#859512 (C++17) No.2271 平方根の１３桁精度近似計算

提出ソース

結果

問題	No.2271 平方根の１３桁精度近似計算
ユーザー	heno239
提出日時	2023-04-14 22:34:33
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	WA
実行時間	-
コード長	7,284 bytes
コンパイル時間	1,892 ms
コンパイル使用メモリ	150,908 KB
実行使用メモリ	11,980 KB
最終ジャッジ日時	2024-10-10 13:31:04
合計ジャッジ時間	23,454 ms
ジャッジサーバーID （参考情報）	judge2 / judge4

このコードへのチャレンジ
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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	9 ms 11,648 KB
testcase_01	AC	8 ms 11,852 KB
testcase_02	AC	8 ms 11,716 KB
testcase_03	AC	8 ms 11,724 KB
testcase_04	AC	8 ms 11,852 KB
testcase_05	AC	9 ms 11,720 KB
testcase_06	AC	9 ms 11,720 KB
testcase_07	AC	1,919 ms 11,720 KB
testcase_08	AC	1,917 ms 11,648 KB
testcase_09	AC	8 ms 11,724 KB
testcase_10	WA	-
testcase_11	AC	8 ms 11,776 KB
testcase_12	WA	-
testcase_13	AC	8 ms 11,844 KB
testcase_14	AC	1,922 ms 11,848 KB
testcase_15	AC	9 ms 11,904 KB
testcase_16	WA	-
testcase_17	AC	8 ms 11,848 KB
testcase_18	AC	1,918 ms 11,720 KB
testcase_19	AC	8 ms 11,848 KB
testcase_20	AC	8 ms 11,724 KB
testcase_21	AC	1,918 ms 11,720 KB
testcase_22	AC	8 ms 11,720 KB
testcase_23	WA	-
testcase_24	AC	8 ms 11,724 KB
testcase_25	AC	1,920 ms 11,776 KB
testcase_26	AC	9 ms 11,724 KB
testcase_27	AC	1,917 ms 11,648 KB
testcase_28	WA	-
testcase_29	AC	8 ms 11,716 KB
testcase_30	AC	1,918 ms 11,776 KB
testcase_31	AC	8 ms 11,716 KB
testcase_32	AC	1,918 ms 11,648 KB
testcase_33	AC	8 ms 11,648 KB
testcase_34	WA	-
testcase_35	AC	9 ms 11,848 KB
testcase_36	WA	-
testcase_37	AC	9 ms 11,844 KB
testcase_38	AC	8 ms 11,776 KB
testcase_39	AC	1,916 ms 11,648 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;
//ll mod = 1;
//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;

using ld = long double;
typedef pair<ld, ld> LDP;
const ld eps = 1e-10;
const ld pi = acosl(-1.0);

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>
vector<T> vmerge(vector<T>& a, vector<T>& b) {
	vector<T> res;
	int ida = 0, idb = 0;
	while (ida < a.size() || idb < b.size()) {
		if (idb == b.size()) {
			res.push_back(a[ida]); ida++;
		}
		else if (ida == a.size()) {
			res.push_back(b[idb]); idb++;
		}
		else {
			if (a[ida] < b[idb]) {
				res.push_back(a[ida]); ida++;
			}
			else {
				res.push_back(b[idb]); idb++;
			}
		}
	}
	return res;
}
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;
}
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 };

//-----------------------------------------


int calc5(ll x) {
	int res = 0;
	while (x % 5 == 0) {
		x /= 5; res++;
	}
	return res;
}
bool issquare(ll x) {
	if (x < 0)return false;
	ll k = sqrt(round(x));
	while (k * k < x)k++;
	while (k * k > x)k--;
	return k * k == x;
}
//x,yがax+by=gcd(a,b)の解になる
ll extgcd(ll a, ll b, ll& x, ll& y) {
	ll d = a;
	if (b != 0) {
		d = extgcd(b, a % b, y, x);
		y -= (a / b) * x;
	}
	else {
		x = 1; y = 0;
	}
	return d;
}
//aのmod mでの逆元を求める
ll mod_inverse(ll a, ll m) {
	ll x, y;
	extgcd(a, m, x, y);
	return (m + x % m) % m;
}
ll sup = (1ll << 58);
void solve() {
	auto start_time = clock();
	ll n; cin >> n;
	int e; cin >> e;
	ll ad = 1;
	rep(i, e)ad *= 5;
	ll r = n % ad;
	if (r < 0)r += ad;

	int de = (e + 1) / 2;
	ll rad = 1; rep(i, de)rad *= 5;
	rep(b, rad) {
		ll z = r - b * b;
		z %= ad; if (z < 0)z += ad;
		ll a;
		if (z == 0) {
			a = 0;
		}
		else {
			ll mm = ad;
			if (b == 0)continue;
			int cnt = 0;
			rep(i, de) {
				if (z % 5 == 0) {
					z /= 5;
					cnt++;
				}
			}
			if (cnt != de)continue;
			rep(i, de)mm /= 5;
			int cb = calc5(b);
			int cz = calc5(z);
			if (cb > cz)continue;
			ll copb = b;
			rep(i, cb) {
				copb /= 5;
				z /= 5;
				mm /= 5;
			}
			ll rev = mod_inverse(2 * copb, mm); rev %= mm;
			a = z * rev % mm;
		}
		ll r = a * rad + b;
		cout << r << "\n"; return;
		if (r <= (1ll << 29)) {
			
		}
	}

	n = r;
	while (n <= sup) {
		auto cur_time = clock();
		ld dif = (cur_time - start_time) / (ld)CLOCKS_PER_SEC;
		if (dif >= 1.9)break;
		if (issquare(n))break;
		n += ad;
	}
	if (n <= sup && issquare(n)) {
		ll k = sqrt(round(n));
		while (k * k < n)k++;
		while (k * k > n)k--;
		cout << k << "\n";
	}
	else {
		cout << "NaN\n";
	}

}



signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	//cout << fixed << setprecision(12);
	//init_f();
	//init();
	//while(true)
	//expr();
	//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