結果
問題 | No.194 フィボナッチ数列の理解(1) |
ユーザー | is_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 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 37 |
ソースコード
#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){//naivevector <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;}/*行列*/typedef vector <ll> vec;typedef vector <vec> mat;const ll M = MOD;mat mul(mat &A,mat &B){//行列掛け算 A*Bmat 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;}