結果

問題 No.194 フィボナッチ数列の理解(1)
ユーザー is_eri23is_eri23
提出日時 2015-05-12 12:07:26
言語 C++11
(gcc 13.3.0)
結果
AC  
実行時間 19 ms / 5,000 ms
コード長 3,987 bytes
コンパイル時間 1,188 ms
コンパイル使用メモリ 167,824 KB
実行使用メモリ 10,972 KB
最終ジャッジ日時 2024-07-06 00:03:33
合計ジャッジ時間 2,609 ms
ジャッジサーバーID
(参考情報)
judge5 / judge1
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 <bits/stdc++.h>
#define EPS 1e-9
#define INF 1070000000LL
#define MOD 1000000007LL
#define fir first
#define foreach(it,X) for(auto it=(X).begin();it!=(X).end();it++)
#define numa(x,a) for(auto x: a)
#define ite iterator
#define mp make_pair
#define rep(i,n) rep2(i,0,n)
#define rep2(i,m,n) for(int i=m;i<(n);i++)
#define pb push_back
#define pf push_front
#define sec second
#define sz(x) ((int)(x).size())
#define ALL( c ) (c).begin(), (c).end()
#define gcd(a,b) __gcd(a,b)
#define mem(x,n) memset(x,n,sizeof(x))
#define endl "\n"
using namespace std;
template <int POS, class TUPLE> void deploy(std::ostream &os, const TUPLE &tuple){}
template <int POS, class TUPLE, class H, class ...Ts> void deploy(std::ostream &os, const TUPLE &t){ os << (POS == 0 ? "" : ", ") << get<POS>(t);
    deploy<POS + 1, TUPLE, Ts...>(os, t); }
template <class T,class U> std::ostream& operator<<(std::ostream &os, std::pair<T,U> &p){ os << "(" << p.first <<", " << p.second <<")";return os; }
template <class T> std::ostream& operator<<(std::ostream &os, std::vector<T> &v){ int remain = v.size(); os << "{"; for(auto e: v) os << e <<
    (--remain == 0 ? "}" : ", "); return os; }
template <class T> std::ostream& operator<<(std::ostream &os, std::set<T> &v){ int remain = v.size(); os << "{"; for(auto e: v) os << e << (--remain
    == 0 ? "}" : ", "); return os; }
template <class T, class K> std::ostream& operator<<(std::ostream &os, std::map<T, K> &mp){ int remain = mp.size(); os << "{"; for(auto e: mp) os <<
    "(" << e.first << " -> " << e.second << ")" << (--remain == 0 ? "}" : ", "); return os; }
#define DEBUG1(var0) { std::cerr << (#var0) << "=" << (var0) << endl; }
#define DEBUG2(var0, var1) { std::cerr << (#var0) << "=" << (var0) << ", ";DEBUG1(var1); }
#define DEBUG3(var0, var1, var2) { std::cerr << (#var0) << "=" << (var0) << ", ";DEBUG2(var1,var2); }
#define DEBUG4(var0, var1, var2, var3) { std::cerr << (#var0) << "=" << (var0) << ", ";DEBUG3(var1,var2,var3); }
using ll = long long;
pair <ll,ll> solve(int N,int K){
//naive
vector <ll> nums(N+1);
rep(i,N){
cin >> nums[i+1];
}
vector <ll> memo(K+5,0);
pair <ll,ll> ans;
for (int i = 1; i <= K; i++) {
if (i <= N) {
memo[i] = nums[i];
}else{
if (i == N + 1) {
memo[i] = ans.sec;
}else{
memo[i] = memo[i-1];
memo[i] -= memo[i-N-1];
memo[i] = (memo[i] % MOD + MOD) % MOD;
memo[i] += memo[i-1];
memo[i] %= MOD;
}
}
ans.sec += memo[i];
ans.sec %= MOD;
}
ans.fir = memo[K];
return ans;
}
/**/
typedef vector <ll> vec;
typedef vector <vec> mat;
const ll M = MOD;
mat mul(mat &A,mat &B){// A*B
mat C(sz(A), vec(sz(B[0]),0));
rep(i,sz(A)){
rep(k,sz(B)){
rep(j,sz(B[0])){
C[i][j] = (C[i][j] + A[i][k] * B[k][j]) % M;
}
}
}
return C;
}
mat pow(mat A,ll n){
mat B(sz(A),vec(sz(A),0));
rep(i,sz(B)){
B[i][i] = 1;
}
while(n > 0){
if(n & 1){
B = mul(B,A);
}
A = mul(A,A);
n >>= 1;
}
return B;
}
pair <ll,ll> solve2(ll N,ll K) {
vector <ll> nums(N);
rep(i,N){
cin >> nums[i];
}
//DEBUG1(nums);
vector <ll> init(N+1);
init[0] = 0;
for (int i = 1; i <= N; i++) {
init[i] = nums[i-1];
}
mat A(N+1,vec(N+1,0));
A[0][0] = 1;
A[0][1] = 1;
for (int i = 1; i <= N-1; i++) {
A[i][i+1] = 1;
}
for (int i = 1; i<= N; i++) {
A[N][i] = 1;
}
auto X = pow(A,K-1);
ll S = 0;
//DEBUG1(X);
rep(i,N+1){
S += (X[0][i] * init[i]) % MOD;
//DEBUG2(X[0][i],init[i]);
S %= MOD;
}
ll Ak = 0;
rep(i,N+1){
Ak += (X[1][i] * init[i]) % MOD;
//DEBUG2(X[1][i],init[i]);
Ak %= MOD;
}
S += Ak;
S %= MOD;
return mp(Ak,S);
}
int main()
{
cin.tie(0);
ios_base::sync_with_stdio(0);
ll N,K;
cin >> N >> K;
pair <ll,ll> ans;
if (N > 30 || K <= 100){
ans = solve(N,K);
}else{
ans = solve2(N,K);
}
cout << ans.fir << " " << ans.sec << endl;
return 0;
}
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