結果
問題 | No.1062 素敵なスコア |
ユーザー |
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提出日時 | 2020-05-23 02:31:03 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 53 ms / 2,000 ms |
コード長 | 4,554 bytes |
コンパイル時間 | 1,926 ms |
コンパイル使用メモリ | 135,640 KB |
最終ジャッジ日時 | 2025-01-10 15:13:08 |
ジャッジサーバーID (参考情報) |
judge5 / judge1 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 32 |
ソースコード
#include <cstdio>#include <cstring>#include <iostream>#include <string>#include <cmath>#include <bitset>#include <vector>#include <map>#include <set>#include <queue>#include <deque>#include <algorithm>#include <complex>#include <unordered_map>#include <unordered_set>#include <random>#include <cassert>#include <fstream>#include <utility>#include <functional>#include <time.h>#include <stack>#include <array>#include <list>#define popcount __builtin_popcountusing namespace std;typedef long long int ll;typedef pair<int, int> P;const ll MOD=998244353;ll powmod(ll a, ll k){ll ap=a, ans=1;while(k){if(k&1){ans*=ap;ans%=MOD;}ap=ap*ap;ap%=MOD;k>>=1;}return ans;}ll inv(ll a){return powmod(a, MOD-2);}ll f[200020], invf[200020];void fac(int n){f[0]=1;for(ll i=1; i<=n; i++) f[i]=f[i-1]*i%MOD;invf[n]=inv(f[n]);for(ll i=n-1; i>=0; i--) invf[i]=invf[i+1]*(i+1)%MOD;}ll comb(int x, int y){if(!(0<=y && y<=x)) return 0;return f[x]*invf[y]%MOD*invf[x-y]%MOD;}template< int mod >struct NumberTheoreticTransform {vector< int > rev, rts;int base, max_base, root;NumberTheoreticTransform() : base(1), rev{0, 1}, rts{0, 1} {assert(mod >= 3 && mod % 2 == 1);auto tmp = mod - 1;max_base = 0;while(tmp % 2 == 0) tmp >>= 1, max_base++;root = 2;while(mod_pow(root, (mod - 1) >> 1) == 1) ++root;assert(mod_pow(root, mod - 1) == 1);root = mod_pow(root, (mod - 1) >> max_base);}inline int mod_pow(int x, int n) {int ret = 1;while(n > 0) {if(n & 1) ret = mul(ret, x);x = mul(x, x);n >>= 1;}return ret;}inline int inverse(int x) {return mod_pow(x, mod - 2);}inline unsigned add(unsigned x, unsigned y) {x += y;if(x >= mod) x -= mod;return x;}inline unsigned mul(unsigned a, unsigned b) {return 1ull * a * b % (unsigned long long) mod;}void ensure_base(int nbase) {if(nbase <= base) return;rev.resize(1 << nbase);rts.resize(1 << nbase);for(int i = 0; i < (1 << nbase); i++) {rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));}assert(nbase <= max_base);while(base < nbase) {int z = mod_pow(root, 1 << (max_base - 1 - base));for(int i = 1 << (base - 1); i < (1 << base); i++) {rts[i << 1] = rts[i];rts[(i << 1) + 1] = mul(rts[i], z);}++base;}}void ntt(vector< int > &a) {const int n = (int) a.size();assert((n & (n - 1)) == 0);int zeros = __builtin_ctz(n);ensure_base(zeros);int shift = base - zeros;for(int i = 0; i < n; i++) {if(i < (rev[i] >> shift)) {swap(a[i], a[rev[i] >> shift]);}}for(int k = 1; k < n; k <<= 1) {for(int i = 0; i < n; i += 2 * k) {for(int j = 0; j < k; j++) {int z = mul(a[i + j + k], rts[j + k]);a[i + j + k] = add(a[i + j], mod - z);a[i + j] = add(a[i + j], z);}}}}vector< int > multiply(vector< int > a, vector< int > b) {int need = a.size() + b.size() - 1;int nbase = 1;while((1 << nbase) < need) nbase++;ensure_base(nbase);int sz = 1 << nbase;a.resize(sz, 0);b.resize(sz, 0);ntt(a);ntt(b);int inv_sz = inverse(sz);for(int i = 0; i < sz; i++) {a[i] = mul(a[i], mul(b[i], inv_sz));}reverse(a.begin() + 1, a.end());ntt(a);a.resize(need);return a;}};int main(){int n, a, b;cin>>n>>a>>b;fac(n);if(a>b) swap(a, b);if(a==b){cout<<f[n]*n%MOD<<endl;return 0;}int x=a, z=n-b, y=n-x-z;ll ans=f[n-1]*x%MOD*x%MOD;(ans+=f[n-1]*z%MOD*z)%=MOD;(ans+=f[n-1]*y%MOD*y)%=MOD;ll u=f[x]*f[y]%MOD*f[z]%MOD;NumberTheoreticTransform<MOD> ntt;vector<int> v1(x), v2(x);for(int i=0; i<x; i++){v1[i]=invf[i]*((z-i-1<0)?0:invf[z-i-1])%MOD;}for(int i=0; i<x; i++){v2[i]=f[x-i-1]*f[y+i]%MOD*f[y+z+i]%MOD*invf[i]%MOD;}auto w=ntt.multiply(v1, v2);for(int i=0; i<x; i++){(ans+=u*w[i]%MOD*invf[y]%MOD*invf[x-i-1]%MOD*invf[y+1+i])%=MOD;}v1.resize(z), v2.resize(z);for(int i=0; i<z; i++){v1[i]=invf[i]*((x-i-1<0)?0:invf[x-i-1])%MOD;}for(int i=0; i<z; i++){v2[i]=f[z-i-1]*f[y+i]%MOD*f[y+x+i]%MOD*invf[i]%MOD;}w=ntt.multiply(v1, v2);for(int i=0; i<z; i++){(ans+=u*w[i]%MOD*invf[y]%MOD*invf[z-i-1]%MOD*invf[y+1+i])%=MOD;}cout<<ans<<endl;return 0;}