結果
問題 | No.444 旨味の相乗効果 |
ユーザー | anta |
提出日時 | 2016-11-11 23:23:43 |
言語 | C++14 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 3 ms / 2,500 ms |
コード長 | 4,930 bytes |
コンパイル時間 | 2,831 ms |
コンパイル使用メモリ | 176,336 KB |
実行使用メモリ | 4,380 KB |
最終ジャッジ日時 | 2023-09-07 02:08:37 |
合計ジャッジ時間 | 3,419 ms |
ジャッジサーバーID (参考情報) |
judge12 / judge14 |
テストケース
テストケース表示入力 | 結果 | 実行時間 実行使用メモリ |
---|---|---|
testcase_00 | AC | 2 ms
4,380 KB |
testcase_01 | AC | 1 ms
4,380 KB |
testcase_02 | AC | 2 ms
4,380 KB |
testcase_03 | AC | 1 ms
4,380 KB |
testcase_04 | AC | 3 ms
4,376 KB |
testcase_05 | AC | 1 ms
4,380 KB |
testcase_06 | AC | 2 ms
4,380 KB |
testcase_07 | AC | 1 ms
4,380 KB |
testcase_08 | AC | 1 ms
4,376 KB |
testcase_09 | AC | 2 ms
4,380 KB |
testcase_10 | AC | 2 ms
4,376 KB |
testcase_11 | AC | 2 ms
4,380 KB |
testcase_12 | AC | 3 ms
4,376 KB |
testcase_13 | AC | 2 ms
4,380 KB |
testcase_14 | AC | 2 ms
4,380 KB |
testcase_15 | AC | 1 ms
4,380 KB |
testcase_16 | AC | 3 ms
4,380 KB |
testcase_17 | AC | 1 ms
4,380 KB |
testcase_18 | AC | 2 ms
4,380 KB |
testcase_19 | AC | 2 ms
4,380 KB |
testcase_20 | AC | 3 ms
4,376 KB |
testcase_21 | AC | 1 ms
4,376 KB |
testcase_22 | AC | 1 ms
4,380 KB |
testcase_23 | AC | 1 ms
4,376 KB |
testcase_24 | AC | 2 ms
4,376 KB |
testcase_25 | AC | 2 ms
4,380 KB |
testcase_26 | AC | 1 ms
4,380 KB |
testcase_27 | AC | 1 ms
4,380 KB |
ソースコード
#include "bits/stdc++.h" using namespace std; #define rep(i,n) for(int (i)=0;(i)<(int)(n);++(i)) #define rer(i,l,u) for(int (i)=(int)(l);(i)<=(int)(u);++(i)) #define reu(i,l,u) for(int (i)=(int)(l);(i)<(int)(u);++(i)) static const int INF = 0x3f3f3f3f; static const long long INFL = 0x3f3f3f3f3f3f3f3fLL; typedef vector<int> vi; typedef pair<int, int> pii; typedef vector<pair<int, int> > vpii; typedef long long ll; template<typename T, typename U> static void amin(T &x, U y) { if(y < x) x = y; } template<typename T, typename U> static void amax(T &x, U y) { if(x < y) x = y; } template<int MOD> struct ModInt { static const int Mod = MOD; unsigned x; ModInt() : x(0) {} ModInt(signed sig) { int sigt = sig % MOD; if(sigt < 0) sigt += MOD; x = sigt; } ModInt(signed long long sig) { int sigt = sig % MOD; if(sigt < 0) sigt += MOD; x = sigt; } int get() const { return (int)x; } ModInt &operator+=(ModInt that) { if((x += that.x) >= MOD) x -= MOD; return *this; } ModInt &operator-=(ModInt that) { if((x += MOD - that.x) >= MOD) x -= MOD; return *this; } ModInt &operator*=(ModInt that) { x = (unsigned long long)x * that.x % MOD; return *this; } ModInt &operator/=(ModInt that) { return *this *= that.inverse(); } ModInt operator+(ModInt that) const { return ModInt(*this) += that; } ModInt operator-(ModInt that) const { return ModInt(*this) -= that; } ModInt operator*(ModInt that) const { return ModInt(*this) *= that; } ModInt operator/(ModInt that) const { return ModInt(*this) /= that; } ModInt inverse() const { signed a = x, b = MOD, u = 1, v = 0; while(b) { signed t = a / b; a -= t * b; std::swap(a, b); u -= t * v; std::swap(u, v); } if(u < 0) u += Mod; ModInt res; res.x = (unsigned)u; return res; } bool operator==(ModInt that) const { return x == that.x; } bool operator!=(ModInt that) const { return x != that.x; } ModInt operator-() const { ModInt t; t.x = x == 0 ? 0 : Mod - x; return t; } }; template<int MOD> ModInt<MOD> operator^(ModInt<MOD> a, unsigned long long k) { ModInt<MOD> r = 1; while(k) { if(k & 1) r *= a; a *= a; k >>= 1; } return r; } typedef ModInt<1000000007> mint; #pragma region for precomputing int berlekampMassey(const vector<mint> &s, vector<mint> &C) { int N = (int)s.size(); C.assign(N + 1, mint()); vector<mint> B(N + 1, mint()); C[0] = B[0] = 1; int degB = 0; vector<mint> T; int L = 0, m = 1; mint b = 1; for(int n = 0; n < N; ++ n) { mint d = s[n]; for(int i = 1; i <= L; ++ i) d += C[i] * s[n - i]; if(d == mint()) { ++ m; } else { if(2 * L <= n) T.assign(C.begin(), C.begin() + (L + 1)); mint coeff = -d * b.inverse(); for(int i = 0; i <= degB; ++ i) C[m + i] += coeff * B[i]; if(2 * L <= n) { L = n + 1 - L; B.swap(T); degB = (int)B.size() - 1; b = d; m = 1; } else { ++ m; } } } C.resize(L + 1); return L; } void computeMinimumPolynomialForLinearlyRecurrentSequence(const vector<mint> &a, vector<mint> &phi) { int n2 = (int)a.size(), n = n2 / 2; assert(n2 % 2 == 0); int L = berlekampMassey(a, phi); reverse(phi.begin(), phi.begin() + (L + 1)); } #pragma endregion mint linearlyRecurrentSequenceValue(long long K, const vector<mint> &initValues, const vector<mint> &annPoly) { assert(K >= 0); if(K < (int)initValues.size()) return initValues[(int)K]; int d = (int)annPoly.size() - 1; assert(d >= 0); assert(annPoly[d].get() == 1); assert(d <= (int)initValues.size()); if(d == 0) return mint(); vector<mint> coeffs(d), square; coeffs[0] = 1; int l = 0; while((K >> l) > 1) ++ l; for(; l >= 0; -- l) { square.assign(d * 2 - 1, mint()); for(int i = 0; i < d; ++ i) for(int j = 0; j < d; ++ j) square[i + j] += coeffs[i] * coeffs[j]; for(int i = d * 2 - 2; i >= d; -- i) { mint c = square[i]; if(c.x == 0) continue; for(int j = 0; j < d; ++ j) square[i - d + j] -= c * annPoly[j]; } for(int i = 0; i < d; ++ i) coeffs[i] = square[i]; if(K >> l & 1) { mint lc = coeffs[d - 1]; for(int i = d - 1; i >= 1; -- i) coeffs[i] = coeffs[i - 1] - lc * annPoly[i]; coeffs[0] = mint() - lc * annPoly[0]; } } mint res; for(int i = 0; i < d; ++ i) res += coeffs[i] * initValues[i]; return res; } mint linearlyRecurrentSequenceValue(long long K, const pair<vector<mint>, vector<mint> > &seqPair) { return linearlyRecurrentSequenceValue(K, seqPair.first, seqPair.second); } int main() { int n; long long c; while(~scanf("%d%lld", &n, &c)) { vector<int> as(n); for(int i = 0; i < n; ++ i) scanf("%d", &as[i]); vector<mint> dp(n * 2); dp[0] = 1; rep(i, n) { mint a = as[i]; rep(j, (int)dp.size() - 1) dp[j + 1] += dp[j] * a; } vector<mint> phi; computeMinimumPolynomialForLinearlyRecurrentSequence(dp, phi); mint ans = linearlyRecurrentSequenceValue(c, dp, phi); rep(i, n) ans -= mint(as[i]) ^ c; printf("%d\n", ans.get()); } return 0; }