Submission #846450


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#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));
}

template<int MOD> int mintToSigned(ModInt<MOD> a) {
	int x = a.get();
	if(x <= MOD / 2)
		return x;
	else
		return x - MOD;
}

int outputPrecomputedMinimalPolynomial(vector<mint> seq, ostream &os) {
	if(seq.size() % 2 == 1) seq.pop_back();
	vector<mint> phi;
	computeMinimumPolynomialForLinearlyRecurrentSequence(seq, phi);
	if(phi.size() >= seq.size() / 2 - 2) {
		cerr << "warning: maybe it is not enough terms" << endl;
	}
	cerr << "/*" << phi.size() - 1 << "*/";
	os << "{{ ";
	rep(i, phi.size() - 1) {
		if(i != 0) os << ", ";
		os << seq[i].get();
	}
	os << " }, { ";
	rep(i, phi.size()) {
		if(i != 0) os << ", ";
		os << mintToSigned(phi[i]);
	}
	os << " }}";
	return (int)phi.size() - 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 H; int W; long long K;
	while(~scanf("%d%d%lld", &H, &W, &K)) {
		vector<string> s(H);
		rep(i, H) {
			char buf[1001];
			scanf("%s", buf);
			s[i] = buf;
		}
		int vert = 0, hori = 0;
		rep(j, W)
			vert += s[0][j] == '#' && s[H - 1][j] == '#';
		rep(i, H)
			hori += s[i][0] == '#' && s[i][W - 1] == '#';
		int num = 0;
		rep(i, H) rep(j, W)
			num += s[i][j] == '#';
		mint ans;
		if(K == 0 || K == 1) {
			ans = 1;
		} else if(!vert && !hori) {
			ans = mint(num) ^ (K - 1);
		} else if(vert && hori) {
			ans = 1;
		} else {
			int minus = 0;
			if(hori) {
				rep(i, H) rep(j, W - 1)
					minus += s[i][j] == '#' && s[i][j + 1] == '#';
			} else {
				rep(i, H - 1) rep(j, W)
					minus += s[i][j] == '#' && s[i + 1][j] == '#';
			}
			ans = 1;
			mint t = minus;
			vector<mint> seq;
			rep(k, 10) {
				seq.push_back(ans);
				ans *= num;
				ans -= t;
				t *= hori + vert;
			}
			vector<mint> phi;
			computeMinimumPolynomialForLinearlyRecurrentSequence(seq, phi);
			ans = linearlyRecurrentSequenceValue(K - 1, seq, phi);
		}
		printf("%d\n", ans.get());
	}
	return 0;
}

Submission Info

Submission Time
Task F - Fraction of Fractal
User anta
Language C++14 (GCC 5.4.1)
Score 1700
Code Size 6456 Byte
Status AC
Exec Time 17 ms
Memory 1280 KB

Compile Error

./Main.cpp: In function ‘int main()’:
./Main.cpp:185:20: warning: ignoring return value of ‘int scanf(const char*, ...)’, declared with attribute warn_unused_result [-Wunused-result]
    scanf("%s", buf);
                    ^

Judge Result

Set Name Sample All
Score / Max Score 0 / 0 1700 / 1700
Status
AC × 3
AC × 47
Set Name Test Cases
Sample s1.txt, s2.txt, s3.txt
All 01.txt, 02.txt, 03.txt, 04.txt, 05.txt, 06.txt, 07.txt, 08.txt, 09.txt, 10.txt, 11.txt, 12.txt, 13.txt, 14.txt, 15.txt, 16.txt, 17.txt, 18.txt, 19.txt, 20.txt, 21.txt, 22.txt, 23.txt, 24.txt, 25.txt, 26.txt, 27.txt, 28.txt, 29.txt, 30.txt, 31.txt, 32.txt, 33.txt, 34.txt, 35.txt, 36.txt, 37.txt, 38.txt, 39.txt, 40.txt, 41.txt, 42.txt, 43.txt, 44.txt, s1.txt, s2.txt, s3.txt
Case Name Status Exec Time Memory
01.txt AC 13 ms 1280 KB
02.txt AC 16 ms 1280 KB
03.txt AC 16 ms 1280 KB
04.txt AC 16 ms 1280 KB
05.txt AC 16 ms 1280 KB
06.txt AC 13 ms 1280 KB
07.txt AC 13 ms 1280 KB
08.txt AC 13 ms 1280 KB
09.txt AC 16 ms 1280 KB
10.txt AC 16 ms 1280 KB
11.txt AC 13 ms 1280 KB
12.txt AC 15 ms 1280 KB
13.txt AC 15 ms 1280 KB
14.txt AC 13 ms 1280 KB
15.txt AC 13 ms 1280 KB
16.txt AC 13 ms 1280 KB
17.txt AC 17 ms 1280 KB
18.txt AC 16 ms 1280 KB
19.txt AC 16 ms 1280 KB
20.txt AC 16 ms 1280 KB
21.txt AC 16 ms 1280 KB
22.txt AC 13 ms 1280 KB
23.txt AC 15 ms 1280 KB
24.txt AC 14 ms 1280 KB
25.txt AC 15 ms 1280 KB
26.txt AC 15 ms 1280 KB
27.txt AC 15 ms 1280 KB
28.txt AC 15 ms 1280 KB
29.txt AC 4 ms 256 KB
30.txt AC 4 ms 256 KB
31.txt AC 4 ms 256 KB
32.txt AC 4 ms 256 KB
33.txt AC 4 ms 256 KB
34.txt AC 4 ms 256 KB
35.txt AC 4 ms 256 KB
36.txt AC 4 ms 256 KB
37.txt AC 4 ms 256 KB
38.txt AC 4 ms 256 KB
39.txt AC 4 ms 256 KB
40.txt AC 4 ms 256 KB
41.txt AC 4 ms 256 KB
42.txt AC 4 ms 256 KB
43.txt AC 4 ms 256 KB
44.txt AC 4 ms 256 KB
s1.txt AC 4 ms 256 KB
s2.txt AC 4 ms 256 KB
s3.txt AC 4 ms 256 KB