) FOR(i, 0, n)
#define ALL(v) v.begin(), v.end()
#define pb push_back
using namespace std;
using ll = long long;
using ld = long double;
using P = pair<ll, ll>;
constexpr ll inf = 1000000000;
constexpr ll mod = 998244353;
constexpr long double eps = 1e-6;
 
template<typename T1, typename T2>
ostream& operator<<(ostream& os, pair<T1, T2> p) {
    os << to_string(p.first) << " " << to_string(p.second);
    return os;
}
template<typename T>
ostream& operator<<(ostream& os, vector<T>& v) {
    REP(i, v.size()) {
        if(i) os << " ";
        os << v[i];
    }
    return os;
}
 
struct modint {
    ll n;
public:
    modint(const ll n = 0) : n((n % mod + mod) % mod) {}
    static modint pow(modint a, int m) {
        modint r = 1;
        while(m > 0) {
            if(m & 1) { r *= a; }
            a = (a * a); m /= 2;
        }
        return r;
    }
    modint &operator++() { *this += 1; return *this; }
    modint &operator--() { *this -= 1; return *this; }
    modint operator++(int) { modint ret = *this; *this += 1; return ret; }
    modint operator--(int) { modint ret = *this; *this -= 1; return ret; }
    modint operator~() const { return (this -> pow(n, mod - 2)); } // inverse
    friend bool operator==(const modint& lhs, const modint& rhs) {
        return lhs.n == rhs.n;
    }
    friend bool operator<(const modint& lhs, const modint& rhs) {
        return lhs.n < rhs.n;
    }
    friend bool operator>(const modint& lhs, const modint& rhs) {
        return lhs.n > rhs.n;
    }
    friend modint &operator+=(modint& lhs, const modint& rhs) {
        lhs.n += rhs.n;
        if (lhs.n >= mod) lhs.n -= mod;
        return lhs;
    }
    friend modint &operator-=(modint& lhs, const modint& rhs) {
        lhs.n -= rhs.n;
        if (lhs.n < 0) lhs.n += mod;
        return lhs;
    }
    friend modint &operator*=(modint& lhs, const modint& rhs) {
        lhs.n = (lhs.n * rhs.n) % mod;
        return lhs;
    }
    friend modint &operator/=(modint& lhs, const modint& rhs) {
        lhs.n = (lhs.n * (~rhs).n) % mod;
        return lhs;
    }
    friend modint operator+(const modint& lhs, const modint& rhs) {
        return modint(lhs.n + rhs.n);
    }
    friend modint operator-(const modint& lhs, const modint& rhs) {
        return modint(lhs.n - rhs.n);
    }
    friend modint operator*(const modint& lhs, const modint& rhs) {
        return modint(lhs.n * rhs.n);
    }
    friend modint operator/(const modint& lhs, const modint& rhs) {
        return modint(lhs.n * (~rhs).n);
    }
};
istream& operator>>(istream& is, modint m) { is >> m.n; return is; }
ostream& operator<<(ostream& os, modint m) { os << m.n; return os; }

using mi = modint;

ll mod_pow(__int128 a, __int128 n, __int128 m = mod) {
    using ll = __int128;
    ll ret = 1;
    ll tmp = a;
    while(n > 0) {
        if(n % 2) ret *= tmp;
        ret %= m;
        tmp = tmp * tmp;
        tmp %= m;
        n /= 2;
    }
    return ret % m;
}

constexpr int MAX_N = 2020202;
mi mod_fact  [MAX_N + 1];
mi mod_fact_i[MAX_N + 1];
mi mod_comb(long long n, long long k) {
    static bool initialized = false;
    if(n < 0 || k < 0 || n < k) return 0;
    if(not initialized) {
        mod_fact[0] = 1;
        for(int i = 1; i <= MAX_N; ++i) {
            mod_fact[i] = i * mod_fact[i - 1];
        }
        mod_fact_i[MAX_N] = mod_pow(mod_fact[MAX_N].n, mod - 2);
        for(int i = MAX_N - 1; i >= 0; --i) {
            mod_fact_i[i] = mod_fact_i[i + 1] * (i + 1);
        }
        initialized = true;
    }
    return mod_fact[n] * mod_fact_i[n - k] * mod_fact_i[k];
}

struct union_find {
    union_find(int n) : par_(n, -1) {}
    void init(int n) { par_.assign(n, -1); }
    int root(int x) { return par_[x] < 0 ? x : par_[x] = root(par_[x]); }
    bool unite(int x, int y) {
        x = root(x); y = root(y);
        if(x == y) return false;
        if(par_[x] < par_[y]) {
            par_[x] += par_[y];
            par_[y] = x;
        } else {
            par_[y] += par_[x];
            par_[x] = y;
        }
        return true;
    }
    bool same(int x, int y) { return root(x) == root(y); }
    int size(int x) { return -par_[root(x)]; }
    vector<int> par_;
};
 
ll gcd(ll a, ll b) {
    if (b == 0) return a;
    return gcd(b, a % b);
}

ll lcm(ll a, ll b) {
    ll g = gcd(a, b);
    return a / g * b;
}

ll N = 202020;
ll bit[202020];
void add(ll a, ll w) {
	a++;
	for (ll x = a; x <= N; x += x & -x) bit[x] += w;
}
ll sum(ll a) {
	a++;
	ll ret = 0;
	for (ll x = a; x > 0; x -= x & -x) ret += bit[x];
	return ret;
}
// return the sum of [a, b)
ll sum(ll a, ll b) {
	ll ret = 0;
	if(b == 0) return 0;
	ret += sum(b - 1);
	if(a) ret -= sum(a - 1);
	return ret;
}

int n, m, k;
string x;

void flip() {
    REP(i, m) {
        if(x[i] == '0') x[i] = '1';
        else            x[i] = '0';
    }
}

vector<vector<mi>> memo;

mi dfs(int rem_digit, int rem_pos) {
    if(rem_digit == 0 || rem_pos == 0) return 1;
    if(memo[rem_digit][rem_pos].n != -1) return memo[rem_digit][rem_pos];

    if(x[m - rem_digit] == '0') {
        mi sum = 0;
        for(int i = 0; i < k; i++) sum += mod_comb(rem_pos, i);
        return memo[rem_digit][rem_pos] = sum * dfs(rem_digit - 1, rem_pos);
    } else {
        mi ret = 0;
        for(int i = 0; i <= rem_pos; i++) {
            ret += mod_comb(rem_pos, i) * dfs(rem_digit - 1, i) * mod_pow(2, (rem_pos - i) * (rem_digit - 1));
        }
        return memo[rem_digit][rem_pos] = ret;
    }


}

mi solve(bool debug) {
    flip();

    memo.clear();
    memo.resize(m + 1);
    REP(i, m + 1) memo[i].resize(n + 1);
    REP(i, m + 1) REP(j, n + 1) memo[i][j].n = -1;

    mi ans = dfs(m, n);

    REP(i, m + 1) REP(j, n + 1) {
        if(debug) cout << i << " " << j << " " << dfs(i, j) << endl;
    }

    flip();

    return ans;
}

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);

    cin >> n >> m >> k >> x;

    bool cont0 = false;
    REP(i, m) if(x[i] == '0') cont0 = true;

    mi ans = solve(false);
    //cout << ans << endl;
    
    if(cont0) {
        for(int i = m - 1; i >= 0; i--) {
            if(x[i] == '1') continue;
            x[i] = '1';
            for(int j = i + 1; j < m; j++) {
                x[j] = '0';
            }
            break;
        }
        ans -= solve(false);
    }

    cout << ans << endl;

    return 0;
}
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