結果
| 問題 |
No.407 鴨等素数間隔列の数え上げ
|
| コンテスト | |
| ユーザー |
 はむこ
|
| 提出日時 | 2016-08-05 22:36:23 |
| 言語 | C++11（廃止可能性あり） (gcc 13.3.0) |
| 結果 |
AC
|
| 実行時間 | 434 ms / 1,000 ms |
| コード長 | 9,491 bytes |
| コンパイル時間 | 1,573 ms |
| コンパイル使用メモリ | 182,104 KB |
| 実行使用メモリ | 87,796 KB |
| 最終ジャッジ日時 | 2024-12-15 19:38:09 |
| 合計ジャッジ時間 | 5,707 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge1 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 5 |
| other | AC * 31 |
ソースコード
#include <bits/stdc++.h>
using namespace std;
#ifdef _WIN32
#define scanfll(x) scanf("%I64d", x)
#define printfll(x) printf("%I64d", x)
#else
#define scanfll(x) scanf("%lld", x)
#define printfll(x) printf("%lld", x)
#endif
#define rep(i,n) for(long long i = 0; i < (long long)(n); i++)
#define repi(i,a,b) for(long long i = (long long)(a); i < (long long)(b); i++)
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define fi first
#define se second
#define mt make_tuple
#define mp make_pair
template<class T1, class T2> bool chmin(T1 &a, T2 b) { return b < a && (a = b, true); }
template<class T1, class T2> bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }
using ll = long long; using ld = long double; using vll = vector<ll>; using vvll = vector<vll>; using vld = vector<ld>;
using vi = vector<int>; using vvi = vector<vi>;
vll conv(vi& v) { vll r(v.size()); rep(i, v.size()) r[i] = v[i]; return r; }
using P = pair<ll, ll>;
template <typename T, typename U> ostream &operator<<(ostream &o, const pair<T, U> &v) { o << "(" << v.first << ", " << v.second << ")"; return o; }
template<size_t...> struct seq{}; template<size_t N, size_t... Is> struct gen_seq : gen_seq<N-1, N-1, Is...>{}; template<size_t... Is> struct gen_seq<0, Is...> : seq<Is...>{};
template<class Ch, class Tr, class Tuple, size_t... Is>
void print_tuple(basic_ostream<Ch,Tr>& os, Tuple const& t, seq<Is...>){ using s = int[]; (void)s{0, (void(os << (Is == 0? "" : ", ") << get<Is>(t)), 0)...}; }
template<class Ch, class Tr, class... Args>
auto operator<<(basic_ostream<Ch, Tr>& os, tuple<Args...> const& t) -> basic_ostream<Ch, Tr>& { os << "("; print_tuple(os, t, gen_seq<sizeof...(Args)>()); return os << ")"; }
ostream &operator<<(ostream &o, const vvll &v) { rep(i, v.size()) { rep(j, v[i].size()) o << v[i][j] << " "; cout << endl; } return o; }
template <typename T> ostream &operator<<(ostream &o, const vector<T> &v) { o << '['; rep(i, v.size()) o << v[i] << (i != v.size()-1 ? ", " : ""); o << "]"; return o; }
template <typename T> ostream &operator<<(ostream &o, const set<T> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]"; return o; }
template <typename T, typename U> ostream &operator<<(ostream &o, const map<T, U> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]"; return o; }
template <typename T, typename U> ostream &operator<<(ostream &o, const unordered_map<T, U> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it; o << "]"; return o; }
void printbits(ll mask, ll n) { rep(i, n) { cout << !!(mask & (1ll << i)); } cout << endl; }
#define ldout fixed << setprecision(40)
static const double EPS = 1e-14;
static const long long INF = 1e18;
static const long long mo = 1e9+7;
/**********************************************************/
// 前処理ありの素数判定
// 素数の最大値Mに対して先にconstructPrimesList(M)が必須！
/**********************************************************/
// O(n log n)
void sieve_of_eratosthenes(vector<ll>& primes, ll n) {
primes.resize(n);
for (ll i = 2; i < n; ++i)
primes[i] = i;
for (ll i = 2; i*i < n; ++i)
if (primes[i])
for (ll j = i*i; j < n; j+=i)
primes[j] = 0;
}
void getPrimesList(ll n, vector<ll>& primes_list) {
vector<ll> tmpList;
primes_list.clear(); primes_list.resize(0); primes_list.reserve(n / 5);
sieve_of_eratosthenes(tmpList, n);
rep(i, n) {
if (tmpList[i])
primes_list.push_back(i);
}
}
// 素数テーブル構築: O(n log n)
vector<ll> primesList; // 素数リスト（primesListMaxまで）。こいつ自体を使うことあるかも。
set<ll> primesSet;
ll primesListMax;
void constructPrimesList(ll n) {
if (primesListMax >= n)
return;
primesListMax = n;
getPrimesList(n, primesList);
for (ll i = 0; i < primesList.size(); i++) {
primesSet.insert(primesList[i]);
}
}
// constructされていないなら、O(n log n)
// constructされているなら、O(log n)
bool isPrimeLookup(ll n) {
return primesSet.count(n);
}
// constructされていないなら、O(sqrt(n) log n)
// constructされているなら、O(log n)
// Divisor系は、最大nをMAXNとしてconstructPrimesList(sqrt(MAXN))で早くなる
void getPrimeFactorizationList(ll n, vector<ll>& divisors_list) {
divisors_list.clear(); divisors_list.resize(0);
if (n <= 1) return;
ll prime = 2;
while (n >= prime * prime) {
if (n % prime == 0) {
divisors_list.push_back(prime);
n /= prime;
} else {
prime++;
}
}
divisors_list.push_back(n);
}
// constructされていないなら、O(sqrt(n) log n)
// constructされているなら、O(log n)
// Divisor系は、最大nをMAXNとしてconstructPrimesList(sqrt(MAXN))で早くなる
void getDivisorsList(ll n, vector<ll>& divisors_list) {
divisors_list.clear(); divisors_list.resize(0);
vector<ll> fac_list;
getPrimeFactorizationList(n, fac_list);
map<ll, ll> counter;
for (auto x : fac_list)
counter[x]++;
divisors_list.push_back(1);
for (auto x : counter) {
ll tmp_size = divisors_list.size();
ll p = 1;
for (ll i = 0; i < x.second; i++) {
p *= x.first;
for (ll j = 0; j < tmp_size; j++)
divisors_list.push_back(divisors_list[j] * p);
}
}
sort(divisors_list.begin(), divisors_list.end());
}
// constructされていないなら、O(sqrt(n) log n)
// constructされているなら、O(log n)
ll getDivisorsNum(ll n) {
vector<ll> divisors_list; getPrimeFactorizationList(n, divisors_list);
map<ll, ll> num;
for (ll i = 0; i < divisors_list.size(); i++) {
num[divisors_list[i]]++;
}
ll p = 1;
for (auto x : num) {
p *= x.second + 1;
}
return p;
}
/**********************************************************/
// 前処理なしの素数判定
/**********************************************************/
// Millar-Rabin Test
using ull = unsigned long long;
bool isPrimeSmall(const ll &n){
if(n == 2) return true;
if(n < 2 || n%2 == 0) return false;
const ll m = n-1, d = m / (m & -m);
auto modpow = [&](ll a, ll b){
ll res = 1;
while(b){
if(b&1) res = res*a%n;
a = a*a%n;
b >>= 1;
}
return res;
};
auto suspect = [&](ll a, ll t){
a = modpow(a,t);
while(t != -1+n && a != 1 && a != -1+n){
a = a*a%n;
t *= 2;
}
return a == n-1 || t%2 == 1;
};
static const ll witness[] = {2,7,61,0}; // n <= 2^32
for(const ll *w = witness; *w < n && *w; w++){
if(!suspect(*w,d)) return false;
}
return true;
}
bool isPrimeLarge(const ll &n){
if(n == 2) return true;
if(n < 2 || n%2 == 0) return false;
const ll m = n-1, d = m / (m & -m);
auto modmul = [&](ll a, ll b){
ll res = 0;
while(b){
if(b&1) res = ((ull)res+a)%n;
a = ((ull)a+a)%n;
b >>= 1;
}
return res;
};
auto modpow = [&](ll a, ll b){
ll res = 1;
while(b){
if(b&1) res = modmul(res,a);
a = modmul(a,a);
b >>= 1;
}
return res;
};
auto suspect = [&](ll a, ll t){
a = modpow(a,t);
while(t != -1+n && a != 1 && a != -1+n){
a = modmul(a,a);
t *= 2;
}
return a == n-1 || t%2 == 1;
};
static const ll witness[] = {2,325,9375,28178,450775,9780504,1795265022,0}; // n <= 2^64
for(const ll *w = witness; *w < n && *w; w++){
if(!suspect(*w,d)) return false;
}
return true;
}
bool isPrime(const ll &n){
return n < INT_MAX ? isPrimeSmall(n) : isPrimeLarge(n);
}
// ガウス素数＝複素数の素数判定
bool isGaussianPrime(ll a, ll b) {
if (a < 0) a = -a;
if (b < 0) b = -b;
if (a == 0) return b % 4 == 3 && isPrime(b);
if (b == 0) return a % 4 == 3 && isPrime(a);
return isPrime(a*a+b*b);
}
// 区間篩
// O( n log n )．
const ll N = 100000000; // MAXPRIME
const ll M = 10000; // SQRT(N)
const ll K = 6000000; // NUMBER OF PRIMES, CHOOSE 9/8 * N / LOG(N)
vector<ll> iterativeSieve() {
static ll p[K], table[M];
for (ll i = 2; i < M; ++i) p[i] = i;
for (ll i = 2; i*i < M; ++i)
if (p[i])
for (ll j = i*i; j < M; j += i)
p[j] = 0;
p[0] = p[1] = 0;
ll num = remove(p, p+M, 0) - p;
for (ll m = M; m < N; m += M) {
for (ll x = m; x < m+M; ++x)
table[x-m] = x;
for (ll i = 0, j; p[i]*p[i] < m+M; ++i) {
if (p[i] >= m) j = p[i] * p[i];
else if (m % p[i] == 0) j = m;
else j = m - (m % p[i]) + p[i];
for (; j < m+M; j += p[i]) table[j-m] = 0;
}
num = remove_copy(table, table+M, p+num, 0) - p;
}
return vector<ll>(p, p+num);
}
int main(void) {
cin.tie(0); ios::sync_with_stdio(false);
ll n, l; cin >> n >> l;
constructPrimesList(l);
ll ret = 0;
for (auto p : primesList) {
ll tmp = p * (n - 1);
if (tmp <= l)
ret += l - tmp + 1;
}
cout << ret << endl;
return 0;
}