結果

問題 No.1594 Three Classes
ユーザー 👑 hitonanodehitonanode
提出日時 2021-07-09 21:24:09
言語 C++17
(gcc 13.2.0 + boost 1.83.0)
結果
AC  
実行時間 7 ms / 2,000 ms
コード長 8,064 bytes
コンパイル時間 1,432 ms
コンパイル使用メモリ 144,084 KB
実行使用メモリ 4,380 KB
最終ジャッジ日時 2023-08-10 06:33:15
合計ジャッジ時間 2,525 ms
ジャッジサーバーID
(参考情報)
judge13 / judge12
このコードへのチャレンジ(β)

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 7 ms
4,376 KB
testcase_01 AC 2 ms
4,380 KB
testcase_02 AC 1 ms
4,376 KB
testcase_03 AC 7 ms
4,376 KB
testcase_04 AC 7 ms
4,376 KB
testcase_05 AC 7 ms
4,380 KB
testcase_06 AC 7 ms
4,376 KB
testcase_07 AC 7 ms
4,376 KB
testcase_08 AC 7 ms
4,380 KB
testcase_09 AC 7 ms
4,376 KB
testcase_10 AC 7 ms
4,380 KB
testcase_11 AC 7 ms
4,380 KB
testcase_12 AC 7 ms
4,376 KB
testcase_13 AC 2 ms
4,380 KB
testcase_14 AC 7 ms
4,376 KB
testcase_15 AC 7 ms
4,376 KB
testcase_16 AC 4 ms
4,380 KB
testcase_17 AC 7 ms
4,376 KB
testcase_18 AC 1 ms
4,376 KB
testcase_19 AC 2 ms
4,376 KB
testcase_20 AC 2 ms
4,376 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 <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
template <typename T> vector<T> sort_unique(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <typename T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <typename T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T, size_t sz> ostream &operator<<(ostream &os, const array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
#if __cplusplus >= 201703L
template <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
#endif
template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T, typename TH> ostream &operator<<(ostream &os, const unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <typename TK, typename TV, typename TH> ostream &operator<<(ostream &os, const unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl
#define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr)
#else
#define dbg(x) (x)
#define dbgif(cond, x) 0
#endif

// Subset sum (fast zeta transform)
// Complexity: O(N 2^N) for array of size 2^N
template <typename T> void subset_sum(std::vector<T> &f) {
    const int sz = f.size(), n = __builtin_ctz(sz);
    assert(__builtin_popcount(sz) == 1);
    for (int d = 0; d < n; d++) {
        for (int S = 0; S < 1 << n; S++)
            if (S & (1 << d)) f[S] += f[S ^ (1 << d)];
    }
}
// Inverse of subset sum (fast moebius transform)
// Complexity: O(N 2^N) for array of size 2^N
template <typename T> void subset_sum_inv(std::vector<T> &g) {
    const int sz = g.size(), n = __builtin_ctz(sz);
    assert(__builtin_popcount(sz) == 1);
    for (int d = 0; d < n; d++) {
        for (int S = 0; S < 1 << n; S++)
            if (S & (1 << d)) g[S] -= g[S ^ (1 << d)];
    }
}

// Superset sum / its inverse (fast zeta/moebius transform)
// Complexity: O(N 2^N) for array of size 2^N
template <typename T> void superset_sum(std::vector<T> &f) {
    const int sz = f.size(), n = __builtin_ctz(sz);
    assert(__builtin_popcount(sz) == 1);
    for (int d = 0; d < n; d++) {
        for (int S = 0; S < 1 << n; S++)
            if (!(S & (1 << d))) f[S] += f[S | (1 << d)];
    }
}
template <typename T> void superset_sum_inv(std::vector<T> &g) {
    const int sz = g.size(), n = __builtin_ctz(sz);
    assert(__builtin_popcount(sz) == 1);
    for (int d = 0; d < n; d++) {
        for (int S = 0; S < 1 << n; S++)
            if (!(S & (1 << d))) g[S] -= g[S | (1 << d)];
    }
}

// Subset convolution
// h[S] = \sum_T f[T] * g[S - T]
// Complexity: O(N^2 2^N) for arrays of size 2^N
template <typename T> std::vector<T> subset_convolution(std::vector<T> f, std::vector<T> g) {
    const int sz = f.size(), m = __builtin_ctz(sz) + 1;
    assert(__builtin_popcount(sz) == 1 and f.size() == g.size());

    std::vector<std::vector<T>> ff(m, std::vector<T>(sz)), fg(m, std::vector<T>(sz));
    for (int i = 0; i < sz; i++) {
        int pc = __builtin_popcount(i);
        ff[pc][i] += f[i], fg[pc][i] += g[i];
    }
    for (auto &vec : ff) subset_sum(vec);
    for (auto &vec : fg) subset_sum(vec);

    std::vector<std::vector<T>> fh(m, std::vector<T>(sz));
    for (int d = 0; d < m; d++) {
        for (int e = 0; d + e < m; e++) {
            for (int i = 0; i < sz; i++) fh[d + e][i] += ff[d][i] * fg[e][i];
        }
    }
    for (auto &vec : fh) subset_sum_inv(vec);
    std::vector<T> ret(sz);
    for (int i = 0; i < sz; i++) ret[i] = fh[__builtin_popcount(i)][i];
    return ret;
}


int main() {
    int N;
    cin >> N;
    vector<int> A(N);
    cin >> A;
    int sum = accumulate(ALL(A), 0);
    vector<int> v(1 << N);
    REP(S, 1 << N) {
        int tot = 0;
        REP(d, N) if ((S >> d) & 1) tot += A[d];
        if (tot * 3 == sum) v[S] = 1;
    }
    auto m = subset_convolution(v, subset_convolution(v, v));
    cout << (m.back() ? "Yes" : "No") << '\n';
}
0