P4238 【模板】多项式乘法逆

https://www.luogu.com.cn/record/96259440

Luogu/P4238/P4238.cpp

@@ -0,0 +1,129 @@
+#include <iostream>
+#include <algorithm>
+#include <vector>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int mod = 998244353;
+
+constexpr long long binpow(long long a, long long b) {
+    a %= mod;
+
+    long long res = 1;
+
+    while (b) {
+        if (b & 1) res = res * a % mod;
+        a = a * a % mod;
+        b >>= 1;
+    }
+
+    return res;
+}
+
+std::vector<long long> number_theoretic_transform(std::vector<long long> a) {
+    // assert(a.size() == (1 << std::__lg(a.size())));
+    int k = std::__lg(a.size());
+
+    for (int i = 0; i < a.size(); i++) {
+        int t = 0;
+
+        for (int j = 0; j < k; j++) {
+            if (i & (1 << j)) {
+                t |= 1 << (k - j - 1);
+            }
+        }
+
+        if (i < t) std::swap(a[i], a[t]);
+    }
+
+    for (int len = 2; len <= a.size(); len <<= 1) {
+        int m = len >> 1;
+        long long wn = binpow(3, (mod - 1) / len);
+
+        for (int i = 0; i < a.size(); i += len) {
+            long long w = 1;
+
+            for (int j = 0; j < m; j++) {
+                long long u = a[i + j],
+                          v = a[i + j + m] * w % mod;
+
+                a[i + j] = ((u + v) % mod + mod) % mod;
+                a[i + j + m] = ((u - v) % mod + mod) % mod;
+                w = w * wn % mod;
+            }
+        }
+    }
+
+    return a;
+}
+
+class Poly : public std::vector<long long> {
+  private:
+  public:
+    using std::vector<long long>::vector;
+
+    Poly() = default;
+
+    Poly(const std::vector<long long> &__v)
+        : std::vector<long long>(__v) {}
+
+    Poly(std::vector<long long> &&__v)
+        : std::vector<long long>(std::move(__v)) {}
+} poly;
+
+Poly inv(Poly a) {
+    if (a.size() == 1) return Poly{binpow(a[0], mod - 2)};
+
+    int n = a.size(),
+        k = 1 << (std::__lg(n << 1) + 1);
+    Poly b{a};
+
+    a.resize(k);
+    a = number_theoretic_transform(a);
+
+    b.resize(n + 1 >> 1);
+    b = inv(b);
+    b.resize(k);
+    b = number_theoretic_transform(b);
+
+    for (int i = 0; i < k; i++) {
+        b[i] = (2 - a[i] * b[i] % mod + mod) % mod * b[i] % mod;
+    }
+
+    long long inv_k = binpow(k, mod - 2);
+    b = number_theoretic_transform(b);
+    std::transform(b.begin(), b.end(), b.begin(), [&](long long x) {
+        return x * inv_k % mod;
+    });
+    std::reverse(b.begin() + 1, b.end());
+    b.resize(n);
+
+    return b;
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    int n;
+
+    cin >> n;
+
+    Poly f(n);
+
+    for (int i = 0; i < n; i++) {
+        cin >> f[i];
+    }
+
+    auto g = inv(f);
+
+    for (int i = 0; i < n; i++) {
+        cout << g[i] << ' ';
+    }
+
+    cout << endl;
+
+    return 0;
+}