线性时间预处理[1,n]阶乘的逆元

Modular-Multiplicative-Inverse-Sieve(Factorial,Linear).cpp

@@ -0,0 +1,49 @@
+#include <cstdio>
+
+#define MAX_N 10000000
+
+typedef long long ll;
+
+using namespace std;
+
+// p must be a prime greater than n.
+ll n, fac_inv[MAX_N], p;
+
+ll qpow(ll x, ll y)
+{
+	if (y == 1) return x;
+	ll t = qpow(x, y >> 1);
+	t = t * t % p;
+	if ((y & 1) == 0) return t;
+	else return t * x % p;
+}
+
+ll fac(ll x)
+{
+	ll res = 1;
+	for (int i = 2; i <= x; i++)
+	{
+		res = res * i % p;
+	}
+	return res;
+}
+
+void fac_inv_sieve()
+{
+	fac_inv[n] = qpow(fac(n), p - 2);
+	for (ll i = n - 1; i >= 1; i--)
+	{
+		fac_inv[i] = fac_inv[i + 1] * (i + 1) % p;
+	}
+}
+
+int main()
+{
+	scanf("%lld%lld", &n, &p);
+	fac_inv_sieve();
+	for (int i = 1; i <= n; i++)
+	{
+		printf("inv(fac(%d)) mod %lld = %lld\n", i, p, fac_inv[i]);
+	}
+	return 0;
+}