結果

問題 No.2911 位相の公理
ユーザー deuteridayodeuteridayo
提出日時 2024-10-04 21:46:48
言語 C++23
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 469 ms / 2,000 ms
コード長 6,083 bytes
コンパイル時間 5,433 ms
コンパイル使用メモリ 325,360 KB
実行使用メモリ 5,248 KB
最終ジャッジ日時 2024-10-04 21:46:56
合計ジャッジ時間 7,408 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
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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 2 ms
5,248 KB
testcase_01 AC 1 ms
5,248 KB
testcase_02 AC 2 ms
5,248 KB
testcase_03 AC 1 ms
5,248 KB
testcase_04 AC 2 ms
5,248 KB
testcase_05 AC 1 ms
5,248 KB
testcase_06 AC 2 ms
5,248 KB
testcase_07 AC 1 ms
5,248 KB
testcase_08 AC 2 ms
5,248 KB
testcase_09 AC 1 ms
5,248 KB
testcase_10 AC 2 ms
5,248 KB
testcase_11 AC 2 ms
5,248 KB
testcase_12 AC 1 ms
5,248 KB
testcase_13 AC 2 ms
5,248 KB
testcase_14 AC 1 ms
5,248 KB
testcase_15 AC 1 ms
5,248 KB
testcase_16 AC 2 ms
5,248 KB
testcase_17 AC 2 ms
5,248 KB
testcase_18 AC 2 ms
5,248 KB
testcase_19 AC 413 ms
5,248 KB
testcase_20 AC 408 ms
5,248 KB
testcase_21 AC 469 ms
5,248 KB
testcase_22 AC 4 ms
5,248 KB
testcase_23 AC 396 ms
5,248 KB
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ソースコード

diff # 

#include<bits/stdc++.h>
#include<atcoder/all>
using namespace std;
using namespace atcoder;
using lint = long long;
using ulint = unsigned long long;
using llint = __int128_t;
struct edge;
using graph = vector<vector<edge>>;
#define endl '\n'
constexpr int INF = 1<<30;
constexpr lint INF64 = 1LL<<61;
constexpr lint mod107 = 1e9+7;
using mint107 = modint1000000007;
constexpr long mod = 998244353;
using mint = modint998244353;
lint ceilDiv(lint x, lint y){if(x >= 0){return (x+y-1)/y;}else{return x/y;}}
lint floorDiv(lint x, lint y){if(x >= 0){return x/y;}else{return (x-y+1)/y;}}
lint Sqrt(lint x) {assert(x >= 0); lint ans = sqrt(x); while(ans*ans > x)ans--; while((ans+1)*(ans+1)<=x)ans++; return ans;}
lint gcd(lint a,lint b){if(a<b)swap(a,b);if(a%b==0)return b;else return gcd(b,a%b);}
lint lcm(lint a,lint b){return (a / gcd(a,b)) * b;}
double Dist(double x1, double y1, double x2, double y2){return sqrt(pow(x1-x2, 2) + pow(y1-y2,2));}
lint DistSqr(lint x1, lint y1, lint x2, lint y2){return (x1-x2)*(x1-x2) + (y1-y2)*(y1-y2); }
string toString(lint n){string ans = "";if(n == 0){ans += "0";}else{while(n > 0){int a = n%10;char b = '0' + a;string c = "";c += b;n /= 10;ans = c + ans;}}return ans;}
string toString(lint n, lint k){string ans = toString(n);string tmp = "";while(ans.length() + tmp.length() < k){tmp += "0";}return tmp + ans;}
vector<lint>prime;void makePrime(lint n){prime.push_back(2);for(lint i=3;i<=n;i+=2){bool chk = true;for(lint j=0;j<prime.size() && prime[j]*prime[j] <= i;j++){if(i % prime[j]==0){chk=false;break;}}if(chk)prime.push_back(i);}}
lint Kai[20000001]; bool firstCallnCr = true; 
lint ncrmodp(lint n,lint r,lint p){ if(firstCallnCr){ Kai[0] = 1; for(int i=1;i<=20000000;i++){ Kai[i] = Kai[i-1] * i; Kai[i] %= p;} firstCallnCr = false;} if(n<0)return 0;
if(n < r)return 0;if(n==0)return 1;lint ans = Kai[n];lint tmp = (Kai[r] * Kai[n-r]) % p;for(lint i=1;i<=p-2;i*=2){if(i & p-2){ans *= tmp;ans %= p;}tmp *= tmp;tmp %= p;}return ans;}
#define rep(i, n) for(int i = 0; i < n; i++)
#define repp(i, x, y) for(int i = x; i < y; i++)
#define rrep(i, x) for(int i = x-1; i >= 0; i--)
#define vec vector
#define pb push_back
#define eb emplace_back
#define se second
#define fi first
#define al(x) x.begin(),x.end()
#define ral(x) x.rbegin(),x.rend()
unsigned long Rand() {
    static random_device seed;
    static mt19937_64 engine(seed());
    return engine();
}

struct Point {
    lint x, y; int quad;
    Point(lint X, lint Y) {
        x = X;
        y = Y;
        quad = getQuad();
    }
    int getQuad() {
        if(x >= 0) {
            if(y >= 0) return 1;
            else return 4;
        } else {
            if(y >= 0) return 2;
            else return 3;
        }
    }
};

bool operator<(const Point &left, const Point &right) {
    if(left.quad == right.quad) {
        return left.y * right.x < left.x * right.y;
    } else {
        return left.quad < right.quad;
    }
}

struct Frac {
    lint upper, lower;
    Frac() { Frac(0,1); }
    Frac(lint u, lint l) {
        assert(l != 0);
        if(u <= 0 && l < 0) { upper = -u; lower = -l; } 
        else { upper = u; lower = l; }
        reduction();
    }

    Frac(lint u) { upper = u;  lower = 1;  } 

    void reduction() {
        if(upper != 0) {
            lint g = gcd(abs(upper), abs(lower));
            upper /= g; lower /= g;
            if(lower < 0) {lower *= -1;  upper *= -1; }
        } else {
            lower = 1; 
        }
    }

    Frac operator+(const Frac &other) {
        lint L = lower * other.lower;
        lint U = upper*other.lower + lower*other.upper;
        return Frac(U, L);
    }

    Frac operator-(const Frac &other) {
        lint L = lower * other.lower;
        lint U = upper*other.lower - lower*other.upper;
        upper = U; lower = L;
        return Frac(U, L);
    }

    bool operator<=(const Frac &other) {
        return upper*other.lower <= lower*other.upper;
    }

    Frac operator*(const Frac &other) {
        lint L = lower * other.lower;
        lint U = upper * other.upper;
        return Frac(U, L);
    }

    Frac operator/(const Frac &other) {
        assert(other.upper != 0);
        lint L = lower * other.upper;
        lint U = upper * other.lower;
        return Frac(U, L);
    }
};

bool operator<(const Frac &left, const Frac &right) {
    llint L = left.upper;
    L *= right.lower;
    llint R = right.upper;
    R *= left.lower;
    return L < R;
}

lint extGCD(lint a, lint b, lint &x, lint &y) {
    if (b == 0) {
        x = 1;  y = 0;
        return a;
    }
    lint d = extGCD(b, a%b, y, x);
    y -= a/b * x;
    return d;
}

struct edge{
    edge(lint v, lint c = 1) {to = v, cost = c;}
    lint to;
    lint cost;
};

vector<lint>dijkstra(int s, graph &g) {
    vec<lint>ret(g.size(), INF64);
    priority_queue<pair<lint, lint>>que;
    que.push({-0, s});
    ret[s] = 0;
    vec<bool>went(g.size(), false);
    while(!que.empty()) {
        auto q = que.top();
        que.pop();
        if(went[q.second]) continue;
        went[q.second] = true;
        ret[q.second] = -q.first;
        for(auto&& e: g[q.second]) {
            if(ret[e.to] > -q.first + e.cost) {
                ret[e.to] = -q.first + e.cost;
                que.push({-ret[e.to], e.to});
            }
        }
    }
    return ret;
}

void no() {
    cout << "No" << endl;
    exit(0);
}

int main(){
    int N, M;
    cin >> N >> M;
    set<lint>S;
    vec<lint>SS;
    rep(i, M) {
        string ss;cin >> ss;
        int s = 0;
        rep(j, N) {
            s *= 2;
            s += (int)(ss[j] - '0');
        }
        S.insert(s);
        SS.pb(s);
    }

    // 条件1
    if(!S.contains((1<<N) - 1)) {
        no();
    }

    // 条件2
    rep(i, M) {
        repp(j,i, M) {
            lint s0 = SS[i];
            lint s1 = SS[j];
            if(!S.contains(s0 & s1)) no();
        }
    }

    // 条件3
    rep(T, 1<<M) {
        int B = 0;
        rep(i, M) {
            if(T & (1<<i)) B |= SS[i];
        }
        if(!S.contains(B)) no();
    }
    cout << "Yes" << endl;


    
}
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