結果
| 問題 | No.3056 量子コンピュータで素因数分解 Easy |
| ユーザー |
 kopricky
|
| 提出日時 | 2020-02-06 04:31:45 |
| 言語 | C++14 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
TLE
(最新)
AC
(最初)
|
| 実行時間 | - |
| コード長 | 16,308 bytes |
| コンパイル時間 | 2,518 ms |
| コンパイル使用メモリ | 193,660 KB |
| 実行使用メモリ | 43,276 KB |
| 最終ジャッジ日時 | 2024-06-10 07:21:36 |
| 合計ジャッジ時間 | 8,929 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge2 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | TLE | - |
| testcase_01 | -- | - |
| testcase_02 | -- | - |
| testcase_03 | -- | - |
| testcase_04 | -- | - |
| testcase_05 | -- | - |
| testcase_06 | -- | - |
| testcase_07 | -- | - |
| testcase_08 | -- | - |
| testcase_09 | -- | - |
| testcase_10 | -- | - |
| testcase_11 | -- | - |
| testcase_12 | -- | - |
| testcase_13 | -- | - |
| testcase_14 | -- | - |
| testcase_15 | -- | - |
| testcase_16 | -- | - |
| testcase_17 | -- | - |
| testcase_18 | -- | - |
| testcase_19 | -- | - |
| testcase_20 | -- | - |
| testcase_21 | -- | - |
| testcase_22 | -- | - |
| testcase_23 | -- | - |
| testcase_24 | -- | - |
| testcase_25 | -- | - |
ソースコード
#include <bits/stdc++.h>
#define ll long long
#define INF 1000000005
#define MOD 1000000007
#define EPS 1e-10
#define rep(i,n) for(int i=0;i<(int)(n);++i)
#define rrep(i,n) for(int i=(int)(n)-1;i>=0;--i)
#define srep(i,s,t) for(int i=(int)(s);i<(int)(t);++i)
#define each(a,b) for(auto& (a): (b))
#define all(v) (v).begin(),(v).end()
#define len(v) (int)(v).size()
#define zip(v) sort(all(v)),v.erase(unique(all(v)),v.end())
#define cmx(x,y) x=max(x,y)
#define cmn(x,y) x=min(x,y)
#define fi first
#define se second
#define pb push_back
#define show(x) cout<<#x<<" = "<<(x)<<endl
#define sar(a,n) {cout<<#a<<":";rep(pachico,n)cout<<" "<<a[pachico];cout<<endl;}
using namespace std;
template<typename S,typename T>auto&operator<<(ostream&o,pair<S,T>p){return o<<"{"<<p.fi<<","<<p.se<<"}";}
template<typename T>auto&operator<<(ostream&o,set<T>s){for(auto&e:s)o<<e<<" ";return o;}
template<typename S,typename T,typename U>
auto&operator<<(ostream&o,priority_queue<S,T,U>q){while(!q.empty())o<<q.top()<<" ",q.pop();return o;}
template<typename K,typename T>auto&operator<<(ostream&o,map<K,T>&m){for(auto&e:m)o<<e<<" ";return o;}
template<typename T>auto&operator<<(ostream&o,vector<T>v){for(auto&e:v)o<<e<<" ";return o;}
void ashow(){cout<<endl;}template<typename T,typename...A>void ashow(T t,A...a){cout<<t<<" ";ashow(a...);}
template<typename S,typename T,typename U>
struct TRI{S fi;T se;U th;TRI(){}TRI(S f,T s,U t):fi(f),se(s),th(t){}
bool operator<(const TRI&_)const{return(fi==_.fi)?((se==_.se)?(th<_.th):(se<_.se)):(fi<_.fi);}};
template<typename S,typename T,typename U>
auto&operator<<(ostream&o,TRI<S,T,U>&t){return o<<"{"<<t.fi<<","<<t.se<<","<<t.th<<"}";}
typedef pair<int, int> P;
typedef pair<ll, ll> pll;
typedef TRI<int, int, int> tri;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<vi> vvi;
typedef vector<vl> vvl;
typedef vector<P> vp;
typedef vector<double> vd;
typedef vector<string> vs;
const int MAX_N = 100005;
class MPI : public vector<int> {
private:
static constexpr int root = 3;
static constexpr int MOD_ = 998244353; // 2^23 * 119 + 1 (2^22 桁以下の数の積を計算可能)
static void trim_sign(MPI& num){
if(num.isZero()) num.sign = false;
}
static void trim_digit(MPI& num){
while(num.back() == 0 && (int)num.size() >= 2) num.pop_back();
}
static bool abs_less(const MPI& a, const MPI& b){
if(a.size() != b.size()) return a.size() < b.size();
for(int index = (int)a.size() - 1; index >= 0; index--){
if(a[index] != b[index]) return a[index] < b[index];
}
return false;
}
static void num_sbst(MPI& a, const MPI& b){
int n = (int)b.size();
a.resize(n);
for(int i = 0; i < n; i++) a[i] = b[i];
}
static void add(const MPI& a, const MPI& b, MPI& res){
num_sbst(res, a);
int mx = (int)max(a.size(), b.size());
res.resize(mx, 0);
int carry = 0;
for(int i = 0; i < mx; i++){
int val = res[i] + ((i < (int)b.size()) ? b[i] : 0) + carry;
carry = val/10;
res[i] = val%10;
}
if(carry) res.push_back(1);
}
static void sub(const MPI& a, const MPI& b, MPI& res){
num_sbst(res, a);
int carry = 0;
for(int i = 0; i < (int)res.size(); i++){
int val = res[i] - carry - ((i < (int)b.size()) ? b[i] : 0);
if(val < 0){
carry = 1, val += 10;
}else{
carry = 0;
}
res[i] = val;
}
trim_digit(res), trim_sign(res);
}
static int add_(const int x, const int y) { return (x + y < MOD_) ? x + y : x + y - MOD_; }
static int mul_(const int x, const int y) { return (ll)x * y % MOD_; }
static int power(int x, int n){
int res = 1;
while(n > 0){
if(n & 1) res = mul_(res, x);
x = mul_(x, x);
n >>= 1;
}
return res;
}
static int inverse(const int x) { return power(x, MOD_ - 2); }
static void ntt(vector<int>& a, const bool rev = false){
int i,j,k,s,t,v,w,wn;
const int size = (int)a.size();
const int height = (int)log2(2 * size - 1);
for(i = 0; i < size; i++){
j = 0;
for(k = 0; k < height; k++) j |= (i >> k & 1) << (height - 1 - k);
if(i < j) std::swap(a[i], a[j]);
}
for(i = 1; i < size; i *= 2) {
w = power(root, (MOD_ - 1) / (i * 2));
if(rev) w = inverse(w);
for(j = 0; j < size; j += i * 2){
wn = 1;
for(k = 0; k < i; k++){
s = a[j + k], t = mul_(a[j + k + i], wn);
a[j + k] = add_(s, t);
a[j + k + i] = add_(s, MOD_ - t);
wn = mul_(wn, w);
}
}
}
if(rev){
v = inverse(size);
for (i = 0; i < size; i++) a[i] = mul_(a[i], v);
}
}
static void mul(const MPI& a, const MPI& b, MPI& res){
const int size = (int)a.size() + (int)b.size() - 1;
int t = 1;
while (t < size) t <<= 1;
vector<int> A(t, 0), B(t, 0);
for(int i = 0; i < (int)a.size(); i++) A[i] = a[i];
for(int i = 0; i < (int)b.size(); i++) B[i] = b[i];
ntt(A), ntt(B);
for(int i = 0; i < t; i++) A[i] = mul_(A[i], B[i]);
ntt(A, true);
res.resize(size);
int carry = 0;
for(int i = 0; i < size; i++){
int val = A[i] + carry;
carry = val / 10;
res[i] = val % 10;
}
if(carry) res.push_back(carry);
trim_digit(res), trim_sign(res);
}
bool isZero() const {
return (int)size() == 1 && (*this)[0] == 0;
}
static bool div_geq(const MPI& mod, const MPI& num){
if((int)mod.size() != (int)num.size()) return (int)mod.size() > (int)num.size();
int n = (int)mod.size();
for(int i = 0; i < n; i++){
if(mod[i] != num[n-1-i]){
return mod[i] > num[n-1-i];
}
}
return true;
}
static void div_(const MPI& a, const MPI& b, MPI& quo, MPI& mod){
vector<MPI> mult(9);
mult[0] = b;
for(int i = 0; i < 8; i++) mult[i+1] = mult[i] + b;
for(int i = (int)a.size() - 1; i >= 0; i--){
if(mod.isZero()){
mod.back() = a[i];
}else{
mod.push_back(a[i]);
}
if(div_geq(mod, b)){
int l = 0, r = 9;
reverse(mod.begin(), mod.end());
while(r-l>1){
int mid = (l+r)/2;
if(mult[mid] > mod){
r = mid;
}else{
l = mid;
}
}
mod -= mult[l];
reverse(mod.begin(), mod.end());
quo.push_back(l+1);
}else{
quo.push_back(0);
}
}
reverse(quo.begin(), quo.end());
trim_digit(quo);
reverse(mod.begin(), mod.end());
}
public:
ll to_ll() const {
ll res = 0, dig = 1;
for(int i = 0; i < (int)size(); i++){
res += dig * (*this)[i], dig *= 10;
}
if(sign) res = -res;
return res;
}
string to_string() const {
int n = (int)size() + sign;
string s(n, ' ');
if(sign) s[0] = '-';
for(int i = sign; i < n; i++) s[i] = (char)('0'+(*this)[n-1-i]);
return s;
}
friend istream& operator>>(istream& is, MPI& num) {
string s;
is >> s;
num = MPI(s);
return is;
}
friend ostream& operator<<(ostream& os, const MPI& num) {
if(num.sign) os << '-';
for(int i = (int)num.size()-1; i >= 0; i--) os << (char)('0'+num[i]);
return os;
}
MPI& operator=(ll val) {
*this = MPI(val);
return *this;
}
bool operator<(const MPI& another) const {
if(sign ^ another.sign) return sign;
if(size() != another.size()) return (size() < another.size()) ^ sign;
for(int index = (int)size() - 1; index >= 0; index--){
if((*this)[index] != another[index]) return ((*this)[index] < another[index]) ^ sign;
}
return false;
}
bool operator<(const ll num) const {
return *this < MPI(num);
}
friend bool operator<(const ll num, const MPI& another){
return MPI(num) < another;
}
bool operator>(const MPI& another) const {
return another < *this;
}
bool operator>(const ll num) const {
return *this > MPI(num);
}
friend bool operator>(const ll num, const MPI& another){
return MPI(num) > another;
}
bool operator<=(const MPI& another) const {
return !(*this > another);
}
bool operator<=(const ll num) const {
return *this <= MPI(num);
}
friend bool operator<=(const ll num, const MPI& another){
return MPI(num) <= another;
}
bool operator>=(const MPI& another) const {
return !(*this < another);
}
bool operator>=(const ll num) const {
return *this >= MPI(num);
}
friend bool operator>=(const ll num, const MPI& another){
return MPI(num) >= another;
}
bool operator==(const MPI& another) const {
if(sign ^ another.sign) return false;
if(size() != another.size()) return false;
for(int index = (int)size() - 1; index >= 0; index--){
if((*this)[index] != another[index]) return false;
}
return true;
}
bool operator==(const ll num) const {
return *this == MPI(num);
}
friend bool operator==(const ll num, const MPI& another){
return MPI(num) == another;
}
bool operator!=(const MPI& another) const {
return !(*this == another);
}
bool operator!=(const ll num) const {
return *this != MPI(num);
}
friend bool operator!=(const ll num, const MPI& another){
return MPI(num) != another;
}
explicit operator bool() const noexcept { return !isZero(); }
bool operator!() const noexcept { return !static_cast<bool>(*this); }
explicit operator int() const noexcept { return (int)this->to_ll(); }
explicit operator long long() const noexcept { return this->to_ll(); }
MPI operator+() const {
return *this;
}
MPI operator-() const {
MPI res = *this;
res.sign = !sign;
return res;
}
friend MPI abs(const MPI& num){
MPI res = num;
res.sign = false;
return res;
}
MPI operator+(const MPI& num) const {
MPI res; res.sign = sign;
if(sign != num.sign){
if(abs_less(*this, num)){
res.sign = num.sign;
sub(num, *this, res);
return res;
}else{
sub(*this, num, res);
return res;
}
}
add(*this, num, res);
return res;
}
MPI operator+(ll num) const {
return *this + MPI(num);
}
friend MPI operator+(ll a, const MPI& b){
return b + a;
}
MPI& operator+=(const MPI& num){
*this = *this + num;
return *this;
}
MPI& operator+=(ll num){
*this = *this + num;
return *this;
}
MPI& operator++(){
return *this += 1;
}
MPI operator++(int){
MPI res = *this;
*this += 1;
return res;
}
MPI operator-(const MPI& num) const {
MPI res; res.sign = sign;
if(sign != num.sign){
add(*this, num, res);
return res;
}
if(abs_less(*this, num)){
res.sign = !sign;
sub(num, *this, res);
}else{
sub(*this, num, res);
}
return res;
}
MPI operator-(ll num) const {
return *this - MPI(num);
}
friend MPI operator-(ll a, const MPI& b){
return MPI(a) - b;
}
MPI& operator-=(const MPI& num){
*this = *this - num;
return *this;
}
MPI& operator-=(ll num){
*this = *this - num;
return *this;
}
MPI& operator--(){
return *this -= 1;
}
MPI operator--(int){
MPI res = *this;
*this -= 1;
return res;
}
MPI operator*(const MPI& num) const {
MPI res; res.sign = (sign^num.sign);
mul(*this, num, res);
return res;
}
MPI operator*(ll num) const {
return *this * MPI(num);
}
friend MPI operator*(ll a, const MPI& b){
return b * a;
}
MPI& operator*=(const MPI& num){
*this = *this * num;
return *this;
}
MPI& operator*=(ll num){
*this = *this * num;
return *this;
}
MPI operator/(const MPI& num) const {
MPI num_ = abs(num);
MPI a, b;
div_(*this, num_, a, b);
a.sign = (sign^num.sign);
trim_sign(a);
return a;
}
MPI operator/(ll num) const {
return *this / MPI(num);
}
friend MPI operator/(ll a, const MPI& b){
return MPI(a) / b;
}
MPI& operator/=(const MPI& num){
*this = *this / num;
return *this;
}
MPI& operator/=(ll num){
*this = *this / num;
return *this;
}
MPI operator%(const MPI& num) const {
MPI num_ = abs(num);
MPI a, b;
div_(*this, num_, a, b);
b.sign = sign;
trim_sign(b);
return b;
}
MPI operator%(ll num) const {
return *this % MPI(num);
}
friend MPI operator%(ll a, const MPI& b){
return MPI(a) % b;
}
MPI& operator%=(const MPI& num){
*this = *this % num;
return *this;
}
MPI& operator%=(ll num){
*this = *this % num;
return *this;
}
MPI div2() const {
MPI res; res.sign = sign;
int n = (int)size(), carry = 0;
for(int i = n-1; i >= 0; i--){
int val = (*this)[i]+carry*10;
carry = val%2;
if(i != n-1 || val >= 2) res.push_back(val/2);
}
reverse(res.begin(), res.end());
trim_digit(res);
return res;
}
friend MPI sqrt(const MPI& x){
if(x <= MPI(0)) return MPI(0);
MPI s = 1, t = x;
while(s < t){
s = s + s, t = t.div2();
}
do{ t = s, s = (x / s + s).div2();
}while(s < t);
return t;
}
friend MPI log10(const MPI& x){
assert(x > MPI(0));
return MPI((int)x.size());
}
friend MPI pow(MPI a, MPI b){
assert(b >= 0);
MPI res(1);
while(b){
if(b[0] % 2){
res *= a;
}
a *= a;
b = b.div2();
}
return res;
}
friend MPI mod_pow(MPI a, MPI b, MPI mod){
assert(b >= 0);
MPI res(1);
while(b){
if(b[0] % 2){
res = res * a % mod;
}
a = a * a % mod;
b = b.div2();
}
return res;
}
bool sign;
MPI() : sign(false){ push_back(0); }
MPI(ll val) : sign(false){
if(val == 0){
push_back(0);
}else{
if(val < 0) sign = true, val = -val;
while(val){
push_back(val%10);
val /= 10;
}
}
}
MPI(const string& s) : sign(false){
if(s.empty()){
push_back(0);
return;
}
if(s[0] == '-') sign = true;
for(int i = (int)s.size() - 1; i >= sign; i--) push_back(s[i]-'0');
}
};
MPI gcd(MPI a, MPI b){
MPI tmp;
while(b) tmp = a, a = b, b = tmp % b;
return a;
}
int main()
{
MPI n;
cin >> n;
MPI a = 2, res, hoge, p, q;
while(true){
if(n % a == 0){
cout << a << " " << n / a << endl;
break;
}
cout << "? " << a << endl;
cin >> res;
if(res[0] % 2){
++a;
continue;
}
hoge = mod_pow(a, res.div2(), n) + 1;
if(hoge == n) continue;
p = gcd(hoge + 1, n);
cout << "! " << p << " " << n / p << endl;
break;
}
return 0;
}