luogu P2791 幼兒園籃球題
阿新 • • 發佈:2021-12-17
https://www.luogu.com.cn/problem/P2791
讚美出題人(bushi
如果做過luogu P6031 CF1278F Cards 加強版
這題,按照套路推一推就可以推出來了
注意其中有一步要用範德蒙德卷積
code:
#include<bits/stdc++.h> #define ll long long #define mod 998244353 #define M 20000050 #define N 800050 using namespace std; inline int rd() { int x = 0; char ch = getchar(); for(; ch < '0' || ch > '9' ;) ch = getchar(); for(; ch >= '0' && ch <= '9'; ) x = (x << 3) + (x << 1) + (ch - '0'), ch = getchar(); return x; } int add(int x, int y) { x += y; if(x >= mod) x -= mod; return x; } int sub(int x, int y) { x -= y; if(x < 0) x += mod; return x; } int mul(int x, int y) { return 1ll * x * y % mod; } int qpow(int x, int y) { int ret = 1; for(; y; y >>= 1, x = mul(x, x)) if(y & 1) ret = mul(ret, x); return ret; } const int G = 3; const int Ginv = qpow(3, mod - 2); int rev[N]; void ntt(int *a, int n, int o) { for(int i = 1; i < n; i ++) if(i > rev[i]) swap(a[i], a[rev[i]]); for(int len = 2; len <= n; len <<= 1) { int w0 = qpow((o == 1)? G : Ginv, (mod - 1) / len); for(int j = 0; j < n; j += len) { int wn = 1; for(int k = j; k < j + (len >> 1); k ++, wn = mul(wn, w0)) { int X = a[k], Y = mul(wn, a[k + (len >> 1)]); a[k] = add(X, Y), a[k + (len >> 1)] = sub(X, Y); } } } int ninv = qpow(n, mod - 2); if(o == -1) for(int i = 0; i < n; i ++) a[i] = mul(a[i], ninv); } int fac[M], ifac[M], a[N], b[N], S[N]; void init(int n) { fac[0] = 1; for(int i = 1; i <= n; i ++) fac[i] = mul(fac[i - 1], i); ifac[n] = qpow(fac[n], mod - 2); for(int i = n - 1; i >= 0; i --) ifac[i] = mul(ifac[i + 1], (i + 1)); } int C(int n, int m) { return mul(fac[n], mul(ifac[m], ifac[n - m])); } int vis[N], prime[N], sz; int idk[N]; void get(int n) { idk[1] = 1; for(int i = 2; i <= n; i ++) { if(!vis[i]) { idk[i] = qpow(i, n); prime[++ sz] = i; } for(int j = 1; j <= sz && i * prime[j] <= n; j ++) { vis[prime[j] * i] = 1; idk[prime[j] * i] = 1ll * idk[prime[j]] * idk[i] % mod; if(i % prime[j] == 0) break; } } } void pre(int n) { get(n); for(int i = 0; i <= n; i ++) a[i] = mul((i & 1)? (mod - 1) : 1, ifac[i]); for(int i = 0; i <= n; i ++) b[i] = mul(idk[i], ifac[i]); int len = 1; for(; len <= n + n; len <<= 1); for(int i = 1; i < len; i ++) rev[i] = (rev[i >> 1] >> 1) | ((i & 1) * (len >> 1)); ntt(a, len, 1), ntt(b, len, 1); for(int i = 0; i < len; i ++) a[i] = mul(a[i], b[i]); ntt(a, len, -1); for(int i = 0; i <= n; i ++) S[i] = a[i]; } int n, m, s, l, k; int main() { n = rd(), m = rd(), s = rd(), l = rd(); init(max(n, l)), pre(l); while(s --) { n = rd(), m = rd(), k = rd(); int ans = 0; for(int j = 0; j <= min(k, min(m, l)); j ++) ans = add(ans, 1ll * S[j] * ifac[m - j] % mod * ifac[k - j] % mod * fac[n - j] % mod); //ans = add(ans, mul(fac[j], mul(S[j], mul(C(m, j), C(n - j, k - j))))); printf("%lld\n", 1ll * ans * fac[m] % mod * fac[k] % mod * ifac[n] % mod); } return 0; }