P3807 【模板】卢卡斯定理/Lucas 定理

https://www.luogu.com.cn/record/79996740

Luogu/P1313/P1313.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 = 1ll * res * a % mod;
+        a = 1ll * a * a % mod;
+        b >>= 1;
+    }
+    return res;
+}
+
+inline int C(int n, int m) {
+    return 1ll * 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] = 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;
+
+    return 0;
+}

Luogu/P3807/P3807.cpp

@@ -0,0 +1,48 @@
+#include <iostream>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 1e5 + 5;
+
+int t, n, m, p, fac[N], inv[N];
+
+inline int C(int n, int m, int p) {
+    if (m > n) return 0;
+    return 1ll * fac[n] * inv[m] % p * inv[n - m] % p;
+}
+
+int lucas(int n, int m, int p) {
+    if (!m) return 1;
+    return static_cast<long long>(C(n % p, m % p, p)) * lucas(n / p, m / p, p) % p;
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> t;
+
+    while (t--) {
+        cin >> n >> m >> p;
+
+        fac[0] = 1;
+        for (int i = 1; i <= 100000; i++) {
+            fac[i] = 1ll * fac[i - 1] * i % p;
+        }
+
+        inv[0] = inv[1] = 1;
+        for (int i = 2; i <= 100000; i++) {
+            inv[i] = static_cast<long long>(p - (p / i)) * inv[p % i] % p;
+        }
+
+        for (int i = 2; i <= 100000; i++) {
+            inv[i] = static_cast<long long>(inv[i - 1]) * inv[i] % p;
+        }
+
+        cout << lucas(n + m, n, p) << endl;
+    }
+
+    return 0;
+}

Luogu/P6146/P6146.cpp

@@ -0,0 +1,51 @@
+#include <iostream>
+#include <algorithm>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 1e5 + 5;
+const int mod = 1e9 + 7;
+
+int n, s[N << 1], f[N];
+std::pair<int, int> a[N];
+
+int pow(int a, int b) {
+    int res = 1;
+
+    while (b) {
+        if (b & 1) res = 1ll * res * a % mod;
+        a = 1ll * a * a % mod;
+        b >>= 1;
+    }
+
+    return res;
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> n;
+
+    for (int i = 1; i <= n; i++) {
+        cin >> a[i].first >> a[i].second;
+
+        s[a[i].second]++;
+    }
+
+    std::sort(a + 1, a + 1 + n);
+
+    for (int i = 1; i <= n << 1; i++) {
+        s[i] += s[i - 1];
+    }
+
+    for (int i = 1; i <= n; i++) {
+        f[i] = (f[i - 1] * 2 % mod + pow(2, s[a[i].first - 1]) % mod) % mod;
+    }
+
+    cout << f[n] << endl;
+
+    return 0;
+}