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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#860857#9980. Boolean Function Reconstructionucup-team112#WA 16ms3712kbC++2014.2kb2025-01-18 15:16:022025-01-18 15:20:31

Judging History

你现在查看的是最新测评结果

  • [2025-01-18 15:20:31]
  • 评测
  • 测评结果:WA
  • 用时:16ms
  • 内存:3712kb
  • [2025-01-18 15:16:02]
  • 提交

answer

// #pragma GCC target("avx2")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")
// #define INTERACTIVE

#include <bits/stdc++.h>
using namespace std;

namespace templates {
// type
using ll  = long long;
using ull = unsigned long long;
using Pii = pair<int, int>;
using Pil = pair<int, ll>;
using Pli = pair<ll, int>;
using Pll = pair<ll, ll>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using qp = priority_queue<T, vector<T>, greater<T>>;
// clang-format off
#define vec(T, A, ...) vector<T> A(__VA_ARGS__);
#define vvec(T, A, h, ...) vector<vector<T>> A(h, vector<T>(__VA_ARGS__));
#define vvvec(T, A, h1, h2, ...) vector<vector<vector<T>>> A(h1, vector<vector<T>>(h2, vector<T>(__VA_ARGS__)));
// clang-format on

// for loop
#define fori1(a) for (ll _ = 0; _ < (a); _++)
#define fori2(i, a) for (ll i = 0; i < (a); i++)
#define fori3(i, a, b) for (ll i = (a); i < (b); i++)
#define fori4(i, a, b, c) for (ll i = (a); ((c) > 0 || i > (b)) && ((c) < 0 || i < (b)); i += (c))
#define overload4(a, b, c, d, e, ...) e
#define fori(...) overload4(__VA_ARGS__, fori4, fori3, fori2, fori1)(__VA_ARGS__)

// declare and input
// clang-format off
#define INT(...) int __VA_ARGS__; inp(__VA_ARGS__);
#define LL(...) ll __VA_ARGS__; inp(__VA_ARGS__);
#define STRING(...) string __VA_ARGS__; inp(__VA_ARGS__);
#define CHAR(...) char __VA_ARGS__; inp(__VA_ARGS__);
#define DOUBLE(...) double __VA_ARGS__; STRING(str___); __VA_ARGS__ = stod(str___);
#define VEC(T, A, n) vector<T> A(n); inp(A);
#define VVEC(T, A, n, m) vector<vector<T>> A(n, vector<T>(m)); inp(A);
// clang-format on

// const value
const ll MOD1   = 1000000007;
const ll MOD9   = 998244353;
const double PI = acos(-1);

// other macro
#if !defined(RIN__LOCAL) && !defined(INTERACTIVE)
#define endl "\n"
#endif
#define spa ' '
#define len(A) ll(A.size())
#define all(A) begin(A), end(A)

// function
vector<char> stoc(string &S) {
    int n = S.size();
    vector<char> ret(n);
    for (int i = 0; i < n; i++) ret[i] = S[i];
    return ret;
}
string ctos(vector<char> &S) {
    int n      = S.size();
    string ret = "";
    for (int i = 0; i < n; i++) ret += S[i];
    return ret;
}

template <class T>
auto min(const T &a) {
    return *min_element(all(a));
}
template <class T>
auto max(const T &a) {
    return *max_element(all(a));
}
template <class T, class S>
auto clamp(T &a, const S &l, const S &r) {
    return (a > r ? r : a < l ? l : a);
}
template <class T, class S>
inline bool chmax(T &a, const S &b) {
    return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
    return (a > b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chclamp(T &a, const S &l, const S &r) {
    auto b = clamp(a, l, r);
    return (a != b ? a = b, 1 : 0);
}

template <typename T>
T sum(vector<T> &A) {
    T tot = 0;
    for (auto a : A) tot += a;
    return tot;
}

template <typename T>
vector<T> compression(vector<T> X) {
    sort(all(X));
    X.erase(unique(all(X)), X.end());
    return X;
}

// input and output
namespace io {
// __int128_t
std::istream &operator>>(std::istream &is, __int128_t &value) {
    std::string str;
    is >> str;
    value    = 0;
    int sign = 1;
    for (size_t i = 0; i < str.size(); i++) {
        if (i == 0 && str[i] == '-') {
            sign = -1;
            continue;
        }
        value = value * 10 + str[i] - '0';
    }
    value *= sign;
    return is;
}

std::ostream &operator<<(std::ostream &dest, __int128_t value) {
    std::ostream::sentry s(dest);
    if (s) {
        __uint128_t tmp = value < 0 ? -value : value;
        char buffer[128];
        char *d = std::end(buffer);
        do {
            --d;
            *d = "0123456789"[tmp % 10];
            tmp /= 10;
        } while (tmp != 0);
        if (value < 0) {
            --d;
            *d = '-';
        }
        int len = std::end(buffer) - d;
        if (dest.rdbuf()->sputn(d, len) != len) {
            dest.setstate(std::ios_base::badbit);
        }
    }
    return dest;
}

// vector<T>
template <typename T>
istream &operator>>(istream &is, vector<T> &A) {
    for (auto &a : A) is >> a;
    return is;
}
template <typename T>
ostream &operator<<(ostream &os, vector<T> &A) {
    for (size_t i = 0; i < A.size(); i++) {
        os << A[i];
        if (i != A.size() - 1) os << ' ';
    }
    return os;
}

// vector<vector<T>>
template <typename T>
istream &operator>>(istream &is, vector<vector<T>> &A) {
    for (auto &a : A) is >> a;
    return is;
}
template <typename T>
ostream &operator<<(ostream &os, vector<vector<T>> &A) {
    for (size_t i = 0; i < A.size(); i++) {
        os << A[i];
        if (i != A.size() - 1) os << endl;
    }
    return os;
}

// pair<S, T>
template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &A) {
    is >> A.first >> A.second;
    return is;
}
template <typename S, typename T>
ostream &operator<<(ostream &os, pair<S, T> &A) {
    os << A.first << ' ' << A.second;
    return os;
}

// vector<pair<S, T>>
template <typename S, typename T>
istream &operator>>(istream &is, vector<pair<S, T>> &A) {
    for (size_t i = 0; i < A.size(); i++) {
        is >> A[i];
    }
    return is;
}
template <typename S, typename T>
ostream &operator<<(ostream &os, vector<pair<S, T>> &A) {
    for (size_t i = 0; i < A.size(); i++) {
        os << A[i];
        if (i != A.size() - 1) os << endl;
    }
    return os;
}

// tuple
template <typename T, size_t N>
struct TuplePrint {
    static ostream &print(ostream &os, const T &t) {
        TuplePrint<T, N - 1>::print(os, t);
        os << ' ' << get<N - 1>(t);
        return os;
    }
};
template <typename T>
struct TuplePrint<T, 1> {
    static ostream &print(ostream &os, const T &t) {
        os << get<0>(t);
        return os;
    }
};
template <typename... Args>
ostream &operator<<(ostream &os, const tuple<Args...> &t) {
    TuplePrint<decltype(t), sizeof...(Args)>::print(os, t);
    return os;
}

// io functions
void FLUSH() {
    cout << flush;
}

void print() {
    cout << endl;
}
template <class Head, class... Tail>
void print(Head &&head, Tail &&...tail) {
    cout << head;
    if (sizeof...(Tail)) cout << spa;
    print(std::forward<Tail>(tail)...);
}

template <typename T, typename S>
void prisep(vector<T> &A, S sep) {
    int n = A.size();
    for (int i = 0; i < n; i++) {
        cout << A[i];
        if (i != n - 1) cout << sep;
    }
    cout << endl;
}
template <typename T, typename S>
void priend(T A, S end) {
    cout << A << end;
}
template <typename T>
void prispa(T A) {
    priend(A, spa);
}
template <typename T, typename S>
bool printif(bool f, T A, S B) {
    if (f)
        print(A);
    else
        print(B);
    return f;
}

template <class... T>
void inp(T &...a) {
    (cin >> ... >> a);
}

} // namespace io
using namespace io;

// read graph
vector<vector<int>> read_edges(int n, int m, bool direct = false, int indexed = 1) {
    vector<vector<int>> edges(n, vector<int>());
    for (int i = 0; i < m; i++) {
        INT(u, v);
        u -= indexed;
        v -= indexed;
        edges[u].push_back(v);
        if (!direct) edges[v].push_back(u);
    }
    return edges;
}
vector<vector<int>> read_tree(int n, int indexed = 1) {
    return read_edges(n, n - 1, false, indexed);
}

template <typename T = long long>
vector<vector<pair<int, T>>> read_wedges(int n, int m, bool direct = false, int indexed = 1) {
    vector<vector<pair<int, T>>> edges(n, vector<pair<int, T>>());
    for (int i = 0; i < m; i++) {
        INT(u, v);
        T w;
        inp(w);
        u -= indexed;
        v -= indexed;
        edges[u].push_back({v, w});
        if (!direct) edges[v].push_back({u, w});
    }
    return edges;
}
template <typename T = long long>
vector<vector<pair<int, T>>> read_wtree(int n, int indexed = 1) {
    return read_wedges<T>(n, n - 1, false, indexed);
}

// yes / no
namespace yesno {

// yes
inline bool yes(bool f = true) {
    cout << (f ? "yes" : "no") << endl;
    return f;
}
inline bool Yes(bool f = true) {
    cout << (f ? "Yes" : "No") << endl;
    return f;
}
inline bool YES(bool f = true) {
    cout << (f ? "YES" : "NO") << endl;
    return f;
}

// no
inline bool no(bool f = true) {
    cout << (!f ? "yes" : "no") << endl;
    return f;
}
inline bool No(bool f = true) {
    cout << (!f ? "Yes" : "No") << endl;
    return f;
}
inline bool NO(bool f = true) {
    cout << (!f ? "YES" : "NO") << endl;
    return f;
}

// possible
inline bool possible(bool f = true) {
    cout << (f ? "possible" : "impossible") << endl;
    return f;
}
inline bool Possible(bool f = true) {
    cout << (f ? "Possible" : "Impossible") << endl;
    return f;
}
inline bool POSSIBLE(bool f = true) {
    cout << (f ? "POSSIBLE" : "IMPOSSIBLE") << endl;
    return f;
}

// impossible
inline bool impossible(bool f = true) {
    cout << (!f ? "possible" : "impossible") << endl;
    return f;
}
inline bool Impossible(bool f = true) {
    cout << (!f ? "Possible" : "Impossible") << endl;
    return f;
}
inline bool IMPOSSIBLE(bool f = true) {
    cout << (!f ? "POSSIBLE" : "IMPOSSIBLE") << endl;
    return f;
}

// Alice Bob
inline bool Alice(bool f = true) {
    cout << (f ? "Alice" : "Bob") << endl;
    return f;
}
inline bool Bob(bool f = true) {
    cout << (f ? "Bob" : "Alice") << endl;
    return f;
}

// Takahashi Aoki
inline bool Takahashi(bool f = true) {
    cout << (f ? "Takahashi" : "Aoki") << endl;
    return f;
}
inline bool Aoki(bool f = true) {
    cout << (f ? "Aoki" : "Takahashi") << endl;
    return f;
}

} // namespace yesno
using namespace yesno;

} // namespace templates
using namespace templates;

void solve() {
    INT(n);
    STRING(S);
    vec(bool, ok, 1 << n, false);
    fori(bit, 1 << n) {
        ok[bit] = S[bit] == '1';
    }
    fori(bit, 1 << n) {
        fori(i, n) {
            if ((bit >> i) & 1) {
                if (ok[bit ^ (1 << i)] and !(ok[bit])) {
                    No();
                    return;
                }
            }
        }
    }

    Yes();
    if (!ok.back()) {
        print("F");
        return;
    }

    vvec(bool, all_T, n + 1);
    vvec(bool, all_F, n + 1);
    all_T[n] = ok;
    all_F[n] = ok;
    fori(i, 1 << n) {
        all_F[n][i] = !all_F[n][i];
    }
    fori(i, n - 1, -1, -1) {
        all_T[i].resize(1 << i);
        all_F[i].resize(1 << i);
        fori(j, 1 << i) {
            all_T[i][j] = all_T[i + 1][j] & all_T[i + 1][j + (1 << i)];
            all_F[i][j] = all_F[i + 1][j] & all_F[i + 1][j + (1 << i)];
        }
    }

    auto dfs = [&](auto &&self, int i, int bit) -> string {
        if (all_T[i][bit]) return "T";
        if (all_F[i][bit]) return "F";
        string res;
        auto l_ = self(self, i + 1, bit | (1 << i));
        auto r_ = self(self, i + 1, bit);
        if (l_ == "F") {
        } else if (l_ == "T") {
            res += char('a' + i);
        } else {
            res += "(";
            res += char('a' + i);
            res += '&';
            res += l_;
            res += ")";
        }
        if (r_ == "F") {
        } else if (r_ == "T") {
            throw;
        } else {
            res = "(" + res;
            res += "|";
            res += r_;
            res += ")";
        }

        return res;
    };

    auto ans = dfs(dfs, 0, 0);
    print(ans);
}

int main() {
#ifndef INTERACTIVE
    std::cin.tie(0)->sync_with_stdio(0);
#endif
    // std::cout << std::fixed << std::setprecision(12);
    int t;
    t = 1;
    std::cin >> t;
    while (t--) solve();
    return 0;
}

// // #pragma GCC target("avx2")
// // #pragma GCC optimize("O3")
// // #pragma GCC optimize("unroll-loops")
// // #define INTERACTIVE
//
// #include "kyopro-cpp/template.hpp"
//
// void solve() {
//     INT(n);
//     STRING(S);
//     vec(bool, ok, 1 << n, false);
//     fori(bit, 1 << n) {
//         ok[bit] = S[bit] == '1';
//     }
//     fori(bit, 1 << n) {
//         fori(i, n) {
//             if ((bit >> i) & 1) {
//                 if (ok[bit ^ (1 << i)] and !(ok[bit])) {
//                     No();
//                     return;
//                 }
//             }
//         }
//     }
//
//     Yes();
//     if (!ok.back()) {
//         print("F");
//         return;
//     }
//
//     vvec(bool, all_T, n + 1);
//     vvec(bool, all_F, n + 1);
//     all_T[n] = ok;
//     all_F[n] = ok;
//     fori(i, 1 << n) {
//         all_F[n][i] = !all_F[n][i];
//     }
//     fori(i, n - 1, -1, -1) {
//         all_T[i].resize(1 << i);
//         all_F[i].resize(1 << i);
//         fori(j, 1 << i) {
//             all_T[i][j] = all_T[i + 1][j] & all_T[i + 1][j + (1 << i)];
//             all_F[i][j] = all_F[i + 1][j] & all_F[i + 1][j + (1 << i)];
//         }
//     }
//
//     auto dfs = [&](auto &&self, int i, int bit) -> string {
//         if (all_T[i][bit]) return "T";
//         if (all_F[i][bit]) return "F";
//         string res;
//         auto l_ = self(self, i + 1, bit | (1 << i));
//         auto r_ = self(self, i + 1, bit);
//         if (l_ == "F") {
//         } else if (l_ == "T") {
//             res += char('a' + i);
//         } else {
//             res += "(";
//             res += char('a' + i);
//             res += '&';
//             res += l_;
//             res += ")";
//         }
//         if (r_ == "F") {
//         } else if (r_ == "T") {
//             throw;
//         } else {
//             res = "(" + res;
//             res += "|";
//             res += r_;
//             res += ")";
//         }
//
//         return res;
//     };
//
//     auto ans = dfs(dfs, 0, 0);
//     print(ans);
// }
//
// int main() {
// #ifndef INTERACTIVE
//     std::cin.tie(0)->sync_with_stdio(0);
// #endif
//     // std::cout << std::fixed << std::setprecision(12);
//     int t;
//     t = 1;
//     std::cin >> t;
//     while (t--) solve();
//     return 0;
// }

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 0ms
memory: 3712kb

input:

7
2
0001
2
0111
2
1111
3
00010111
1
10
2
0101
5
00000000000000000000000000000001

output:

Yes
(a&b)
Yes
(a|b)
Yes
T
Yes
((a&(b|c))|(b&c))
No
Yes
a
Yes
(a&(b&(c&(d&e))))

result:

ok 7 lines, tightest: 4 out of 14 (7 test cases)

Test #2:

score: 0
Accepted
time: 0ms
memory: 3584kb

input:

4
1
00
1
10
1
01
1
11

output:

Yes
F
No
Yes
a
Yes
T

result:

ok 4 lines, tightest: 0 out of 11 (4 test cases)

Test #3:

score: 0
Accepted
time: 0ms
memory: 3712kb

input:

16
2
0000
2
1000
2
0100
2
1100
2
0010
2
1010
2
0110
2
1110
2
0001
2
1001
2
0101
2
1101
2
0011
2
1011
2
0111
2
1111

output:

Yes
F
No
No
No
No
No
No
No
Yes
(a&b)
No
Yes
a
No
Yes
((a&b)|b)
No
Yes
(a|b)
Yes
T

result:

ok 16 lines, tightest: 2 out of 12 (16 test cases)

Test #4:

score: 0
Accepted
time: 0ms
memory: 3584kb

input:

256
3
00000000
3
10000000
3
01000000
3
11000000
3
00100000
3
10100000
3
01100000
3
11100000
3
00010000
3
10010000
3
01010000
3
11010000
3
00110000
3
10110000
3
01110000
3
11110000
3
00001000
3
10001000
3
01001000
3
11001000
3
00101000
3
10101000
3
01101000
3
11101000
3
00011000
3
10011000
3
01011000...

output:

Yes
F
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
...

result:

ok 256 lines, tightest: 6 out of 14 (256 test cases)

Test #5:

score: 0
Accepted
time: 16ms
memory: 3584kb

input:

65536
4
0000000000000000
4
1000000000000000
4
0100000000000000
4
1100000000000000
4
0010000000000000
4
1010000000000000
4
0110000000000000
4
1110000000000000
4
0001000000000000
4
1001000000000000
4
0101000000000000
4
1101000000000000
4
0011000000000000
4
1011000000000000
4
0111000000000000
4
1111000...

output:

Yes
F
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
...

result:

ok 65536 lines, tightest: 14 out of 18 (65536 test cases)

Test #6:

score: 0
Accepted
time: 1ms
memory: 3712kb

input:

168
4
0000000000000000
4
0000000000000001
4
0000000000000011
4
0000000000000101
4
0000000000000111
4
0000000000001111
4
0000000000010001
4
0000000000010011
4
0000000000010101
4
0000000000010111
4
0000000000011111
4
0000000000110011
4
0000000000110111
4
0000000000111111
4
0000000001010101
4
000000000...

output:

Yes
F
Yes
(a&(b&(c&d)))
Yes
((a&(b&(c&d)))|(b&(c&d)))
Yes
(a&((b&(c&d))|(c&d)))
Yes
((a&((b&(c&d))|(c&d)))|(b&(c&d)))
Yes
((a&((b&(c&d))|(c&d)))|((b&(c&d))|(c&d)))
Yes
(a&(b&((c&d)|d)))
Yes
((a&(b&((c&d)|d)))|(b&(c&d)))
Yes
(a&((b&((c&d)|d))|(c&d)))
Yes
((a&((b&((c&d)|d))|(c&d)))|(b&(c&d)))
Yes
((a&...

result:

ok 168 lines, tightest: 14 out of 18 (168 test cases)

Test #7:

score: -100
Wrong Answer
time: 15ms
memory: 3712kb

input:

7581
5
00000000000000000000000000000000
5
00000000000000000000000000000001
5
00000000000000000000000000000011
5
00000000000000000000000000000101
5
00000000000000000000000000000111
5
00000000000000000000000000001111
5
00000000000000000000000000010001
5
00000000000000000000000000010011
5
0000000000000...

output:

Yes
F
Yes
(a&(b&(c&(d&e))))
Yes
((a&(b&(c&(d&e))))|(b&(c&(d&e))))
Yes
(a&((b&(c&(d&e)))|(c&(d&e))))
Yes
((a&((b&(c&(d&e)))|(c&(d&e))))|(b&(c&(d&e))))
Yes
((a&((b&(c&(d&e)))|(c&(d&e))))|((b&(c&(d&e)))|(c&(d&e))))
Yes
(a&(b&((c&(d&e))|(d&e))))
Yes
((a&(b&((c&(d&e))|(d&e))))|(b&(c&(d&e))))
Yes
(a&((b&(...

result:

wrong answer 27 operations, you can't use more than 26 operations (test case 134)