結果
| 問題 |
No.1322 Totient Bound
|
| コンテスト | |
| ユーザー |
 noimi
|
| 提出日時 | 2020-12-09 19:11:18 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 1,020 ms / 5,000 ms |
| コード長 | 15,994 bytes |
| コンパイル時間 | 2,995 ms |
| コンパイル使用メモリ | 227,516 KB |
| 最終ジャッジ日時 | 2025-01-16 20:57:05 |
|
ジャッジサーバーID （参考情報） |
judge2 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 36 |
ソースコード
#pragma region Macros
#include <bits/stdc++.h>
#define ll long long
#define ld long double
#define rep2(i, a, b) for(ll i = a; i <= b; ++i)
#define rep(i, n) for(ll i = 0; i < n; ++i)
#define rep3(i, a, b) for(ll i = a; i >= b; --i)
#define pii pair<int, int>
#define pll pair<ll, ll>
#define pb push_back
#define eb emplace_back
#define vi vector<int>
#define vll vector<ll>
#define vpi vector<pii>
#define vpll vector<pll>
#define overload2(_1, _2, name, ...) name
#define vec(type, name, ...) vector<type> name(__VA_ARGS__)
#define VEC(type, name, size) \
vector<type> name(size); \
IN(name)
#define vv(type, name, h, ...) vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define VV(type, name, h, w) \
vector<vector<type>> name(h, vector<type>(w)); \
IN(name)
#define vvv(type, name, h, w, ...) vector<vector<vector<type>>> name(h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...) \
vector<vector<vector<vector<type>>>> name(a, vector<vector<vector<type>>>(b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
#define mt make_tuple
#define fi first
#define se second
#define all(c) begin(c), end(c)
#define lb(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define ub(c, x) distance((c).begin(), upper_bound(all(c), (x)))
using namespace std;
constexpr pii dx4[4] = {pii{1, 0}, pii{0, 1}, pii{-1, 0}, pii{0, -1}};
constexpr pii dx8[8] = {{1, 0}, {1, 1}, {0, 1}, {-1, 1}, {-1, 0}, {-1, -1}, {0, -1}, {1, -1}};
const string YESNO[2] = {"NO", "YES"};
const string YesNo[2] = {"No", "Yes"};
const string yesno[2] = {"no", "yes"};
void YES(bool t = 1) { cout << YESNO[t] << endl; }
void Yes(bool t = 1) { cout << YesNo[t] << endl; }
void yes(bool t = 1) { cout << yesno[t] << endl; }
template <class T> using vc = vector<T>;
template <class T> using vvc = vector<vc<T>>;
template <class T> using vvvc = vector<vvc<T>>;
template <class T> using vvvvc = vector<vvvc<T>>;
template <class T> using pq = priority_queue<T>;
template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>;
#define si(c) (int)(c).size()
#define INT(...) \
int __VA_ARGS__; \
IN(__VA_ARGS__)
#define LL(...) \
ll __VA_ARGS__; \
IN(__VA_ARGS__)
#define STR(...) \
string __VA_ARGS__; \
IN(__VA_ARGS__)
#define CHR(...) \
char __VA_ARGS__; \
IN(__VA_ARGS__)
#define DBL(...) \
double __VA_ARGS__; \
IN(__VA_ARGS__)
int scan() { return getchar(); }
void scan(int &a) { cin >> a; }
void scan(long long &a) { cin >> a; }
void scan(char &a) { cin >> a; }
void scan(double &a) { cin >> a; }
void scan(string &a) { cin >> a; }
template <class T, class S> void scan(pair<T, S> &p) { scan(p.first), scan(p.second); }
template <class T> void scan(vector<T> &);
template <class T> void scan(vector<T> &a) {
for(auto &i : a) scan(i);
}
template <class T> void scan(T &a) { cin >> a; }
void IN() {}
template <class Head, class... Tail> void IN(Head &head, Tail &... tail) {
scan(head);
IN(tail...);
}
template <class T, class S> inline bool chmax(T &a, const S &b) { return (a < b ? a = b, 1 : 0); }
template <class T, class S> inline bool chmin(T &a, const S &b) { return (a > b ? a = b, 1 : 0); }
vi iota(int n) {
vi a(n);
iota(all(a), 0);
return a;
}
template <typename T> vi iota(vector<T> &a, bool greater = false) {
vi res(a.size());
iota(all(res), 0);
sort(all(res), [&](int i, int j) {
if(greater) return a[i] > a[j];
return a[i] < a[j];
});
return res;
}
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end())
template <class T> T POW(T x, int n) {
T res = 1;
for(; n; n >>= 1, x *= x)
if(n & 1) res *= x;
return res;
}
vector<pll> factor(ll x) {
vector<pll> ans;
for(ll i = 2; i * i <= x; i++)
if(x % i == 0) {
ans.push_back({i, 1});
while((x /= i) % i == 0) ans.back().second++;
}
if(x != 1) ans.push_back({x, 1});
return ans;
}
template <class T> vector<T> divisor(T x) {
vector<T> ans;
for(T i = 1; i * i <= x; i++)
if(x % i == 0) {
ans.pb(i);
if(i * i != x) ans.pb(x / i);
}
return ans;
}
template <typename T> void zip(vector<T> &x) {
vector<T> y = x;
sort(all(y));
for(int i = 0; i < x.size(); ++i) { x[i] = lb(y, x[i]); }
}
int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
int topbit(ll t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
int botbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); }
int botbit(ll a) { return a == 0 ? 64 : __builtin_ctzll(a); }
int allbit(int n) { return (1 << n) - 1; }
int popcount(signed t) { return __builtin_popcount(t); }
int popcount(ll t) { return __builtin_popcountll(t); }
bool ispow2(int i) { return i && (i & -i) == i; }
int in() {
int x;
cin >> x;
return x;
}
ll lin() {
unsigned long long x;
cin >> x;
return x;
}
template <class T> pair<T, T> operator-(const pair<T, T> &x, const pair<T, T> &y) { return pair<T, T>(x.fi - y.fi, x.se - y.se); }
template <class T> pair<T, T> operator+(const pair<T, T> &x, const pair<T, T> &y) { return pair<T, T>(x.fi + y.fi, x.se + y.se); }
template <class T> ll operator*(const pair<T, T> &x, const pair<T, T> &y) { return (ll)x.fi * y.fi + (ll)x.se * y.se; }
template <typename T> struct edge {
int from, to;
T cost;
int id;
edge(int to, T cost) : from(-1), to(to), cost(cost) {}
edge(int from, int to, T cost) : from(from), to(to), cost(cost) {}
edge(int from, int to, T cost, int id) : from(from), to(to), cost(cost), id(id) {}
edge &operator=(const int &x) {
to = x;
return *this;
}
operator int() const { return to; }
};
template <typename T> using Edges = vector<edge<T>>;
using Tree = vector<vector<int>>;
using Graph = vector<vector<int>>;
template <class T> using Wgraph = vector<vector<edge<T>>>;
Graph getG(int n, int m = -1, bool directed = false, int margin = 1) {
Tree res(n);
if(m == -1) m = n - 1;
while(m--) {
int a, b;
cin >> a >> b;
a -= margin, b -= margin;
res[a].emplace_back(b);
if(!directed) res[b].emplace_back(a);
}
return move(res);
}
template <class T> Wgraph<T> getWg(int n, int m = -1, bool directed = false, int margin = 1) {
Wgraph<T> res(n);
if(m == -1) m = n - 1;
while(m--) {
int a, b;
T c;
cin >> a >> b >> c;
a -= margin, b -= margin;
res[a].emplace_back(b, c);
if(!directed) res[b].emplace_back(a, c);
}
return move(res);
}
#define i128 __int128_t
#define ull unsigned long long int
#define TEST \
INT(testcases); \
while(testcases--)
template <class T> ostream &operator<<(ostream &os, const vector<T> &v) {
for(auto it = begin(v); it != end(v); ++it) {
if(it == begin(v))
os << *it;
else
os << " " << *it;
}
return os;
}
template <class T, class S> ostream &operator<<(ostream &os, const pair<T, S> &p) {
os << p.first << " " << p.second;
return os;
}
template <class S, class T> string to_string(pair<S, T> p) { return "(" + to_string(p.first) + "," + to_string(p.second) + ")"; }
template <class A> string to_string(A v) {
if(v.empty()) return "{}";
string ret = "{";
for(auto &x : v) ret += to_string(x) + ",";
ret.back() = '}';
return ret;
}
void dump() { cerr << endl; }
template <class Head, class... Tail> void dump(Head head, Tail... tail) {
cerr << to_string(head) << " ";
dump(tail...);
}
#define endl '\n'
#ifdef _LOCAL
#undef endl
#define debug(x) \
cout << #x << ": "; \
dump(x)
#else
#define debug(x)
#endif
template <typename T> static constexpr T inf = numeric_limits<T>::max() / 2;
struct Setup_io {
Setup_io() {
ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
cout << fixed << setprecision(15);
}
} setup_io;
#define drop(s) cout << #s << endl, exit(0)
#pragma endregion
// from https://judge.yosupo.jp/submission/5147
vector<int> prime_sieve(const int N, const int Q = 17, const int L = 1 << 15) {
using u8 = unsigned char;
static const int rs[] = {1, 7, 11, 13, 17, 19, 23, 29};
struct P {
P(int p) : p(p) {}
int p;
int pos[8];
};
auto approx_prime_count = [](const int N) -> int { return N > 60184 ? N / (log(N) - 1.1) : max(1., N / (log(N) - 1.11)) + 1; };
const int v = sqrt(N), vv = sqrt(v);
vector<bool> isp(v + 1, true);
for(int i = 2; i <= vv; ++i)
if(isp[i]) {
for(int j = i * i; j <= v; j += i) isp[j] = false;
}
const int rsize = approx_prime_count(N + 30);
vector<int> primes = {2, 3, 5};
int psize = 3;
primes.resize(rsize);
vector<P> sprimes;
size_t pbeg = 0;
int prod = 1;
for(int p = 7; p <= v; ++p) {
if(!isp[p]) continue;
if(p <= Q) prod *= p, ++pbeg, primes[psize++] = p;
auto pp = P(p);
for(int t = 0; t < 8; ++t) {
int j = (p <= Q) ? p : p * p;
while(j % 30 != rs[t]) j += p << 1;
pp.pos[t] = j / 30;
}
sprimes.push_back(pp);
}
vector<u8> pre(prod, 0xFF);
for(size_t pi = 0; pi < pbeg; ++pi) {
auto pp = sprimes[pi];
const int p = pp.p;
for(int t = 0; t < 8; ++t) {
const u8 m = ~(1 << t);
for(int i = pp.pos[t]; i < prod; i += p) pre[i] &= m;
}
}
const int block_size = (L + prod - 1) / prod * prod;
vector<u8> block(block_size);
u8 *pblock = block.data();
const int M = (N + 29) / 30;
for(int beg = 0; beg < M; beg += block_size, pblock -= block_size) {
int end = min(M, beg + block_size);
for(int i = beg; i < end; i += prod) { copy(pre.begin(), pre.end(), pblock + i); }
if(beg == 0) pblock[0] &= 0xFE;
for(size_t pi = pbeg; pi < sprimes.size(); ++pi) {
auto &pp = sprimes[pi];
const int p = pp.p;
for(int t = 0; t < 8; ++t) {
int i = pp.pos[t];
const u8 m = ~(1 << t);
for(; i < end; i += p) pblock[i] &= m;
pp.pos[t] = i;
}
}
for(int i = beg; i < end; ++i) {
for(int m = pblock[i]; m > 0; m &= m - 1) { primes[psize++] = i * 30 + rs[__builtin_ctz(m)]; }
}
}
assert(psize <= rsize);
while(psize > 0 && primes[psize - 1] > N) --psize;
primes.resize(psize);
return primes;
}
ll prime_pi(const ll n) {
if(n <= 1) return 0;
if(n == 2) return 1;
const int sq = sqrtl(n);
int s = 1 + sq >> 1;
vector<int> smalls(s);
for(int i = 1; i < s; ++i) smalls[i] = i;
vector<int> roughs(s);
for(int i = 0; i < s; ++i) roughs[i] = i << 1 | 1;
vector<ll> larges(s);
for(int i = 0; i < s; ++i) larges[i] = (n / (i << 1 | 1) - 1) >> 1;
vector<bool> skip(sq + 1);
const auto divide = [](ll n, ll d) -> int { return (long double)n / d; };
const auto half = [](int n) -> int { return (n - 1) >> 1; };
int pc = 0;
for(int p = 3; p <= sq; p += 2)
if(!skip[p]) {
int q = p * p;
if((ll)q * q > n) break;
skip[p] = true;
for(int i = q; i <= sq; i += p << 1) skip[i] = true;
int ns = 0;
for(int k = 0; k < s; ++k) {
int i = roughs[k];
if(skip[i]) continue;
ll d = (ll)i * p;
larges[ns] = larges[k] - (d <= sq ? larges[smalls[d >> 1] - pc] : smalls[half(divide(n, d))]) + pc;
roughs[ns++] = i;
}
s = ns;
for(int i = half(sq), j = ((sq / p) - 1) | 1; j >= p; j -= 2) {
int c = smalls[j >> 1] - pc;
for(int e = (j * p) >> 1; i >= e; --i) smalls[i] -= c;
}
++pc;
}
larges[0] += (ll)(s + 2 * (pc - 1)) * (s - 1) / 2;
for(int k = 1; k < s; ++k) larges[0] -= larges[k];
for(int l = 1; l < s; ++l) {
int q = roughs[l];
ll m = n / q;
int e = smalls[half(m / q)] - pc;
if(e < l + 1) break;
ll t = 0;
for(int k = l + 1; k <= e; ++k) t += smalls[half(divide(m, roughs[k]))];
larges[0] += t - (ll)(e - l) * (pc + l - 1);
}
return larges[0] + 1;
}
int main() {
LL(n);
ll ans = 0;
const int N = 10000000, M = 110000;
auto P = prime_sieve(N);
vector<ll> cnt(N + 1);
for(auto e : P) cnt[e] = 1;
rep(i, N) cnt[i + 1] += cnt[i];
unordered_map<ll, ll> mem;
auto prime_count = [&](ll x) -> ll {
if(x > N) {
if(mem.count(x)) return mem[x];
return mem[x] = prime_pi(x);
}
return cnt[x];
};
auto primes = prime_sieve(M);
vector<unordered_map<ll, ll>> dp(si(primes));
auto rec = [&](auto &&self, int i, ll x) -> ll {
if(dp[i].count(x)) return dp[i][x];
auto &res = dp[i][x];
if((ll)primes[i] * (primes[i] - 1) > x) {
res = prime_count(x + 1) - i + 1;
chmax(res, 1);
return res;
} else {
res = self(self, i + 1, x);
x /= primes[i] - 1;
while(x) {
res += self(self, i + 1, x);
x /= primes[i];
}
return res;
}
};
cout << rec(rec, 0, n) << endl;
}