結果

問題 No.2770 Coupon Optimization
ユーザー GOTKAKOGOTKAKO
提出日時 2024-05-31 22:04:50
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
AC  
実行時間 788 ms / 3,000 ms
コード長 11,888 bytes
コンパイル時間 3,477 ms
コンパイル使用メモリ 230,260 KB
実行使用メモリ 30,504 KB
最終ジャッジ日時 2024-12-20 23:34:11
合計ジャッジ時間 14,526 ms
ジャッジサーバーID
(参考情報)
judge3 / judge1
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 2
other AC * 16
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#include <bits/stdc++.h>
using namespace std;
long long mod = 998244353;
//mod使.
struct mint{
long long v = 0;
mint(){} mint(int a){v = a;} mint(long long a){v = a;} mint(unsigned long long a){v = a;}
long long val(){return v;}
void modu(){v %= mod;}
mint repeat2mint(const long long a,long long b){
mint ret = 1,p = a;
while(b){
if(b&1) ret *= p;
p *= p; b >>= 1;
}
return ret;
};
mint operator+(const mint b){return mint(v)+=b;}
mint operator-(const mint b){return mint(v)-=b;}
mint operator*(const mint b){return mint(v)*=b;}
mint operator/(const mint b){return mint(v)/=b;}
mint operator+=(const mint b){
v += b.v; if(v >= mod) v -= mod;
return *this;
}
mint operator-=(const mint b){
v -= b.v; if(v < 0) v += mod;
return *this;
}
mint operator*=(const mint b){v = v*b.v%mod; return *this;}
mint operator/=(mint b){
if(b == 0) assert(false);
int left = mod-2;
while(left){if(left&1) *this *= b; b *= b; left >>= 1;}
return *this;
}
mint operator++(int){*this += 1; return *this;}
mint operator--(int){*this -= 1; return *this;}
bool operator==(const mint b){return v == b.v;}
bool operator!=(const mint b){return v != b.v;}
bool operator>(const mint b){return v > b.v;}
bool operator>=(const mint b){return v >= b.v;}
bool operator<(const mint b){return v < b.v;}
bool operator<=(const mint b){return v <= b.v;}
mint pow(const long long x){return repeat2mint(v,x);}
mint inv(){return mint(1)/v;}
};
namespace to_fold{ // ACL.
__int128_t safemod(__int128_t a,long long m){a %= m; if(a < 0) a += m; return a;}
pair<long long,long long> invgcd(long long a,long long b){
//return {gcd(a,b),x} (xa≡g(mod b))
a = safemod(a,b);
if(a == 0) return {b,0};
long long x = 0,y = 1,memob = b;
while(a){
long long q = b/a;
b -= a*q;
swap(x,y); y -= q*x;
swap(a,b);
}
if(x < 0) x += memob/b;
return {b,x};
}
long long Garner(vector<long long> &A,vector<long long> &M){
__int128_t mulM = 1,x = A.at(0)%M.at(0); //M.
for(int i=1; i<A.size(); i++){
//assert(gcd(mulM,M.at(i-1)) == 1);
mulM *= M.at(i-1); //2__int128_t
long long t = safemod((A.at(i)-x)*invgcd(mulM,M.at(i)).second,M.at(i));
x += t*mulM;
}
return x%mod;
}
int countzero(unsigned long long x){
if(x == 0) return 64;
else return __popcount((x&-x)-1);
}
struct fftinfo{
vector<mint> root,iroot,rate2,irate2,rate3,irate3;
fftinfo(mint g){
int rank2 = countzero(mod-1);
root.resize(rank2+1),iroot = root;
rate2.resize(max(0,rank2-2+1)); irate2 = rate2;
rate3.resize(max(0,rank2-3+1)); irate3 = rate3;
root[rank2] = g.pow((mod-1)>>rank2);
iroot[rank2] = root[rank2].inv();
for(int i=rank2-1; i>=0; i--){
root[i] = root[i+1]*root[i+1];
iroot[i] = iroot[i+1]*iroot[i+1];
}
mint mul = 1,imul = 1;
for(int i=0; i<=rank2-2; i++){
rate2[i] = root[i+2]*mul;
irate2[i] = iroot[i+2]*imul;
mul *= iroot[i+2],imul *= root[i+2];
}
mul = 1,imul = 1;
for(int i=0; i<=rank2-3; i++){
rate3[i] = root[i+3]*mul;
irate3[i] = iroot[i+3]*imul;
mul *= iroot[i+3],imul *= root[i+3];
}
}
};
mint findroot(){
if(mod == 998244353) return mint(3);
else if(mod == 754974721) return mint(11);
else if(mod == 167772161) return mint(3);
else if(mod == 469762049) return mint(3);
long long p = mod-1;
vector<long long> P;
for(long long i=2; i*i<=p; i++){
if(p%i) continue;
while(p%i == 0) p /= i;
P.push_back(i);
}
if(p != 1) P.push_back(p);
p = mod-1;
random_device rnd; mt19937 mt(rnd());
while(true){
mint ret = mt()%mod;
if(ret == 1 || ret == 0) continue;
if(ret.pow(p) != 1) continue;
bool ok = true;
for(auto check : P) if(ret.pow(p/check) == 1){ok = false; break;}
if(ok) return ret;
} //O(√P).
}
void NTT(vector<mint> &A,fftinfo &info){
int N = A.size(),ln = countzero(N);
int dep = 0;
while(dep < ln){
if(ln-dep == 1){
int p = 1<<(ln-dep-1);
mint rot = 1;
for(int o=0; o<(1<<dep); o++){
int offset = o<<(ln-dep);
for(int i=0; i<p; i++){
mint l = A.at(i+offset),r = A.at(i+offset+p)*rot;
A.at(i+offset) = l+r; A.at(i+offset+p) = l-r;
}
if(o+1 != (1<<dep)) rot *= info.rate2[countzero(~(unsigned int)o)];
}
dep++;
}
else{
int p = 1<<(ln-dep-2);
mint rot = 1,imag = info.root[2];
for(int o=0; o<(1<<dep); o++){
mint rot2 = rot*rot,rot3 = rot2*rot;
int offset = o<<(ln-dep);
for(int i=0; i<p; i++){
auto mod2 = 1ULL*mod*mod;
auto a0 = 1ULL*A.at(i+offset).v;
auto a1 = 1ULL*A.at(i+offset+p).v*rot.v;
auto a2 = 1ULL*A.at(i+offset+p+p).v*rot2.v;
auto a3 = 1ULL*A.at(i+offset+p+p+p).v*rot3.v;
auto a1m2a3im = 1ULL*(a1+mod2-a3+mod)%mod*imag.v;
auto m2a2 = mod2-a2;
A.at(i+offset) = (long long)((a0+a2+a1+a3)%mod);
A.at(i+offset+p) = (long long)((a0+a2+(2*mod2-(a1+a3)))%mod);
A.at(i+offset+p+p) = (long long)((a0+m2a2+a1m2a3im)%mod);
A.at(i+offset+p+p+p) = (long long)((a0+m2a2+(mod2-a1m2a3im))%mod);
}
if(o+1 != (1<<dep)) rot *= info.rate3[countzero(~(unsigned int)o)];
}
dep += 2;
}
}
}
void INTT(vector<mint> &A,fftinfo &info){
int N = A.size(),ln = countzero(N);
int dep = ln;
while(dep){
if(dep == 1){
int p = 1<<(ln-dep);
mint irot = 1;
for(int o=0; o<(1<<(dep-1)); o++){
int offset = o<<(ln-dep+1);
for(int i=0; i<p; i++){
mint l = A.at(i+offset),r = A.at(i+offset+p);
A.at(i+offset) = l+r;
A.at(i+offset+p) = (long long)((unsigned long long)((mod+l.v-r.v)*irot.v)%mod);
}
if(o+1 != (1<<(dep-1))) irot *= info.irate2[countzero(~(unsigned int)o)];
}
dep--;
}
else{
int p = 1<<(ln-dep);
mint irot = 1,iimag = info.iroot[2];
for(int o=0; o<(1<<(dep-2)); o++){
mint irot2 = irot*irot,irot3 = irot2*irot;
int offset = o<<(ln-dep+2);
for(int i=0; i<p; i++){
auto a0 = 1ULL*A.at(i+offset).v,a1 = 1ULL*A.at(i+offset+p).v;
auto a2 = 1ULL*A.at(i+offset+p+p).v,a3 = 1ULL*A.at(i+offset+p+p+p).v;
auto gotyagotya = 1ULL*((mod+a2-a3)*iimag.v%mod);
A.at(i+offset) = (long long)((a0+a1+a2+a3)%mod);
A.at(i+offset+p) = (long long)((a0+(mod-a1)+gotyagotya)*irot.v%mod);
A.at(i+offset+p+p) = (long long)((a0+a1+(mod-a2)+(mod-a3))*irot2.v%mod);
A.at(i+offset+p+p+p) = (long long)((a0+(mod-a1)+(mod-gotyagotya))*irot3.v%mod);
}
if(o+1 != (1<<(dep-2))) irot *= info.irate3[countzero(~(unsigned int)o)];
}
dep -= 2;
}
}
}
vector<mint> convolutionnaive(vector<mint> &A,vector<mint> &B){
vector<mint> ret(A.size()+B.size()-1);
for(int i=0; i<A.size(); i++) for(int k=0; k<B.size(); k++) ret.at(i+k) += A.at(i)*B.at(k);
return ret;
}
vector<mint> convolution(vector<mint> &A,vector<mint> &B){
int siza = A.size(),sizb = B.size(),sizc = siza+sizb-1,N = 1;
if(siza == 0 || sizb == 0) return {};
while(N <= sizc) N <<= 1;
vector<mint> ca = A,cb = B;
ca.resize(N),cb.resize(N);
if(min(siza,sizb) <= 40) return convolutionnaive(A,B);
assert((mod-1)%N == 0);
mint root = findroot();
fftinfo info(root);
NTT(ca,info); NTT(cb,info);
for(int i=0; i<N; i++) ca.at(i) *= cb.at(i);
INTT(ca,info); ca.resize(sizc);
mint divN = mint(N).inv();
for(int i=0; i<sizc; i++) ca.at(i) *= divN;
return ca;
}
vector<long long> convolution_ll(vector<long long> &A,vector<long long> &B){
int siza = A.size(),sizb = B.size(),sizc = siza+sizb-1;
if(siza == 0 || sizb == 0) return {};
unsigned long long mod1 = 754974721,mod2 = 167772161,mod3 = 469762049;
unsigned long long m1m2 = mod1*mod2,m2m3 = mod2*mod3,m3m1 = mod3*mod1,m1m2m3 = mod1*mod2*mod3;
unsigned long long i1 = invgcd(m2m3,mod1).second,i2 = invgcd(m3m1,mod2).second,i3 = invgcd(m1m2,mod3).second;
assert(sizc <= (1<<24));
mod = mod1;
vector<mint> a(siza),b(sizb);
for(int i=0; i<siza; i++) a.at(i) = A.at(i)%mod;
for(int i=0; i<sizb; i++) b.at(i) = B.at(i)%mod;
vector<mint> C1 = convolution(a,b);
mod = mod2;
for(int i=0; i<siza; i++) a.at(i) = A.at(i)%mod;
for(int i=0; i<sizb; i++) b.at(i) = B.at(i)%mod;
vector<mint> C2 = convolution(a,b);
mod = mod3;
for(int i=0; i<siza; i++) a.at(i) = A.at(i)%mod;
for(int i=0; i<sizb; i++) b.at(i) = B.at(i)%mod;
vector<mint> C3 = convolution(a,b);
vector<long long> ret(sizc);
vector<unsigned long long> offset = {0,0,m1m2m3,2*m1m2m3,3*m1m2m3};
for(int i=0; i<sizc; i++){
unsigned long long x = 0;
x += (C1.at(i).v*i1)%mod1*m2m3;
x += (C2.at(i).v*i2)%mod2*m3m1;
x += (C3.at(i).v*i3)%mod3*m1m2;
long long diff = C1.at(i).v-((long long)x+(long long)mod1)%mod1;
if(diff < 0) diff += mod1;
x -= offset.at(diff%5);
ret.at(i) = x;
}
return ret;
}
vector<mint> convolution_llmod(vector<mint> &A,vector<mint> &B,long long memomod){
int siza = A.size(),sizb = B.size(),sizc = siza+sizb-1;
if(siza == 0 || sizb == 0) return {};
long long mod1 = 754974721,mod2 = 167772161,mod3 = 469762049;
assert(sizc <= (1<<24));
mod = mod1;
vector<mint> a(siza),b(sizb);
for(int i=0; i<siza; i++) a.at(i) = A.at(i).v%mod;
for(int i=0; i<sizb; i++) b.at(i) = B.at(i).v%mod;
vector<mint> C1 = convolution(a,b);
mod = mod2;
for(int i=0; i<siza; i++) a.at(i) = A.at(i).v%mod;
for(int i=0; i<sizb; i++) b.at(i) = B.at(i).v%mod;
vector<mint> C2 = convolution(a,b);
mod = mod3;
for(int i=0; i<siza; i++) a.at(i) = A.at(i).v%mod;
for(int i=0; i<sizb; i++) b.at(i) = B.at(i).v%mod;
vector<mint> C3 = convolution(a,b);
mod = memomod;
vector<mint> ret(sizc);
for(int i=0; i<sizc; i++){
vector<long long> A = {C1.at(i).v,C2.at(i).v,C3.at(i).v};
vector<long long> M = {mod1,mod2,mod3};
ret.at(i) = Garner(A,M);
}
return ret;
}
}
using namespace to_fold;
int main() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
int N,M; cin >> N >> M;
vector<long long> A(N),B(M);
for(auto &a : A) cin >> a,a /= 100;
for(auto &b : B) cin >> b;
sort(A.begin(),A.end());
sort(B.rbegin(),B.rend());
while(B.size() < N) B.push_back(0);
while(B.size() > N) B.pop_back();
vector<long long> C = convolution_ll(A,B);
long long answer = 0;
for(int i=0; i<N; i++){
answer += A.at(i)*100;
cout << answer-C.at(i) << "\n";
}
}
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