結果

問題 No.194 フィボナッチ数列の理解(1)
ユーザー heno239heno239
提出日時 2020-08-09 17:00:48
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 21 ms / 5,000 ms
コード長 3,967 bytes
コンパイル時間 1,462 ms
コンパイル使用メモリ 123,644 KB
実行使用メモリ 26,916 KB
最終ジャッジ日時 2024-10-05 00:49:37
合計ジャッジ時間 2,887 ms
ジャッジサーバーID
(参考情報)
judge2 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 37
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 #
プレゼンテーションモードにする

#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
using namespace std;
//#define int long long
typedef long long ll;
typedef unsigned long long ul;
typedef unsigned int ui;
constexpr ll mod = 1000000007;
const ll INF = mod * mod;
typedef pair<int, int>P;
#define stop char nyaa;cin>>nyaa;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
#define all(v) (v).begin(),(v).end()
typedef pair<ll, ll> LP;
typedef double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-12;
const ld pi = acos(-1.0);
ll mod_pow(ll x, ll n, ll m) {
ll res = 1;
while (n) {
if (n & 1)res = res * x % m;
x = x * x % m; n >>= 1;
}
return res;
}
struct modint {
ll n;
modint() :n(0) { ; }
modint(ll m) :n(m) {
if (n >= mod)n %= mod;
else if (n < 0)n = (n % mod + mod) % mod;
}
operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; }
modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; }
modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; }
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, ll n) {
if (n == 0)return modint(1);
modint res = (a * a) ^ (n / 2);
if (n % 2)res = res * a;
return res;
}
ll inv(ll a, ll p) {
return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }
const int max_n = 1 << 17;
modint fact[max_n], factinv[max_n];
void init_f() {
fact[0] = modint(1);
for (int i = 0; i < max_n - 1; i++) {
fact[i + 1] = fact[i] * modint(i + 1);
}
factinv[max_n - 1] = modint(1) / fact[max_n - 1];
for (int i = max_n - 2; i >= 0; i--) {
factinv[i] = factinv[i + 1] * modint(i + 1);
}
}
modint comb(int a, int b) {
if (a < 0 || b < 0 || a < b)return 0;
return fact[a] * factinv[b] * factinv[a - b];
}
typedef vector<vector<modint>> mat;
typedef vector<modint> vec;
mat mtmul(mat& A, mat& B) {
mat C(A.size(), vec(B[0].size()));
rep(i, (int)A.size()) {
rep(k, (int)B.size()) {
rep(j, (int)B[0].size()) {
C[i][j] += A[i][k] * B[k][j];
}
}
}
return C;
}
mat mtpow(mat A, ll n) {
mat B(A.size(), vec(A.size()));
rep(i, (int)A.size()) {
B[i][i] = 1;
}
while (n > 0) {
if (n & (ll)1)B = mtmul(B, A);
A = mtmul(A, A);
n >>= 1;
}
return B;
}
void solve() {
int n;ll k; cin >> n >> k;
vector<modint> a(n);
rep(i, n) {
ll in; cin >> in; a[i] = in;
}
if (n <= 30) {
mat A(n+1, vector<modint>(n + 1, 0));
rep(j, n) {
A[0][j] = 1;
}
rep(j, n + 1)A[n][j] = 1;
rep1(j, n - 1) {
A[j][j - 1] = 1;
}
mat B = mtpow(A, k - n);
reverse(all(a));
modint ans1 = 0, ans2 = 0;
modint sum = 0; rep(i, n)sum += a[i];
a.push_back(sum);
rep(i, n+1) {
ans1 += B[0][i] * a[i];
ans2 += B[n][i] * a[i];
}
cout << ans1 << " " << ans2 << "\n";
}
else {
vector<modint> ra(n + 1);
rep(i, n) {
ra[i + 1] = ra[i] + a[i];
}
while (a.size() < k) {
modint sum = ra[a.size()] - ra[a.size() - n];
ra.push_back(sum + ra.back());
a.push_back(sum);
}
cout << a.back() << " " << ra.back() << "\n";
}
}
signed main() {
ios::sync_with_stdio(false);
cin.tie(0);
//cout << fixed << setprecision(10);
//init_f();
//expr();
//int t; cin >> t; rep(i, t)
solve();
return 0;
}
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