結果
| 問題 | No.219 巨大数の概算 |
| ユーザー |
 kopricky
|
| 提出日時 | 2018-10-07 09:40:59 |
| 言語 | C++11 (gcc 11.4.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 18,765 bytes |
| コンパイル時間 | 1,948 ms |
| コンパイル使用メモリ | 174,780 KB |
| 実行使用メモリ | 13,824 KB |
| 最終ジャッジ日時 | 2024-10-12 14:08:41 |
| 合計ジャッジ時間 | 7,664 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge2 |
（要ログイン）
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 | -- | - |
| testcase_26 | -- | - |
| testcase_27 | -- | - |
| testcase_28 | -- | - |
| testcase_29 | -- | - |
| testcase_30 | -- | - |
| testcase_31 | -- | - |
| testcase_32 | -- | - |
| testcase_33 | -- | - |
| testcase_34 | -- | - |
| testcase_35 | -- | - |
| testcase_36 | -- | - |
| testcase_37 | -- | - |
| testcase_38 | -- | - |
| testcase_39 | -- | - |
| testcase_40 | -- | - |
| testcase_41 | -- | - |
| testcase_42 | -- | - |
| testcase_43 | -- | - |
| testcase_44 | -- | - |
| testcase_45 | -- | - |
| testcase_46 | -- | - |
| testcase_47 | -- | - |
| testcase_48 | -- | - |
| testcase_49 | -- | - |
| testcase_50 | -- | - |
| testcase_51 | -- | - |
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 spair(p) cout<<#p<<": "<<p.fi<<" "<<p.se<<endl
#define sar(a,n) cout<<#a<<":";rep(pachico,n)cout<<" "<<a[pachico];cout<<endl
#define svec(v) cout<<#v<<":";rep(pachico,v.size())cout<<" "<<v[pachico];cout<<endl
#define svecp(v) cout<<#v<<":";each(pachico,v)cout<<" {"<<pachico.first<<":"<<pachico.second<<"}";cout<<endl
#define sset(s) cout<<#s<<":";each(pachico,s)cout<<" "<<pachico;cout<<endl
#define smap(m) cout<<#m<<":";each(pachico,m)cout<<" {"<<pachico.first<<":"<<pachico.second<<"}";cout<<endl
using namespace std;
const int MAX_N = 100005;
template<int acc> class BMPI : public deque<int> {
private:
static constexpr int root = 5;
static constexpr int MOD_ = 924844033;
static void trim_digit(BMPI& num){
while((int)num.size() >= 1 && num.back() == 0) num.pop_back();
if((int)num.size() == 1 && num[0] == 0){ num.zero = true; return; }
while((int)num.size() < acc) num.push_front(0), num.ex--;
while((int)num.size() > acc + 1) num.pop_front(), num.ex++;
rounding(num);
}
static void rounding(BMPI& num){
if((int)num.size() != acc + 1) return;
if(num[0] >= 5){
int pos = 1;
do{ num[pos]++;
if(num[pos] != 10) break;
num[pos] = 0;
}while(++pos <= acc);
if(pos == acc+1) num.push_back(1), num.pop_back(), num.ex++;
}
num.pop_front(), num.ex++;
}
static bool abs_less(const BMPI& a, const BMPI& b){
if(a.ex != b.ex) return a.ex < b.ex;
for(int index = acc - 1; index >= 0; index--){
if(a[index] != b[index]) return a[index] < b[index];
}
return false;
}
static void num_sbst(BMPI& a, const BMPI& b){
a.resize(acc), a.zero = false, a.ex = b.ex;
for(int i = 0; i < acc; i++) a[i] = b[i];
}
static void add(const BMPI& a, const BMPI& b, BMPI& res){
int diff = a.ex - b.ex, carry = 0;
if(abs(diff) > acc) return (diff > 0) ? num_sbst(res, a) : num_sbst(res, b);
if(diff >= 0){
num_sbst(res, a);
if(diff) res.push_front(0), res.ex--;
for(int i = !diff; i <= acc; i++){
int val = res[i-!diff] + (i <= acc-diff ? b[i+diff-1] : 0) + carry;
carry = val/10;
res[i-!diff] = val%10;
}
if(carry) res.push_back(1);
}else{
num_sbst(res, b);
res.push_front(0), res.ex--;
for(int i = 0; i <= acc; i++){
int val = res[i] + (i <= acc+diff ? a[i-diff-1] : 0) + carry;
carry = val/10;
res[i] = val%10;
}
if(carry) res.push_back(1);
}
trim_digit(res);
}
static void sub(const BMPI& a, const BMPI& b, BMPI& res){
int diff = a.ex - b.ex, carry = 0;
num_sbst(res, a);
if(diff > acc) return;
if(diff){
res.push_front(0), res.ex--;
int carry = 0;
for(int i = 0; i <= acc; i++){
int val = res[i] - carry - (i <= acc-diff ? b[i+diff-1] : 0);
if(val < 0){
carry = 1, val += 10;
}else{
carry = 0;
}
res[i] = val;
}
}else{
for(int i = 0; i < acc; i++){
int val = res[i] - carry - b[i];
if(val < 0){
carry = 1, val += 10;
}else{
carry = 0;
}
res[i] = val;
}
}
trim_digit(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 (long long)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 BMPI& a, const BMPI& b, BMPI& 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);
}
class MPI : public deque<int> {
public:
MPI(){ push_back(0); }
inline static void trim_digit(MPI& num){
while(num.back() == 0 && (int)num.size() >= 2) num.pop_back();
}
bool isZero() const {
return (int)size() == 1 && (*this)[0] == 0;
}
static void add(const MPI& a, const MPI& b, MPI& res){
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){
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);
}
bool operator<(const MPI& another) const {
if(size() != another.size()) return size() < another.size();
for(int index = (int)size() - 1; index >= 0; index--){
if((*this)[index] != another[index]) return (*this)[index] < another[index];
}
return false;
}
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[n-1-i] != num[n-1-i]){
return mod[n-1-i] > num[n-1-i];
}
}
return true;
}
static void div_(const MPI& a, const MPI& b, MPI& res){
vector<MPI> mult(9);
MPI mod;
mult[0] = b;
for(int i = 0; i < 8; i++) add(mult[i], b, mult[i+1]);
for(int i = (int)a.size() - 1; i >= 0; i--){
if(mod.isZero()){
mod.back() = a[i];
}else{
mod.push_front(a[i]);
}
if(div_geq(mod, b)){
int l = 0, r = 9;
while(r-l>1){
int mid = (l+r)/2;
if(mod < mult[mid]){
r = mid;
}else{
l = mid;
}
}
MPI mod_ = mod;
sub(mod_, mult[l], mod);
res.push_front(l+1);
}else{
res.push_front(0);
}
}
trim_digit(res);
}
};
static void mpi_bmpi(MPI& a, const BMPI& b){
if(b.zero){ a = MPI(0); return; }
int n = (int)b.size();
a.resize(n);
for(int i = 0; i < n; i++) a[i] = b[i];
}
static void bmpi_mpi(BMPI& a, const MPI& b){
if(b.isZero()){ a = BMPI(); return; }
int n = (int)b.size();
a.resize(n);
for(int i = 0; i < n; i++) a[i] = b[i];
}
public:
bool sign, zero;
long long ex;
BMPI() : zero(true){}
BMPI(long long val) : sign(false), zero(false), ex(0){
if(val == 0){ zero = true; return; }
if(val < 0) sign = true, val = -val;
while(val) push_back(val%10), val /= 10;
trim_digit(*this);
}
BMPI(const string& s) : sign(false), zero(false), ex(0){
if(s.empty() || s == "0"){ zero = true; return; }
if(s[0] == '-') sign = true;
for(int i = (int)s.size() - 1; i >= sign; i--){
if(s[i] == '.'){
ex = i + 1 - (int)s.size();
}else{
push_back(s[i]-'0');
}
}
trim_digit(*this);
}
friend ostream& operator<<(ostream& os, const BMPI& num) {
if(num.zero){ os << "0."; for(int i = 0; i < acc-1; i++) os << '0';
os << "+e0"; return os; }
if(num.sign) os << '-';
os << num.back() << '.';
for(int i = 0; i < acc-1; i++) os << num[acc-2-i];
os << 'e';
if(num.ex+acc-1 >= 0) os << '+';
os << num.ex+acc-1;
return os;
}
friend istream& operator>>(istream& is, BMPI& num) {
string s;
is >> s;
num = BMPI(s);
return is;
}
void print_decimal(int decimal) const {
if(zero){ cout << "0."; for(int i = 0; i < decimal; i++) cout << '0';}
if(sign) cout << '-';
for(int i = max(ex+acc-1,0LL); i >= -decimal; i--){
cout << ((i-ex >= 0 || i-ex >= acc)?(*this)[i-ex]:'0');
if(i == 0) cout << '.';
}
}
BMPI& operator=(long long num) {
*this = BMPI(num);
return *this;
}
bool operator<(const BMPI& num) const {
if(zero) return !num.zero && !num.sign;
if(num.zero) return sign;
if(sign ^ num.sign) return sign;
if(ex != num.ex) return (ex < num.ex) ^ sign;
for(int index = acc - 1; index >= 0; index--){
if((*this)[index] != num[index]) return ((*this)[index] < num[index]) ^ sign;
}
return false;
}
bool operator<(const long long num) const {
return *this < BMPI(num);
}
friend bool operator<(const long long num, const BMPI& another){
return BMPI(num) < another;
}
bool operator>(const BMPI& num) const {
return num < *this;
}
bool operator>(const long long num) const {
return *this > BMPI(num);
}
friend bool operator>(const long long num, const BMPI& another){
return BMPI(num) > another;
}
bool operator<=(const BMPI& num) const {
return !(*this > num);
}
bool operator<=(const long long num) const {
return *this <= BMPI(num);
}
friend bool operator<=(const long long num, const BMPI& another){
return BMPI(num) <= another;
}
bool operator>=(const BMPI& num) const {
return !(*this < num);
}
bool operator>=(const long long num) const {
return *this >= BMPI(num);
}
friend bool operator>=(const long long num, const BMPI& another){
return BMPI(num) >= another;
}
bool operator==(const BMPI& num) const {
if(zero || num.zero) return zero && num.zero;
if(sign ^ num.sign) return false;
if(ex != num.ex) return false;
for(int index = acc - 1; index >= 0; index--){
if((*this)[index] != num[index]) return false;
}
return true;
}
bool operator==(const long long num) const {
return *this == BMPI(num);
}
friend bool operator==(const long long num, const BMPI& another){
return BMPI(num) == another;
}
bool operator!=(const BMPI& num) const {
return !(*this == num);
}
bool operator!=(const long long num) const {
return *this != BMPI(num);
}
friend bool operator!=(const long long num, const BMPI& another){
return BMPI(num) != another;
}
explicit operator bool() const noexcept { return !zero; }
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(); }
BMPI operator+() const {
return *this;
}
BMPI operator-() const {
BMPI res = *this;
res.sign = !sign;
return res;
}
friend BMPI abs(const BMPI& num){
BMPI res = num;
res.sign = false;
return res;
}
BMPI operator+(const BMPI& num) const {
if(zero){ BMPI res = num; return res; }
if(num.zero){ BMPI res = *this; return res; }
BMPI 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;
}
BMPI operator+(long long num) const {
return *this + BMPI(num);
}
friend BMPI operator+(long long a, const BMPI& b){
return b + a;
}
BMPI& operator+=(const BMPI& num){
*this = *this + num;
return *this;
}
BMPI& operator+=(long long num){
*this = *this + num;
return *this;
}
BMPI& operator++(){
return *this += 1;
}
BMPI operator++(int){
BMPI res = *this;
*this += 1;
return res;
}
BMPI operator-(const BMPI& num) const {
if(zero){ BMPI res = num; res.sign = !res.sign; return res; }
if(num.zero){ BMPI res = *this; return res; }
if(sign != num.sign){
BMPI res; res.sign = sign;
add(*this, num, res);
return res;
}
BMPI res; res.sign = (abs_less(*this, num) ^ sign);
if(res.sign){
sub(num, *this, res);
}else{
sub(*this, num, res);
}
return res;
}
BMPI operator-(long long num) const {
return *this - BMPI(num);
}
friend BMPI operator-(long long a, const BMPI& b){
return b - a;
}
BMPI& operator-=(const BMPI& num){
*this = *this - num;
return *this;
}
BMPI& operator-=(long long num){
*this = *this - num;
return *this;
}
BMPI& operator--(){
return *this -= 1;
}
BMPI operator--(int){
BMPI res = *this;
*this -= 1;
return res;
}
BMPI operator*(const BMPI& num) const {
if(zero || num.zero) return BMPI();
BMPI res; res.zero = false; res.sign = (sign^num.sign);
res.ex = ex + num.ex;
mul(*this, num, res);
return res;
}
BMPI operator*(long long num) const {
return *this * BMPI(num);
}
friend BMPI operator*(long long a, const BMPI& b){
return b * a;
}
BMPI& operator*=(const BMPI& num){
*this = *this * num;
return *this;
}
BMPI& operator*=(long long num){
*this = *this * num;
return *this;
}
BMPI operator/(const BMPI& num) const {
assert(!num.zero);
if(zero){ return BMPI(); }
MPI kp, res_, num_;
mpi_bmpi(num_, num);
BMPI res; res.zero = false; res.sign = (sign^num.sign); res.ex = ex - num.ex;
mpi_bmpi(kp, *this);
if(abs_less(*this, num)) kp.push_front(0), res.ex--;
for(int i = 0; i < acc; i++) kp.push_front(0), res.ex--;
MPI::div_(kp, num_, res_);
bmpi_mpi(res, res_);
trim_digit(res);
return res;
}
BMPI operator/(long long num) const {
return *this / BMPI(num);
}
friend BMPI operator/(long long a, const BMPI& b){
return b / a;
}
BMPI& operator/=(const BMPI& num){
*this = *this / num;
return *this;
}
BMPI& operator/=(long long num){
*this = *this / num;
return *this;
}
BMPI div2() const {
if(zero) return BMPI();
BMPI res = *this;
int carry = 0;
for(int i = acc-1; i >= 0; i--){
int val = (*this)[i]+carry*10;
carry = val%2;
if(i != acc-1 || val >= 2){
res[i] = val/2;
}else{
res[i] = 0;
}
}
if(carry) res.push_front(5), res.ex--;
trim_digit(res);
return res;
}
friend BMPI sqrt(BMPI x){
if(x <= BMPI(0)) return BMPI();
BMPI s = 1, t = x;
while(s < t){
s = s + s, t = t.div2();
}
do{ t = s, s = (x / s + s).div2();
}while(s < t);
trim_digit(t);
return t;
}
friend BMPI log10(const BMPI& x){
assert(x > BMPI(0));
return BMPI(acc + x.ex);
}
friend BMPI pow(BMPI a, long long b){
if(a.zero) return BMPI();
assert(b >= 0);
BMPI res(1);
while(b){
if(b % 2) res *= a;
a *= a;
b = b/2;
}
return res;
}
};
const int ACC = 25;
int main()
{
cin.tie(0);
ios::sync_with_stdio(false);
int n;
cin >> n;
rep(i,n){
BMPI<ACC> x;
ll y;
cin >> x >> y;
BMPI<ACC> z = pow(x,y);
cout << z[ACC-1] << " " << z[ACC-2] << " " << z.ex+ACC-1 << "\n";
}
return 0;
}