P1306 斐波那契公约数

https://www.luogu.com.cn/record/80117613

LibreOJ/2599/2599.cpp

@@ -0,0 +1,51 @@
+#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;
+}

Luogu/P1306/P1306.cpp

@@ -0,0 +1,79 @@
+#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;
+}

Luogu/P1313/P1313.cpp

@@ -1,4 +1,6 @@
 #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;

Luogu/P2822/P2822.cpp

@@ -0,0 +1,41 @@
+#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;
+}