#833060 (C++17) No.2192 平方数の下１４桁

提出ソース

結果

問題	No.2192 平方数の下１４桁
ユーザー	heno239
提出日時	2023-01-13 23:22:17
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	113 ms / 2,000 ms
コード長	7,378 bytes
コンパイル時間	2,369 ms
コンパイル使用メモリ	157,300 KB
実行使用メモリ	11,852 KB
最終ジャッジ日時	2024-06-07 00:11:23
合計ジャッジ時間	4,946 ms
ジャッジサーバーID （参考情報）	judge5 / judge3

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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	AC	8 ms 11,720 KB
testcase_01	AC	8 ms 11,716 KB
testcase_02	AC	8 ms 11,720 KB
testcase_03	AC	8 ms 11,724 KB
testcase_04	AC	9 ms 11,720 KB
testcase_05	AC	8 ms 11,724 KB
testcase_06	AC	8 ms 11,596 KB
testcase_07	AC	8 ms 11,724 KB
testcase_08	AC	8 ms 11,716 KB
testcase_09	AC	9 ms 11,720 KB
testcase_10	AC	9 ms 11,852 KB
testcase_11	AC	9 ms 11,720 KB
testcase_12	AC	8 ms 11,724 KB
testcase_13	AC	9 ms 11,592 KB
testcase_14	AC	9 ms 11,592 KB
testcase_15	AC	9 ms 11,716 KB
testcase_16	AC	9 ms 11,724 KB
testcase_17	AC	14 ms 11,720 KB
testcase_18	AC	14 ms 11,592 KB
testcase_19	AC	106 ms 11,848 KB
testcase_20	AC	110 ms 11,596 KB
testcase_21	AC	111 ms 11,720 KB
testcase_22	AC	113 ms 11,716 KB
testcase_23	AC	111 ms 11,588 KB
testcase_24	AC	112 ms 11,592 KB
testcase_25	AC	113 ms 11,716 KB
testcase_26	AC	113 ms 11,720 KB
testcase_27	AC	8 ms 11,716 KB
testcase_28	AC	8 ms 11,716 KB
testcase_29	AC	9 ms 11,724 KB
testcase_30	AC	9 ms 11,720 KB
testcase_31	AC	8 ms 11,720 KB
testcase_32	AC	8 ms 11,592 KB
testcase_33	AC	8 ms 11,720 KB
testcase_34	AC	8 ms 11,716 KB
testcase_35	AC	8 ms 11,716 KB
testcase_36	AC	8 ms 11,592 KB
testcase_37	AC	9 ms 11,844 KB
testcase_38	AC	8 ms 11,592 KB
testcase_39	AC	8 ms 11,724 KB
testcase_40	AC	111 ms 11,848 KB
testcase_41	AC	111 ms 11,720 KB
testcase_42	AC	113 ms 11,596 KB
testcase_43	AC	112 ms 11,588 KB

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ソースコード

raw source code

#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<unordered_set>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
#include<array>
#include<chrono>
using namespace std;

//#define int long long
typedef long long ll;

typedef unsigned long long ul;
typedef unsigned int ui;
constexpr ll mod = 998244353;
//constexpr ll mod = 1000000007;
const ll INF = mod * mod;
typedef pair<int, int>P;

#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
#define all(v) (v).begin(),(v).end()
typedef pair<ll, ll> LP;

template<typename T>
void chmin(T& a, T b) {
	a = min(a, b);
}
template<typename T>
void chmax(T& a, T b) {
	a = max(a, b);
}
template<typename T>
void cinarray(vector<T>& v) {
	rep(i, v.size())cin >> v[i];
}
template<typename T>
void coutarray(vector<T>& v) {
	rep(i, v.size()) {
		if (i > 0)cout << " "; cout << v[i];
	}
	cout << "\n";
}
ll mod_pow(ll x, ll n, ll m = mod) {
	if (n < 0) {
		ll res = mod_pow(x, -n, m);
		return mod_pow(res, m - 2, m);
	}
	if (abs(x) >= m)x %= m;
	if (x < 0)x += m;
	//if (x == 0)return 0;
	ll res = 1;
	while (n) {
		if (n & 1)res = res * x % m;
		x = x * x % m; n >>= 1;
	}
	return res;
}
//mod should be <2^31
struct modint {
	int n;
	modint() :n(0) { ; }
	modint(ll m) {
		if (m < 0 || mod <= m) {
			m %= mod; if (m < 0)m += mod;
		}
		n = m;
	}
	operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
bool operator<(modint a, modint b) { return a.n < b.n; }
modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= (int)mod; return a; }
modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += (int)mod; return a; }
modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; }
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, ll n) {
	if (n == 0)return modint(1);
	modint res = (a * a) ^ (n / 2);
	if (n % 2)res = res * a;
	return res;
}

ll inv(ll a, ll p) {
	return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }
modint operator/=(modint& a, modint b) { a = a / b; return a; }
const int max_n = 1 << 20;
modint fact[max_n], factinv[max_n];
void init_f() {
	fact[0] = modint(1);
	for (int i = 0; i < max_n - 1; i++) {
		fact[i + 1] = fact[i] * modint(i + 1);
	}
	factinv[max_n - 1] = modint(1) / fact[max_n - 1];
	for (int i = max_n - 2; i >= 0; i--) {
		factinv[i] = factinv[i + 1] * modint(i + 1);
	}
}
modint comb(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[b] * factinv[a - b];
}
modint combP(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[a - b];
}

ll gcd(ll a, ll b) {
	a = abs(a); b = abs(b);
	if (a < b)swap(a, b);
	while (b) {
		ll r = a % b; a = b; b = r;
	}
	return a;
}
using ld = long double;
//typedef long double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-10;
const ld pi = acosl(-1.0);
template<typename T>
void addv(vector<T>& v, int loc, T val) {
	if (loc >= v.size())v.resize(loc + 1, 0);
	v[loc] += val;
}
/*const int mn = 2000005;
bool isp[mn];
vector<int> ps;
void init() {
	fill(isp + 2, isp + mn, true);
	for (int i = 2; i < mn; i++) {
		if (!isp[i])continue;
		ps.push_back(i);
		for (int j = 2 * i; j < mn; j += i) {
			isp[j] = false;
		}
	}
}*/

//[,val)
template<typename T>
auto prev_itr(set<T>& st, T val) {
	auto res = st.lower_bound(val);
	if (res == st.begin())return st.end();
	res--; return res;
}

//[val,)
template<typename T>
auto next_itr(set<T>& st, T val) {
	auto res = st.lower_bound(val);
	return res;
}
using mP = pair<modint, modint>;
mP operator+(mP a, mP b) {
	return { a.first + b.first,a.second + b.second };
}
mP operator+=(mP& a, mP b) {
	a = a + b; return a;
}
mP operator-(mP a, mP b) {
	return { a.first - b.first,a.second - b.second };
}
mP operator-=(mP& a, mP b) {
	a = a - b; return a;
}
LP operator+(LP a, LP b) {
	return { a.first + b.first,a.second + b.second };
}
LP operator+=(LP& a, LP b) {
	a = a + b; return a;
}
LP operator-(LP a, LP b) {
	return { a.first - b.first,a.second - b.second };
}
LP operator-=(LP& a, LP b) {
	a = a - b; return a;
}

mt19937 mt(time(0));

const string drul = "DRUL";
string senw = "SENW";
//DRUL,or SENW
int dx[4] = { 1,0,-1,0 };
int dy[4] = { 0,1,0,-1 };
//-----------------------------------------

using T = __int128;
using PT = pair<T, T>;
//x^2=y mod p
bool exi_sqrt(ll _p, ll y) {
	T p = _p;
	if (y == 0)return true;
	if (p == 2)return true;
	uniform_int_distribution<ll> udp(0, p - 1);
	auto mul = [&](PT a, PT b) {
		PT res;
		res.first = 0, res.second = 0;
		res.first = (a.first * b.first + a.second * b.second % p * y) % p;
		res.second = (a.first * b.second + a.second * b.first) % p;
		return res;
	};
	auto cur_pow = [&](T a) {
		T res = 1;
		ll cop = p - 2;
		while (cop > 0) {
			if (cop & 1) {
				res = res * a % p;
			}
			cop >>= 1; if (cop == 0)break; a = a * a % p;
		}
		return res;
	};
	rep(_, 100) {
		ll h = udp(mt);
		//(x-h)^((p-1)/2)-1 mod x^2-d
		PT cur = { (p - h) % p,1 };
		PT z = { 1,0 };
		ll cop = (p - 1) / 2;
		while (cop > 0) {
			if (cop & 1)z = mul(z, cur);
			cop >>= 1; if (cop == 0)break; cur = mul(cur, cur);
		}
		z.first--;
		if (z.first < 0)z.first += p;
		if (z.second > 0) {
			T a = z.second, b = z.first;
			T ra = cur_pow(a);
			T rr = ra * ra % p * b % p * b % p - y;
			if (rr % p == 0) {
				return true;
			}
		}
	}
	return false;
}

//x^2 = A mod p^r
bool iscan(ll A, ll p, int r) {
	if (r == 1) {
		return exi_sqrt(p, A);
	}
	else {
		vector<ll> ps(r + 1);
		ps[0] = 1;
		rep(i, r)ps[i + 1] = ps[i] * p;
		vector<ll> objs(r + 1);
		rep(i, r + 1)objs[i] = A % ps[i];
		T cur = 0;
		bool res = false;
		/*if (p == 5) {
			cout << A << " "<<objs[1]<<"\n";
		}*/
		function<void(int)>dfs = [&](int dep) {
			if (dep == r) {
				res = true;
				return;
			}
			rep(i, p) {
				cur += ps[dep] * i;
				if (cur * cur % ps[dep + 1] == objs[dep + 1]) {
					dfs(dep + 1);
					if (res)return;
				}
				cur -= ps[dep] * i;
			}
		};
		dfs(0);
		return res;
	}
	return false;
}
void solve() {
	ll b, A; cin >> b >> A;
	vector<LP> ps;
	for (int i = 2; (ll)i * i <= b; i++) {
		if (b % i == 0) {
			int cnt = 0;
			while (b % i == 0) {
				cnt++; b /= i;
			}
			ps.push_back({ i,cnt });
		}
	}
	if (b > 1) {
		ps.push_back({ b,1 });
	}
	for (auto p : ps) {
		ll pp = 1;
		rep(i, p.second)pp *= p.first;
		ll obj = A % pp;
		if (!iscan(obj, p.first, p.second)) {
			//cout << "? " << p.first << " " << p.second << "\n";
			cout << "NO\n"; return;
		}
	}
	cout << "YES\n";
}


signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	//cout << fixed << setprecision(10);
	//init_f();
	//init();
	//expr();
	//while(true)
	//int t; cin >> t; rep(i, t)
	solve();
	return 0;
}

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結果

テストケース

ソースコード