結果

問題 No.1086 桁和の桁和2
ユーザー kibunakibuna
提出日時 2020-06-19 23:27:19
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 689 ms / 3,000 ms
コード長 4,575 bytes
コンパイル時間 1,962 ms
コンパイル使用メモリ 174,628 KB
実行使用メモリ 7,168 KB
最終ジャッジ日時 2024-07-22 17:53:54
合計ジャッジ時間 13,073 ms
ジャッジサーバーID
(参考情報)
judge1 / judge5
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 * 5
other AC * 31
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>
using namespace std;
using lint = long long;
const lint inf = 1LL << 60;
const lint mod = 1000000007;
template <int mod>
struct modint {
lint v;
modint() : v(0) {}
modint(signed v) : v(v) {}
modint(lint t) {
v = t % mod;
if (v < 0)
v += mod;
}
modint pow(lint k) {
modint res(1), tmp(v);
while (k) {
if (k & 1)
res *= tmp;
tmp *= tmp;
k >>= 1;
}
return res;
}
static modint add_identity() { return modint(0); }
static modint mul_identity() { return modint(1); }
modint inv() { return pow(mod - 2); }
modint &operator+=(modint a) {
v += a.v;
if (v >= mod)
v -= mod;
return *this;
}
modint &operator-=(modint a) {
v += mod - a.v;
if (v >= mod)
v -= mod;
return *this;
}
modint &operator*=(modint a) {
v = v * a.v % mod;
return *this;
}
modint &operator/=(modint a) { return (*this) *= a.inv(); }
modint operator+(modint a) const { return modint(v) += a; };
modint operator-(modint a) const { return modint(v) -= a; };
modint operator*(modint a) const { return modint(v) *= a; };
modint operator/(modint a) const { return modint(v) /= a; };
modint operator-() const { return v ? modint(mod - v) : modint(v); }
bool operator==(const modint a) const { return v == a.v; }
bool operator!=(const modint a) const { return v != a.v; }
bool operator<(const modint a) const { return v < a.v; }
};
using mint = modint<mod>;
ostream &operator<<(ostream &os, mint m) { return os << m.v; }
template <size_t N, typename R>
struct SquareMatrix {
using arr = array<R, N>;
using mat = array<arr, N>;
mat dat;
SquareMatrix() {
for (size_t i = 0; i < N; i++)
for (size_t j = 0; j < N; j++)
dat[i][j] = R::add_identity();
}
SquareMatrix &operator=(const SquareMatrix &a) {
dat = a.dat;
return (*this);
}
bool operator==(const SquareMatrix &a) const { return dat == a.dat; }
size_t size() const { return N; };
arr &operator[](size_t k) { return dat[k]; };
const arr &operator[](size_t k) const { return dat[k]; };
static SquareMatrix add_identity() { return SquareMatrix(); }
static SquareMatrix mul_identity() {
SquareMatrix res;
for (size_t i = 0; i < N; i++)
res[i][i] = R::mul_identity();
return res;
}
SquareMatrix operator*(const SquareMatrix &B) const {
SquareMatrix res;
for (size_t i = 0; i < N; i++)
for (size_t j = 0; j < N; j++)
for (size_t k = 0; k < N; k++)
res[i][j] = res[i][j] + (dat[i][k] * B[k][j]);
return res;
}
SquareMatrix operator+(const SquareMatrix &B) const {
SquareMatrix res;
for (size_t i = 0; i < N; i++)
for (size_t j = 0; j < N; j++)
res[i][j] = dat[i][j] + B[i][j];
return res;
}
SquareMatrix pow(long long n) const {
SquareMatrix a = *this, res = mul_identity();
while (n) {
if (n & 1)
res = res * a;
a = a * a;
n >>= 1;
}
return res;
}
};
int main() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
lint n;
cin >> n;
vector<lint> l(n + 1), r(n + 1);
for (int i = 1; i <= n; ++i) {
cin >> l[i];
}
for (int i = 1; i <= n; ++i) {
cin >> r[i];
}
vector<lint> c(n + 1, 0);
for (int i = 1; i <= n; ++i) {
cin >> c[i];
}
auto d = c;
for (int i = n; i > 0; --i) {
d[i] = (d[i] - d[i - 1] + 9);
if (i != 1)
d[i] %= 9;
}
vector<mint> dp(n + 1, 0);
dp[0] = 1;
SquareMatrix<2, mint> mat;
mat[0][0] = 1;
mat[0][1] = 1;
mat[1][0] = 0;
mat[1][1] = 10;
bool zero = true;
for (int i = 1; i <= n; ++i) {
if (c[i] == 0) {
if (!zero) {
cout << 0 << "\n";
return 0;
} else {
dp[i] = 1;
continue;
}
}
zero = false;
int add = d[i];
auto ml = mat.pow(l[i]);
auto mr = mat.pow(r[i]);
mint ls = ml[0][1];
mint rs = mr[0][1];
if (add == 0)
rs += 1;
dp[i] = dp[i - 1] * (rs - ls);
}
cout << dp[n] << "\n";
return 0;
}
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