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답안 #914382

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
914382 2024-01-21T20:27:05 Z tfgs Magneti (COCI21_magneti) C++17
110 / 110
 384 ms 424368 KB 
#include <bits/stdc++.h>
using namespace std;

using ll = long long;
using db = long double; // or double, if TL is tight
using str = string; // yay python! 

// pairs
using pi = pair<int,int>;
using pl = pair<ll,ll>;
using pd = pair<db,db>;
#define mp make_pair
#define f first
#define s second

#define tcT template<class T
#define tcTU tcT, class U
// ^ lol this makes everything look weird but I'll try it
tcT> using V = vector<T>; 
tcT, size_t SZ> using AR = array<T,SZ>; 
using vi = V<int>;
using vb = V<bool>;
using vl = V<ll>;
using vd = V<db>;
using vs = V<str>;
using vpi = V<pi>;
using vpl = V<pl>;
using vpd = V<pd>;

// vectors
// oops size(x), rbegin(x), rend(x) need C++17
#define sz(x) ll((x).size())
#define bg(x) begin(x)
#define all(x) bg(x), end(x)
#define rall(x) x.rbegin(), x.rend() 
#define sor(x) sort(all(x)) 
#define rsz resize
#define ins insert 
#define pb push_back
#define eb emplace_back
#define ft front()
#define bk back()

#define lb lower_bound
#define ub upper_bound
tcT> ll lwb(V<T>& a, const T& b) { return ll(lb(all(a),b)-bg(a)); }
tcT> ll upb(V<T>& a, const T& b) { return ll(ub(all(a),b)-bg(a)); }

// loops
#define FOR(i,a,b) for (ll i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define F1R(i,a) FOR(i,1,a+1)
#define ROF(i,a,b) for (ll i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define R1F(i,a) ROF(i,1,a+1)
#define rep(a) F0R(_,a)
#define each(a,x) for (auto& a: x)

const ll P = 1e9+7; // 998244353;
const ll MX = 2e5+5;
const ll BIG = 1e18; // not too close to LLONG_MAX
const db PI = acos((db)-1);
const ll dx[4]{1,0,-1,0}, dy[4]{0,1,0,-1}; // for every grid problem!!
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count()); 
template<class T> using pqg = priority_queue<T,vector<T>,greater<T>>;

ll binpow(ll a, ll b) {
    ll res = 1;
    while (b) {
        if (b & 1) res = res * a % P;
        b >>= 1;
        a = a * a % P;
    }

    return res;
}

// bitwise ops
// also see https://gcc.gnu.org/onlinedocs/gcc/Other-Builtins.html
constexpr ll pct(ll x) { return __builtin_popcount(x); } // # of bits set
constexpr ll bits(ll x) { // assert(x >= 0); // make C++11 compatible until USACO updates ...
    return x == 0 ? 0 : 31-__builtin_clz(x); } // floor(log2(x)) 
constexpr ll p2(ll x) { return 1<<x; }
constexpr ll msk2(ll x) { return p2(x)-1; }

ll cdiv(ll a, ll b) { return a/b+((a^b)>0&&a%b); } // divide a by b rounded up
ll fdiv(ll a, ll b) { return a/b-((a^b)<0&&a%b); } // divide a by b rounded down

tcT> bool ckmin(T& a, const T& b) {
    return b < a ? a = b, 1 : 0; } // set a = min(a,b)
tcT> bool ckmax(T& a, const T& b) {
    return a < b ? a = b, 1 : 0; } // set a = max(a,b)
// m is max, M is second max
tcT> T tmax(T x, T& m, T& M) {
    if (x <= m) return ckmax(M, x);
    return ckmax(m, x);
}
tcT> T tmin(T x, T& m, T& M) {
    if (x >= m) return ckmin(M, x);
    return ckmin(m, x);
}

tcTU> T fstTrue(T lo, T hi, U f) {
    ++hi; assert(lo <= hi); // assuming f is increasing
    while (lo < hi) { // find first index such that f is true 
        T mid = lo+(hi-lo)/2;
        f(mid) ? hi = mid : lo = mid+1; 
    } 
    return lo;
}
tcTU> T lstTrue(T lo, T hi, U f) {
    --lo; assert(lo <= hi); // assuming f is decreasing
    while (lo < hi) { // find first index such that f is true 
        T mid = lo+(hi-lo+1)/2;
        f(mid) ? lo = mid : hi = mid-1;
    } 
    return lo;
}
tcT> void UNIQUE(vector<T>& v) { // sort and remove duplicates
    sort(all(v)); v.erase(unique(all(v)),end(v)); }
tcTU> void safeErase(T& t, const U& u) { // don't erase
    auto it = t.find(u); assert(it != end(t));
    t.erase(it); } // element that doesn't exist from (multi)set

#define tcTUU tcT, class ...U

inline namespace Helpers {
    //////////// is_iterable
    // https://stackoverflow.com/questions/13830158/check-if-a-variable-type-is-iterable
    // this gets used only when we can call begin() and end() on that type
    tcT, class = void> struct is_iterable : false_type {};
    tcT> struct is_iterable<T, void_t<decltype(begin(declval<T>())),
                                                                                                                                            decltype(end(declval<T>()))
                                                                                                                                        >
                                                                                                > : true_type {};
    tcT> constexpr bool is_iterable_v = is_iterable<T>::value;

    //////////// is_readable
    tcT, class = void> struct is_readable : false_type {};
    tcT> struct is_readable<T,
                                    typename std::enable_if_t<
                                                    is_same_v<decltype(cin >> declval<T&>()), istream&>
                                    >
                    > : true_type {};
    tcT> constexpr bool is_readable_v = is_readable<T>::value;

    //////////// is_printable
    // // https://nafe.es/posts/2020-02-29-is-printable/
    tcT, class = void> struct is_printable : false_type {};
    tcT> struct is_printable<T,
                                    typename std::enable_if_t<
                                                    is_same_v<decltype(cout << declval<T>()), ostream&>
                                    >
                    > : true_type {};
    tcT> constexpr bool is_printable_v = is_printable<T>::value;
}

#define def(t, args...)                                                        \
    t args;                                                                    \
    re(args);

inline namespace Input {
    tcT> constexpr bool needs_input_v = !is_readable_v<T> && is_iterable_v<T>;
    tcTUU> void re(T& t, U&... u);
    tcTU> void re(pair<T,U>& p); // pairs

    // re: read
    tcT> typename enable_if<is_readable_v<T>,void>::type re(T& x) { cin >> x; } // default
    tcT> void re(complex<T>& c) { T a,b; re(a,b); c = {a,b}; } // complex
    tcT> typename enable_if<needs_input_v<T>,void>::type re(T& i); // ex. vectors, arrays
    tcTU> void re(pair<T,U>& p) { re(p.f,p.s); }
    tcT> typename enable_if<needs_input_v<T>,void>::type re(T& i) {
        each(x,i) re(x); }
    tcTUU> void re(T& t, U&... u) { re(t); re(u...); } // read multiple

    // rv: resize and read vectors
    void rv(size_t) {}
    tcTUU> void rv(size_t N, V<T>& t, U&... u);
    template<class...U> void rv(size_t, size_t N2, U&... u);
    tcTUU> void rv(size_t N, V<T>& t, U&... u) {
        t.rsz(N); re(t);
        rv(N,u...); }
    template<class...U> void rv(size_t, size_t N2, U&... u) {
        rv(N2,u...); }

    // dumb shortcuts to read in ints
    void decrement() {} // subtract one from each
    tcTUU> void decrement(T& t, U&... u) { --t; decrement(u...); }
    #define ints(...) int __VA_ARGS__; re(__VA_ARGS__);
    #define int1(...) ints(__VA_ARGS__); decrement(__VA_ARGS__);
}

inline namespace ToString {
    tcT> constexpr bool needs_output_v = !is_printable_v<T> && is_iterable_v<T>;

    // ts: string representation to print
    tcT> typename enable_if<is_printable_v<T>,str>::type ts(T v) {
        stringstream ss; ss << fixed << setprecision(15) << v;
        return ss.str(); } // default
    tcT> str bit_vec(T t) { // bit vector to string
        str res = "{"; F0R(i,sz(t)) res += ts(t[i]);
        res += "}"; return res; }
    str ts(V<bool> v) { return bit_vec(v); }
    template<size_t SZ> str ts(bitset<SZ> b) { return bit_vec(b); } // bit vector
    tcTU> str ts(pair<T,U> p); // pairs
    tcT> typename enable_if<needs_output_v<T>,str>::type ts(T v); // vectors, arrays
    tcTU> str ts(pair<T,U> p) { return "("+ts(p.f)+", "+ts(p.s)+")"; }
    tcT> typename enable_if<is_iterable_v<T>,str>::type ts_sep(T v, str sep) {
        // convert container to string w/ separator sep
        bool fst = 1; str res = "";
        for (const auto& x: v) {
            if (!fst) res += sep;
            fst = 0; res += ts(x);
        }
        return res;
    }
    tcT> typename enable_if<needs_output_v<T>,str>::type ts(T v) {
        return "{"+ts_sep(v,", ")+"}"; }

    // for nested DS
    template<int, class T> typename enable_if<!needs_output_v<T>,vs>::type 
            ts_lev(const T& v) { return {ts(v)}; }
    template<int lev, class T> typename enable_if<needs_output_v<T>,vs>::type 
            ts_lev(const T& v) {
        if (lev == 0 || !sz(v)) return {ts(v)};
        vs res;
        for (const auto& t: v) {
            if (sz(res)) res.bk += ",";
            vs tmp = ts_lev<lev-1>(t);
            res.ins(end(res),all(tmp));
        }
        F0R(i,sz(res)) {
            str bef = " "; if (i == 0) bef = "{";
            res[i] = bef+res[i];
        }
        res.bk += "}";
        return res;
    }
}

inline namespace Output {
    template<class T> void pr_sep(ostream& os, str, const T& t) { os << ts(t); }
    template<class T, class... U> void pr_sep(ostream& os, str sep, const T& t, const U&... u) {
        pr_sep(os,sep,t); os << sep; pr_sep(os,sep,u...); }
    // print w/ no spaces
    template<class ...T> void pr(const T&... t) { pr_sep(cout,"",t...); } 
    // print w/ spaces, end with newline
    void ps() { cout << "\n"; }
    template<class ...T> void ps(const T&... t) { pr_sep(cout," ",t...); ps(); } 
    // debug to cerr
    template<class ...T> void dbg_out(const T&... t) {
        pr_sep(cerr," | ",t...); cerr << endl; }
    void loc_info(int line, str names) {
        cerr << "Line(" << line << ") -> [" << names << "]: "; }
    template<int lev, class T> void dbgl_out(const T& t) {
        cerr << "\n\n" << ts_sep(ts_lev<lev>(t),"\n") << "\n" << endl; }
    #ifdef I_AM_NOOB
        #define gg(...) loc_info(__LINE__,#__VA_ARGS__), dbg_out(__VA_ARGS__)
        #define ggl(lev,x) loc_info(__LINE__,#x), dbgl_out<lev>(x)
    #else // don't actually submit with this
        #define gg(...) 777771449
        #define ggl(lev,x)
    #endif

    // https://stackoverflow.com/questions/47980498/accurate-c-c-clock-on-a-multi-core-processor-with-auto-overclock?noredirect=1&lq=1
    const auto beg = std::chrono::high_resolution_clock::now();
    void dbg_time() {
        auto duration = chrono::duration<double>(
            std::chrono::high_resolution_clock::now() - beg);
        gg(duration.count());
    }
}

inline namespace FileIO {
    void setIn(str s)  { freopen(s.c_str(),"r",stdin); }
    void setOut(str s) { freopen(s.c_str(),"w",stdout); }
    void setIO(str s = "") {
        cin.tie(0)->sync_with_stdio(0); // unsync C / C++ I/O streams
        // cin.exceptions(cin.failbit);
        // throws exception when do smth illegal
        // ex. try to read letter into int
        if (sz(s) && fopen((s+".in").c_str(), "r")) setIn(s+".in"), setOut(s+".out"); // for old USACO
    }
}

// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2016/p0200r0.html
template<class Fun> class y_combinator_result {
    Fun fun_;
public:
    template<class T> explicit y_combinator_result(T &&fun): fun_(std::forward<T>(fun)) {}
    template<class ...Args> decltype(auto) operator()(Args &&...args) { return fun_(std::ref(*this), std::forward<Args>(args)...); }
};
template<class Fun> decltype(auto) yy(Fun &&fun) { return y_combinator_result<std::decay_t<Fun>>(std::forward<Fun>(fun)); }

struct chash {
    // any random-ish large odd number will do
    const uint64_t C = uint64_t(2e18 * PI) + 71;
    // random 32-bit number
    const uint32_t RANDOM =
                    chrono::steady_clock::now().time_since_epoch().count();
    size_t operator()(uint64_t x) const {
        // see https://gcc.gnu.org/onlinedocs/gcc/Other-Builtins.html
        return __builtin_bswap64((x ^ RANDOM) * C);
    }
};
template <class K, class V> using cmap = unordered_map<K, V, chash>;
// example usage: cmap<int, int>

const ll N = 20002;
ll fact[N], inv[N];

ll C(ll n, ll r) {
    return fact[n]*inv[r]%P * inv[n-r]%P;
}

void init() {
    fact[0] = 1;
    F1R(i, N-1) fact[i] = fact[i-1]*i % P;
    inv[N-1] = binpow(fact[N-1], P-2);
    ROF(i, 0, N-1) inv[i] = inv[i+1]*(i+1) % P;
}

ll len(vl& p) {
    ll res = 1;
    F0R(i, sz(p)-1) res += max(p[i], p[i+1]);
    return res;
}

ll n, L;
const ll MAX = 52;
ll dp[MAX][MAX][N];

void solve() {
    memset(dp, 0, sizeof dp);

    vl a(n+1); F1R(i, n) re(a[i]);
    sort(1+all(a));
    
    dp[0][0][0] = 1;
    F0R(i, n) R0F(j, n+1) F0R(d, L) {
        // new
        (dp[i+1][j+1][d+1] += dp[i][j][d]%P) %= P;
        // augment
        (dp[i+1][j][d+a[i+1]] += dp[i][j][d]*2*j%P) %= P;
        // new & merge
        if (j > 0) (dp[i+1][j-1][d+2*a[i+1]-1] += dp[i][j][d]*j%P*(j-1)%P) %= P;

        // // new
        // (dp[i+1][j+1][d+1] += dp[i][j][d]*(j+1)%P) %= P;
        // // augment
        // (dp[i+1][j][d+a[i+1]] += dp[i][j][d]*2*j%P) %= P;
        // // merge
        // if (i > 1 && j > 0) (dp[i][j-1][d+a[i]] += dp[i][j][d]) %= P;
    }

    ll ans = 0;
    F0R(d, L+1) {
        ll ways = dp[n][1][d];
        ll x = C(L-d+n, n);
        (ans += x*ways) %= P;
    }

    ps(ans);
}

signed main() {
    setIO();
    
    init();
    // while (cin >> n >> L) solve();
    // ll tc; cin >> tc; while (tc--) {
        cin >> n >> L;
        solve();
    // }

    return 0;
}

Compilation message

Main.cpp: In function 'void Output::dbg_time()':
Main.cpp:261:25: warning: statement has no effect [-Wunused-value]
  261 |         #define gg(...) 777771449
      |                         ^~~~~~~~~
Main.cpp:270:9: note: in expansion of macro 'gg'
  270 |         gg(duration.count());
      |         ^~
Main.cpp: In function 'void FileIO::setIn(str)':
Main.cpp:275:33: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  275 |     void setIn(str s)  { freopen(s.c_str(),"r",stdin); }
      |                          ~~~~~~~^~~~~~~~~~~~~~~~~~~~~
Main.cpp: In function 'void FileIO::setOut(str)':
Main.cpp:276:33: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  276 |     void setOut(str s) { freopen(s.c_str(),"w",stdout); }
      |                          ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~

Subtask #1
10.0 / 10.0

# 결과 실행 시간 메모리 Grader output
1 Correct 363 ms 424272 KB Output is correct
2 Correct 119 ms 423980 KB Output is correct
3 Correct 127 ms 424020 KB Output is correct
4 Correct 120 ms 424020 KB Output is correct
5 Correct 147 ms 423884 KB Output is correct
6 Correct 186 ms 424120 KB Output is correct
7 Correct 243 ms 424020 KB Output is correct
8 Correct 123 ms 424096 KB Output is correct
9 Correct 173 ms 424020 KB Output is correct
10 Correct 118 ms 424020 KB Output is correct

Subtask #2
20.0 / 20.0

# 결과 실행 시간 메모리 Grader output
1 Correct 131 ms 424164 KB Output is correct
2 Correct 119 ms 424020 KB Output is correct
3 Correct 129 ms 423872 KB Output is correct
4 Correct 122 ms 424016 KB Output is correct
5 Correct 133 ms 424020 KB Output is correct
6 Correct 119 ms 424016 KB Output is correct
7 Correct 127 ms 424020 KB Output is correct
8 Correct 118 ms 423964 KB Output is correct
9 Correct 118 ms 424016 KB Output is correct
10 Correct 121 ms 423964 KB Output is correct

Subtask #3
30.0 / 30.0

# 결과 실행 시간 메모리 Grader output
1 Correct 119 ms 424016 KB Output is correct
2 Correct 121 ms 423964 KB Output is correct
3 Correct 121 ms 423924 KB Output is correct
4 Correct 123 ms 424048 KB Output is correct
5 Correct 121 ms 423924 KB Output is correct
6 Correct 117 ms 423872 KB Output is correct
7 Correct 123 ms 424052 KB Output is correct
8 Correct 117 ms 424104 KB Output is correct
9 Correct 117 ms 424012 KB Output is correct
10 Correct 119 ms 424096 KB Output is correct

Subtask #4
50.0 / 50.0

# 결과 실행 시간 메모리 Grader output
1 Correct 363 ms 424272 KB Output is correct
2 Correct 119 ms 423980 KB Output is correct
3 Correct 127 ms 424020 KB Output is correct
4 Correct 120 ms 424020 KB Output is correct
5 Correct 147 ms 423884 KB Output is correct
6 Correct 186 ms 424120 KB Output is correct
7 Correct 243 ms 424020 KB Output is correct
8 Correct 123 ms 424096 KB Output is correct
9 Correct 173 ms 424020 KB Output is correct
10 Correct 118 ms 424020 KB Output is correct
11 Correct 131 ms 424164 KB Output is correct
12 Correct 119 ms 424020 KB Output is correct
13 Correct 129 ms 423872 KB Output is correct
14 Correct 122 ms 424016 KB Output is correct
15 Correct 133 ms 424020 KB Output is correct
16 Correct 119 ms 424016 KB Output is correct
17 Correct 127 ms 424020 KB Output is correct
18 Correct 118 ms 423964 KB Output is correct
19 Correct 118 ms 424016 KB Output is correct
20 Correct 121 ms 423964 KB Output is correct
21 Correct 119 ms 424016 KB Output is correct
22 Correct 121 ms 423964 KB Output is correct
23 Correct 121 ms 423924 KB Output is correct
24 Correct 123 ms 424048 KB Output is correct
25 Correct 121 ms 423924 KB Output is correct
26 Correct 117 ms 423872 KB Output is correct
27 Correct 123 ms 424052 KB Output is correct
28 Correct 117 ms 424104 KB Output is correct
29 Correct 117 ms 424012 KB Output is correct
30 Correct 119 ms 424096 KB Output is correct
31 Correct 350 ms 424016 KB Output is correct
32 Correct 260 ms 424116 KB Output is correct
33 Correct 353 ms 424016 KB Output is correct
34 Correct 163 ms 424016 KB Output is correct
35 Correct 360 ms 424368 KB Output is correct
36 Correct 134 ms 424012 KB Output is correct
37 Correct 372 ms 424280 KB Output is correct
38 Correct 160 ms 424016 KB Output is correct
39 Correct 379 ms 424016 KB Output is correct
40 Correct 188 ms 424324 KB Output is correct
41 Correct 353 ms 423984 KB Output is correct
42 Correct 117 ms 424056 KB Output is correct
43 Correct 352 ms 424020 KB Output is correct
44 Correct 139 ms 424020 KB Output is correct
45 Correct 384 ms 424236 KB Output is correct
46 Correct 119 ms 423928 KB Output is correct
47 Correct 209 ms 424116 KB Output is correct
48 Correct 158 ms 424084 KB Output is correct
49 Correct 125 ms 423996 KB Output is correct
50 Correct 118 ms 424016 KB Output is correct