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24 changed files with 283 additions and 15 deletions

51
LibreOJ/2599/2599.cpp Normal file
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#include <iostream>
using std::cin;
using std::cout;
const char endl = '\n';
const int N = 1005;
const int mod = 1e4 + 7;
int a, b, k, n, m;
int fac[N], inv[N];
int binpow(int a, int b) {
int res = 1;
a %= mod;
while (b) {
if (b & 1) res = static_cast<long long>(res) * a % mod;
a = static_cast<long long>(a) * a % mod;
b >>= 1;
}
return res;
}
inline int C(int n, int m) {
return static_cast<long long>(fac[n]) * inv[m] % mod * inv[n - m] % mod;
}
int main() {
std::ios::sync_with_stdio(false);
cin.tie(nullptr);
fac[0] = 1;
for (int i = 1; i <= 1000; i++) {
fac[i] = static_cast<long long>(fac[i - 1]) * i % mod;
}
inv[0] = inv[1] = 1;
for (int i = 2; i <= 1000; i++) {
inv[i] = static_cast<long long>(mod - (mod / i)) * inv[mod % i] % mod;
}
for (int i = 2; i <= 1000; i++) {
inv[i] = static_cast<long long>(inv[i - 1]) * inv[i] % mod;
}
cin >> a >> b >> k >> n >> m;
cout << static_cast<long long>(C(k, n)) * binpow(a, n) % mod * binpow(b, m) % mod << endl;
return 0;
}

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Luogu/P1306/P1306.cpp Normal file
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#include <iostream>
#include <algorithm>
#include <cstring>
using std::cin;
using std::cout;
const char endl = '\n';
const int N = 10;
const int mod = 1e8;
class Matrix {
private:
long long data[N][N];
public:
Matrix() {
memset(data, 0x00, sizeof(data));
}
long long* operator[](int i) {
return data[i];
}
Matrix operator*(Matrix b) const {
Matrix c;
int n = 2;
for (int i = 1; i <= n; i++) {
for (int j = 1; j <= n; j++) {
for (int k = 1; k <= n; k++) {
c[i][j] = (c[i][j] + data[i][k] * b[k][j] % mod) % mod;
}
}
}
return c;
}
} base, ans;
Matrix binpow(Matrix a, int k) {
Matrix res;
res[1][1] = 1;
res[1][2] = 1;
while (k) {
if (k & 1) res = res * a;
a = a * a;
k >>= 1;
}
return res;
}
long long fib(int n) {
if (n <= 2) {
return !!n;
}
Matrix tmp;
tmp[1][1] = 1, tmp[1][2] = 1;
tmp[2][1] = 1, tmp[2][2] = 0;
return binpow(tmp, n - 2)[1][1];
}
int n, m;
int main() {
std::ios::sync_with_stdio(false);
cin >> n >> m;
cout << fib(std::__gcd(n, m)) % mod << endl;
return 0;
}

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#include <iostream>
#include <array>
#include <type_traits>
using std::cin;
using std::cout;
@ -7,8 +9,57 @@ const char endl = '\n';
const int N = 1005;
const int mod = 1e4 + 7;
template <int x>
using number = std::integral_constant<int, x>;
template <int n>
struct factorial : number<static_cast<long long>(n) * factorial<n - 1>::value % mod> {};
template <>
struct factorial<0> : number<1> {};
template <int... S>
constexpr std::array<int, sizeof...(S)> get_factorial_table_impl(std::integer_sequence<int, S...>) {
return {factorial<S>::value...};
}
template <int S>
constexpr auto get_factorial_table() {
return get_factorial_table_impl(std::make_integer_sequence<int, S>{});
}
template <int n>
struct inverse : number<static_cast<long long>(mod - (mod / n)) * inverse<mod % n>::value % mod> {};
template <>
struct inverse<1> : number<1> {};
template <>
struct inverse<0> : number<1> {};
template <int n>
struct factorial_inverse : number<static_cast<long long>(factorial_inverse<n - 1>::value) * inverse<n>::value % mod> {};
template <>
struct factorial_inverse<1> : number<1> {};
template <>
struct factorial_inverse<0> : number<1> {};
template <int... S>
constexpr std::array<int, sizeof...(S)> get_factorial_inverse_table_impl(std::integer_sequence<int, S...>) {
return {factorial_inverse<S>::value...};
}
template <int S>
constexpr auto get_factorial_inverse_table() {
return get_factorial_inverse_table_impl(std::make_integer_sequence<int, S>{});
}
int a, b, k, n, m;
int fac[N], inv[N];
constexpr auto fac = get_factorial_table<N>(),
inv = get_factorial_inverse_table<N>();
int binpow(int a, int b) {
int res = 1;
@ -29,20 +80,6 @@ int main() {
std::ios::sync_with_stdio(false);
cin.tie(nullptr);
fac[0] = 1;
for (int i = 1; i <= 1000; i++) {
fac[i] = 1ll * fac[i - 1] * i % mod;
}
inv[0] = inv[1] = 1;
for (int i = 2; i <= 1000; i++) {
inv[i] = static_cast<long long>(mod - (mod / i)) * inv[mod % i] % mod;
}
for (int i = 2; i <= 1000; i++) {
inv[i] = static_cast<long long>(inv[i - 1]) * inv[i] % mod;
}
cin >> a >> b >> k >> n >> m;
cout << static_cast<long long>(C(k, n)) * binpow(a, n) % mod * binpow(b, m) % mod << endl;

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Luogu/P2822/P2822.cpp Normal file
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#include <iostream>
using std::cin;
using std::cout;
const char endl = '\n';
const int N = 2005;
int t, k, n, m, c[N][N], f[N][N];
int main() {
cin >> t >> k;
c[1][1] = 1;
for (int i = 1; i <= 2000; i++) {
c[i][0] = c[i][i] = 1;
}
for (int i = 2; i <= 2000; i++) {
for (int j = 1; j < i; j++) {
c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % k;
}
}
for (int i = 1; i <= 2000; i++) {
for (int j = 1; j <= i; j++) {
f[i][j] = f[i][j - 1] + f[i - 1][j] - f[i - 1][j - 1];
if (!c[i][j]) f[i][j]++;
}
f[i][i + 1] = f[i][i];
}
while (t--) {
cin >> n >> m;
cout << f[n][std::min(n, m)] << endl;
}
return 0;
}