結果
| 問題 | No.1977 Extracting at Constant Intervals |
| ユーザー |
 tokusakurai
|
| 提出日時 | 2022-06-10 23:16:27 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 208 ms / 2,000 ms |
| コード長 | 9,578 bytes |
| コンパイル時間 | 2,915 ms |
| コンパイル使用メモリ | 223,096 KB |
| 最終ジャッジ日時 | 2025-01-29 20:18:04 |
|
ジャッジサーバーID （参考情報） |
judge3 / judge2 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 31 |
ソースコード
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (ll i = 0; i < n; i++)
#define rep2(i, x, n) for (ll i = x; i <= n; i++)
#define rep3(i, x, n) for (ll i = x; i >= n; i--)
#define each(e, v) for (auto &e : v)
#define pb push_back
#define eb emplace_back
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define sz(x) (int)x.size()
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
template <typename T>
bool chmax(T &x, const T &y) {
return (x < y) ? (x = y, true) : false;
}
template <typename T>
bool chmin(T &x, const T &y) {
return (x > y) ? (x = y, true) : false;
}
template <typename T>
int flg(T x, int i) {
return (x >> i) & 1;
}
template <typename T>
void print(const vector<T> &v, T x = 0) {
int n = v.size();
for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' ');
if (v.empty()) cout << '\n';
}
template <typename T>
void printn(const vector<T> &v, T x = 0) {
int n = v.size();
for (int i = 0; i < n; i++) cout << v[i] + x << '\n';
}
template <typename T>
int lb(const vector<T> &v, T x) {
return lower_bound(begin(v), end(v), x) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, T x) {
return upper_bound(begin(v), end(v), x) - begin(v);
}
template <typename T>
void rearrange(vector<T> &v) {
sort(begin(v), end(v));
v.erase(unique(begin(v), end(v)), end(v));
}
template <typename T>
vector<int> id_sort(const vector<T> &v, bool greater = false) {
int n = v.size();
vector<int> ret(n);
iota(begin(ret), end(ret), 0);
sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; });
return ret;
}
template <typename S, typename T>
pair<S, T> operator+(const pair<S, T> &p, const pair<S, T> &q) {
return make_pair(p.first + q.first, p.second + q.second);
}
template <typename S, typename T>
pair<S, T> operator-(const pair<S, T> &p, const pair<S, T> &q) {
return make_pair(p.first - q.first, p.second - q.second);
}
template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &p) {
S a;
T b;
is >> a >> b;
p = make_pair(a, b);
return is;
}
template <typename S, typename T>
ostream &operator<<(ostream &os, const pair<S, T> &p) {
return os << p.first << ' ' << p.second;
}
struct io_setup {
io_setup() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout << fixed << setprecision(15);
}
} io_setup;
const int inf = (1 << 30) - 1;
const ll INF = (1LL << 60) - 1;
const int MOD = 1000000007;
// const int MOD = 998244353;
template <int mod>
struct Mod_Int {
int x;
Mod_Int() : x(0) {}
Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
static int get_mod() { return mod; }
Mod_Int &operator+=(const Mod_Int &p) {
if ((x += p.x) >= mod) x -= mod;
return *this;
}
Mod_Int &operator-=(const Mod_Int &p) {
if ((x += mod - p.x) >= mod) x -= mod;
return *this;
}
Mod_Int &operator*=(const Mod_Int &p) {
x = (int)(1LL * x * p.x % mod);
return *this;
}
Mod_Int &operator/=(const Mod_Int &p) {
*this *= p.inverse();
return *this;
}
Mod_Int &operator++() { return *this += Mod_Int(1); }
Mod_Int operator++(int) {
Mod_Int tmp = *this;
++*this;
return tmp;
}
Mod_Int &operator--() { return *this -= Mod_Int(1); }
Mod_Int operator--(int) {
Mod_Int tmp = *this;
--*this;
return tmp;
}
Mod_Int operator-() const { return Mod_Int(-x); }
Mod_Int operator+(const Mod_Int &p) const { return Mod_Int(*this) += p; }
Mod_Int operator-(const Mod_Int &p) const { return Mod_Int(*this) -= p; }
Mod_Int operator*(const Mod_Int &p) const { return Mod_Int(*this) *= p; }
Mod_Int operator/(const Mod_Int &p) const { return Mod_Int(*this) /= p; }
bool operator==(const Mod_Int &p) const { return x == p.x; }
bool operator!=(const Mod_Int &p) const { return x != p.x; }
Mod_Int inverse() const {
assert(*this != Mod_Int(0));
return pow(mod - 2);
}
Mod_Int pow(long long k) const {
Mod_Int now = *this, ret = 1;
for (; k > 0; k >>= 1, now *= now) {
if (k & 1) ret *= now;
}
return ret;
}
friend ostream &operator<<(ostream &os, const Mod_Int &p) { return os << p.x; }
friend istream &operator>>(istream &is, Mod_Int &p) {
long long a;
is >> a;
p = Mod_Int<mod>(a);
return is;
}
};
using mint = Mod_Int<MOD>;
template <typename T>
struct Number_Theoretic_Transform {
static int max_base;
static T root;
static vector<T> r, ir;
Number_Theoretic_Transform() {}
static void init() {
if (!r.empty()) return;
int mod = T::get_mod();
int tmp = mod - 1;
root = 2;
while (root.pow(tmp >> 1) == 1) root++;
max_base = 0;
while (tmp % 2 == 0) tmp >>= 1, max_base++;
r.resize(max_base), ir.resize(max_base);
for (int i = 0; i < max_base; i++) {
r[i] = -root.pow((mod - 1) >> (i + 2)); // r[i] := 1 の 2^(i+2) 乗根
ir[i] = r[i].inverse(); // ir[i] := 1/r[i]
}
}
static void ntt(vector<T> &a) {
init();
int n = a.size();
assert((n & (n - 1)) == 0);
assert(n <= (1 << max_base));
for (int k = n; k >>= 1;) {
T w = 1;
for (int s = 0, t = 0; s < n; s += 2 * k) {
for (int i = s, j = s + k; i < s + k; i++, j++) {
T x = a[i], y = w * a[j];
a[i] = x + y, a[j] = x - y;
}
w *= r[__builtin_ctz(++t)];
}
}
}
static void intt(vector<T> &a) {
init();
int n = a.size();
assert((n & (n - 1)) == 0);
assert(n <= (1 << max_base));
for (int k = 1; k < n; k <<= 1) {
T w = 1;
for (int s = 0, t = 0; s < n; s += 2 * k) {
for (int i = s, j = s + k; i < s + k; i++, j++) {
T x = a[i], y = a[j];
a[i] = x + y, a[j] = w * (x - y);
}
w *= ir[__builtin_ctz(++t)];
}
}
T inv = T(n).inverse();
for (auto &e : a) e *= inv;
}
static vector<T> convolve(vector<T> a, vector<T> b) {
if (a.empty() || b.empty()) return {};
int k = (int)a.size() + (int)b.size() - 1, n = 1;
while (n < k) n <<= 1;
a.resize(n), b.resize(n);
ntt(a), ntt(b);
for (int i = 0; i < n; i++) a[i] *= b[i];
intt(a), a.resize(k);
return a;
}
};
template <typename T>
int Number_Theoretic_Transform<T>::max_base = 0;
template <typename T>
T Number_Theoretic_Transform<T>::root = T();
template <typename T>
vector<T> Number_Theoretic_Transform<T>::r = vector<T>();
template <typename T>
vector<T> Number_Theoretic_Transform<T>::ir = vector<T>();
using NTT = Number_Theoretic_Transform<mint>;
const int m1 = 880803841; // 105*2^23 + 1
const int m2 = 897581057; // 107*2^23 + 1
const int m3 = 998244353; // 119*2^23 + 1
struct Fast_Fourier_Transform_Integer {
using mint_1 = Mod_Int<m1>;
using mint_2 = Mod_Int<m2>;
using mint_3 = Mod_Int<m3>;
using NTT_1 = Number_Theoretic_Transform<mint_1>;
using NTT_2 = Number_Theoretic_Transform<mint_2>;
using NTT_3 = Number_Theoretic_Transform<mint_3>;
Fast_Fourier_Transform_Integer() {}
static vector<long long> convolve(const vector<long long> &a, const vector<long long> &b) {
if (a.empty() || b.empty()) return {};
int n = a.size(), m = b.size();
vector<mint_1> a1(n), b1(m);
vector<mint_2> a2(n), b2(m);
vector<mint_3> a3(n), b3(m);
for (int i = 0; i < n; i++) a1[i] = a[i], a2[i] = a[i], a3[i] = a[i];
for (int i = 0; i < m; i++) b1[i] = b[i], b2[i] = b[i], b3[i] = b[i];
vector<mint_1> c1 = NTT_1::convolve(a1, b1);
vector<mint_2> c2 = NTT_2::convolve(a2, b2);
vector<mint_3> c3 = NTT_3::convolve(a3, b3);
mint_2 m1_inv_m2 = mint_2(m1).inverse();
mint_3 m1m2_inv_m3 = (mint_3(m1) * m2).inverse();
vector<long long> c(n + m - 1);
for (int i = 0; i < n + m - 1; i++) {
long long t1 = (m1_inv_m2 * (c2[i].x - c1[i].x)).x;
long long t = (m1m2_inv_m3 * (c3[i].x - t1 * m1 - c1[i].x)).x;
if (t > m3 - t) t -= m3;
c[i] = t * m1 * m2 + t1 * m1 + c1[i].x;
}
return c;
}
};
using FFT = Fast_Fourier_Transform_Integer;
int main() {
ll N, M, L;
cin >> N >> M >> L;
vector<ll> a(N, 0);
rep(i, N) cin >> a[i];
vector<ll> cnt(N, 0);
ll K = (N * M + L - 1) / L;
ll P = L * (K - 1);
// cout << K << ' ' << P << '\n';
rep(i, N) {
ll x = L * i % N;
if (K > i) cnt[x] += (K - i + N - 1) / N;
}
vector<ll> b(2 * N), c(N);
rep(i, 2 * N) b[i] = a[i % N];
rep(i, N) c[i] = cnt[N - 1 - i];
auto f = FFT::convolve(b, c);
vector<ll> s(N, 0);
rep(i, N) s[i] = f[N - 1 + i];
ll ans = -INF;
rep(i, N) {
if (P + i < N * M) chmax(ans, s[i]);
ll X = (L - i + N - 1) / N;
ll Y = i + N * (X - 1);
if (P + Y >= N * M) chmax(ans, s[i] - a[(P + i) % N]);
}
cout << ans << '\n';
}