Submission #11651184

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Source Code Expand

// #pragma GCC target ("avx")
// #pragma GCC optimize("Ofast")
// #pragma GCC optimize("unroll-loops")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#include <bits/stdc++.h>
using namespace std;
// #define int long long
// #define endl '\n'

#pragma region TEMPLATE

/* TYPE */
typedef long long ll;       typedef long double ld;
typedef pair<int, int> pii; typedef pair<ll, ll> pll;
typedef vector<pii> vpii;   typedef vector<pll> vpll;
typedef vector<int> vi;     typedef vector<ll> vl;
typedef vector<string> vst; typedef vector<bool> vb;
typedef vector<ld> vld;     typedef vector<vector<int>> vvi;
template<typename T, typename Cmp = less<>> using prique = priority_queue<T, vector<T>, Cmp>;
template<typename T> using prique_r = prique<T, greater<>>;
/* CONSTANT */
#define ln '\n'
const int INF = 1 << 30;    const ll INFF = 1LL << 60;  const string ALPHABET = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const int MOD = 1e9 + 7;    const int MODD = 998244353; const string alphabet = "abcdefghijklmnopqrstuvwxyz";
const double EPS = 1e-9;    const ld PI = 3.14159265358979323846264338327950288;
const int dx[] = { 1, 0, -1,  0,  1, -1, -1, 1, 0 };
const int dy[] = { 0, 1,  0, -1, -1, -1,  1, 1, 0 };
/* CONTAINER */
#define PB              emplace_back
#define ALL(v)          (v).begin(), (v).end()
#define RALL(v)         (v).rbegin(), (v).rend()
#define SORT(v)         sort(ALL(v))
#define RSORT(v)        sort(RALL(v))
#define LESS(x, val)    (lower_bound(x.begin(), x.end(), val) - x.begin())
#define LEQ(x, val)     (upper_bound(x.begin(), x.end(), val) - x.begin())
#define GREATER(x, val) (int)(x).size() - LEQ((x), (val))
#define GEQ(x, val)     (int)(x).size() - LESS((x), (val))
#define UNIQUE(v)       sort(ALL(v)); (v).erase(unique(ALL(v)), (v).end())
template<typename T> vector<T> make_v(size_t a) { return vector<T>(a); }
template<typename T, typename... Ts> auto make_v(size_t a, Ts... ts) { return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...)); }
template<typename T, typename U, typename... V> enable_if_t<is_same<T, U>::value != 0> fill_v(U &u, const V... v) { u = U(v...); }
template<typename T, typename U, typename... V> enable_if_t<is_same<T, U>::value == 0> fill_v(U &u, const V... v) { for (auto &e : u) fill_v<T>(e, v...); }
/* LOOP */
#define _overload3(_1, _2, _3, name, ...) name
#define _REP(i, n)      REPI(i, 0, n)
#define REPI(i, a, b)   for (ll i = (ll)a; i < (ll)b; ++i)
#define REP(...)        _overload3(__VA_ARGS__, REPI, _REP,)(__VA_ARGS__)
#define _RREP(i, n)     RREPI(i, n, 0)
#define RREPI(i, a, b)  for (ll i = (ll)a; i >= (ll)b; --i)
#define RREP(...)       _overload3(__VA_ARGS__, RREPI, _RREP,)(__VA_ARGS__)
#define EACH(e, v)      for (auto& e : v)
#define PERM(v)         sort(ALL(v)); for (bool c##p = true; c##p; c##p = next_permutation(ALL(v)))
/* INPUT */
template<typename T> void SSS(T& t) { cin >> t; }
template<typename Head, typename... Tail> void SSS(Head&& head, Tail&&... tail) { cin >> head; SSS(tail...); }
#define SS(T, ...)      T __VA_ARGS__; SSS(__VA_ARGS__);
#define SV(T, v, n)     vector<T> v(n); for (auto& i : v) cin >> i;
#define SVV(T, v, n, m) vector<vector<T>> v(n, vector<T>(m)); for (auto& r : v) for (auto& i : r) cin >> i;
/* OUTPUT */
// PROTOTYPE DECLARATION
template<typename T, typename U> ostream &operator<<(ostream &os, const pair<T, U> &j);
template<typename... T> ostream &operator<<(ostream &os, const tuple<T...> &t);
template<class C, enable_if_t<!is_same<C, string>::value, decltype(declval<const C &>().begin(), nullptr)> = nullptr> ostream& operator<<(ostream &os, const C &c);
template<typename T> ostream &operator<<(ostream &os, const stack<T> &j);
template<typename T> ostream &operator<<(ostream &os, const queue<T> &j);
template<typename T, typename C, typename Cmp> ostream &operator<<(ostream &os, const priority_queue<T, C, Cmp> &j);
// IMPLEMENTATION
template<typename T, typename U> ostream &operator<<(ostream &os, const pair<T, U> &j) { return os << '{' << j.first << ", " << j.second << '}'; }
template<size_t num = 0, typename... T> enable_if_t<num == sizeof...(T)> PRINT_TUPLE(ostream &os, const tuple<T...> &t) {}
template<size_t num = 0, typename... T> enable_if_t<num <  sizeof...(T)> PRINT_TUPLE(ostream &os, const tuple<T...> &t) { os << get<num>(t); if (num + 1 < sizeof...(T)) os << ", "; PRINT_TUPLE<num + 1>(os, t); }
template<typename... T> ostream &operator<<(ostream &os, const tuple<T...> &t) { PRINT_TUPLE(os << '{', t); return os << '}'; }
template<class C, enable_if_t<!is_same<C, string>::value, decltype(declval<const C &>().begin(), nullptr)>> ostream& operator<<(ostream &os, const C &c) { os << '{'; for (auto it = begin(c); it != end(c); it++) { if (begin(c) != it) os << ", "; os << *it; } return os << '}'; }
template<typename T> ostream &operator<<(ostream &os, const stack<T> &j) { deque<T> d; for (auto c = j; !c.empty(); c.pop()) d.push_front(c.top());  return os << d; }
template<typename T> ostream &operator<<(ostream &os, const queue<T> &j) { deque<T> d; for (auto c = j; !c.empty(); c.pop()) d.push_back(c.front()); return os << d; }
template<typename T, typename C, typename Cmp> ostream &operator<<(ostream &os, const priority_queue<T, C, Cmp> &j) { deque<T> d; for (auto c = j; !c.empty(); c.pop()) d.push_front(c.top());  return os << d; }
// OUTPUT FUNCTION
template<typename T> int PV(T &v) { int sz = v.size(); for (int i = 0; i < sz; ++i) cout << v[i] << " \n"[i == sz - 1]; return 0; }
inline int print() { cout << endl; return 0; }
template<typename Head> int print(Head&& head){ cout << head; return print(); }
template<typename Head, typename... Tail> int print(Head&& head, Tail&&... tail) { cout << head << " "; return print(forward<Tail>(tail)...); }
#ifdef LOCAL
inline void dump() { cerr << endl; }
template<typename Head> void dump(Head&& head) { cerr << head; dump(); }
template<typename Head, typename... Tail> void dump(Head&& head, Tail&&... tail) { cerr << head << ", "; dump(forward<Tail>(tail)...); }
#define debug(...) do {cerr << __LINE__ << ":\t" << #__VA_ARGS__ << " = "; dump(__VA_ARGS__); } while (false)
#else
#define dump(...)
#define debug(...)
#endif
/* OTHER */
#define fi              first
#define se              second
#define MP              make_pair
#define MT              make_tuple
#define tmax(x, y, z)   max((x), max((y), (z)))
#define tmin(x, y, z)   min((x), min((y), (z)))
template<typename T, typename A, typename B> inline bool between(T x, A a, B b) { return ((a <= x) && (x < b)); }
template<typename A, typename B> inline bool chmax(A &a, const B &b) { if (a < b) { a = b; return true; } return false; }
template<typename A, typename B> inline bool chmin(A &a, const B &b) { if (a > b) { a = b; return true; } return false; }
inline ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
inline ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }
inline ll POW(ll a, ll b)                    { ll r = 1; do { if (b & 1)  r *= a;        a *= a; }       while (b >>= 1); return r; }
inline ll MOP(ll a, ll b, const ll &m = MOD) { ll r = 1; do { if (b & 1) (r *= a) %= m; (a *= a) %= m; } while (b >>= 1); return r; }
struct abracadabra {
    abracadabra() {
        cin.tie(nullptr); ios::sync_with_stdio(false);
        cout << fixed << setprecision(20);
        cerr << fixed << setprecision(5);
    };
} ABRACADABRA;

#pragma endregion

template <typename Monoid, typename OperatorMonoid, typename F, typename G, typename H, typename P> struct LazySegmentTree {
    // typedef function< Monoid(Monoid, Monoid) > F;
    // typedef function< Monoid(Monoid, OperatorMonoid) > G;
    // typedef function< OperatorMonoid(OperatorMonoid, OperatorMonoid) > H;
    // typedef function< OperatorMonoid(OperatorMonoid, int) > P;
    int sz;
    F f; G g; H h; P p;
    Monoid d1; OperatorMonoid d0;
    vector< Monoid > dat;
    vector< OperatorMonoid > laz;
    LazySegmentTree(int n, F f, G g, H h, Monoid d1, OperatorMonoid d0,
        vector< Monoid > v = vector< Monoid >(), P p = [] (OperatorMonoid a, int b) { return a; })
        : f(f), g(g), h(h), d1(d1), d0(d0), p(p) {
        sz = 1; while (sz < n) sz <<= 1;
        dat.assign(2 * sz - 1, d1);
        laz.assign(2 * sz - 1, d0);
        if (n == (int)v.size()) build(n, v);
    }
    void build(int n, vector<Monoid> &v) {
        for (int i = 0; i < n; ++i) dat[i + sz - 1] = v[i];
        for (int i = sz - 2; i >= 0; --i) dat[i] = f(dat[2 * i + 1], dat[2 * i + 2]);
    }
    inline void eval(int len, int k) {
        if (laz[k] == d0) return;
        if (2 * k + 1 < 2 * sz - 1) {
            laz[2 * k + 1] = h(laz[2 * k + 1], laz[k]);
            laz[2 * k + 2] = h(laz[2 * k + 2], laz[k]);
        }
        dat[k] = g(dat[k], p(laz[k], len));
        laz[k] = d0;
    }
    Monoid update(int a, int b, OperatorMonoid x, int k, int l, int r) {
        eval(r - l, k);
        if (r <= a or b <= l) return dat[k];
        if (a <= l and r <= b) {
            laz[k] = h(laz[k], x);
            return g(dat[k], p(laz[k], r - l));
        }
        return dat[k] = f(update(a, b, x, 2 * k + 1, l, (l + r) / 2), update(a, b, x, 2 * k + 2, (l + r) / 2, r));
    }
    Monoid update(int a, int b, OperatorMonoid x) {
        return update(a, b, x, 0, 0, sz);
    }
    Monoid query(int a, int b, int k, int l, int r) {
        eval(r - l, k);
        if (r <= a or b <= l) return d1;
        if (a <= l and r <= b) return dat[k];
        Monoid vl = query(a, b, 2 * k + 1, l, (l + r) / 2);
        Monoid vr = query(a, b, 2 * k + 2, (l + r) / 2, r);
        return f(vl, vr);
    }
    Monoid query(int a, int b) {
        return query(a, b, 0, 0, sz);
    }
    Monoid operator[](const int &k) {
        return query(k, k + 1);
    }
};

/*
・遅延評価セグメント木
    > query, update O(logN)
[引数]
LazySegmentTree<Monoid, OperatorMonoid> seg(sz, f, g, h, d1, d0, v, p);
> sz : 要素数
>  f : 要素と要素をマージする関数
>  g : 要素に作用素を作用させる関数
>  h : 作用素と作用素をマージする関数
> d1 : 要素のモノイド
> d0 : 作用素のモノイド
>  v : 初期化用の配列
>  p : 区間に対する操作が要素数に比例して変化する場合 ( p(a, b) = g(a, a, ..., a) [aはb個] )
[備考]
以下の3つの条件を満たすときに使える
1. g(f(a, b), c) = f(g(a, c), g(b, c))
( 1'. g(f(a, b), p(c, d)) = f(g(a, p(c, d / 2)), g(b, p(c, d / 2))) )
2. g(g(a, b), c) = g(a, h(b, c))
3. g(a, d0) = a
[典型例]
> 区間加算 -> 区間和
LazySegmentTree<ll> seg(N, plus<ll>(), plus<ll>(), plus<ll>(), 0, 0, vector<ll>(N, 0), multiplies<ll>());
> 区間加算 -> 区間最小
LazySegmentTree<ll> seg(N, [](ll a, ll b){ return min(a, b); }, plus<ll>(), plus<ll>(), INFF, 0);
> 区間更新 -> 区間和
LazySegmentTree<ll> seg(N, plus<ll>(), [](ll a, ll b){ return b; }, [](ll a, ll b){ return b; }, 0, INFF, vector<ll>(N, 0), multiplies<ll>());
> 区間更新 -> 区間最小
LazySegmentTree<ll> seg(N, [](ll a,ll b){ return min(a,b); }, [](ll a, ll b){ return b; }, [](ll a, ll b){ return b; }, INFF, INFF);
[使用例]
seg.update(l, r, x);        // 半開区間[l, r)に作用素xを作用
seg.query(l, r);            // 半開区間[l, r)に対する演算の結果
seg[k];                     // k番目の要素を取得
*/

signed main() {

    SS(int, N);

    auto f = [](int x, int y) -> int { return (x + y) % MOD; };
    auto p = [](int x, int y) -> int { return ((ll)x * y) % MOD; };

    LazySegmentTree<int, int, decltype(f), decltype(f), decltype(f), decltype(p)> dp(
        2 * N + 1, f, f, f, 0, 0, vector<int>(N, 0), p
    );
    dp.update(0, 1, 1);

    auto pri = [&]() -> void {
        REP(i, 2 * N + 1) cerr << dp[i] << ' ';
        cerr << endl;
    };

    REP(i, N) {
        int cur = dp[i];
        dp.update(i + 1, i + 2, cur);                                       // 1 x 1
        dp.update(i + 3, i + 3 + N - 1, cur);                               // (1以外) x 1
        if (i < N - 1) dp.update(N, N + 1, p(p(cur, N - 1), N - 1));        // (1以外) x (1以外)
    }

    print(dp.query(N, 2 * N + 1));

}

Submission Info

Judge Result