QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#125295 | #6740. Function | hos_lyric | AC ✓ | 498ms | 3708kb | C++14 | 5.5kb | 2023-07-16 14:59:28 | 2023-07-16 14:59:29 |
Judging History
answer
#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using Int = long long;
template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
static constexpr unsigned M = M_;
unsigned x;
constexpr ModInt() : x(0U) {}
constexpr ModInt(unsigned x_) : x(x_ % M) {}
constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
ModInt pow(long long e) const {
if (e < 0) return inv().pow(-e);
ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
}
ModInt inv() const {
unsigned a = M, b = x; int y = 0, z = 1;
for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
assert(a == 1U); return ModInt(y);
}
ModInt operator+() const { return *this; }
ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
explicit operator bool() const { return x; }
bool operator==(const ModInt &a) const { return (x == a.x); }
bool operator!=(const ModInt &a) const { return (x != a.x); }
friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////
constexpr unsigned MO = 998244353;
using Mint = ModInt<MO>;
inline long long divide(long long a, int b) {
return static_cast<double>(a) / b;
}
inline long long divide(long long a, long long b) {
return static_cast<double>(a) / b;
}
struct Quotients {
long long N;
int N2, N3, N4, N6;
int len;
Quotients(long long N_ = 0) : N(N_) {
N2 = sqrt(static_cast<long double>(N));
N3 = cbrt(static_cast<long double>(N));
for (; static_cast<long long>(N3) * N3 * N3 < N; ++N3) {}
for (; static_cast<long long>(N3) * N3 * N3 > N; --N3) {}
N4 = sqrt(static_cast<long double>(N2));
N6 = sqrt(static_cast<long double>(N3));
len = 2 * N2 + ((static_cast<long long>(N2) * (N2 + 1) <= N) ? 1 : 0);
}
long long operator[](int i) const {
return (i <= N2) ? i : divide(N, len - i);
}
int indexOf(long long x) const {
return (x <= N2) ? x : (len - divide(N, x));
}
friend std::ostream &operator<<(std::ostream &os, const Quotients &quo) {
os << "[";
for (int i = 0; i < quo.len; ++i) {
if (i > 0) os << ", ";
os << quo[i];
}
os << "]";
return os;
}
};
/*
f(x) = [x <= n] (1 + \sum[1<k<=K] f(k x))
g(N/x) := f(x)
g(x) = [x >= 1] (1 + \sum[1<k<=K] g(x/k))
*/
constexpr Int K = 20210926;
int main() {
Int N;
for (; ~scanf("%lld", &N); ) {
Quotients quo(N);
// cerr<<"|quo| = "<<quo.len<<", quo = "<<quo<<endl;
vector<Mint> dp(quo.len);
for (int i = 1; i < quo.len; ++i) {
dp[i] = 1;
const Int n = quo[i];
for (Int a = 0, b; a < n; a = b) {
const Int k = divide(n, a + 1);
b = divide(n, k);
// (a, b]: k
const Int lb = max(a, 1LL);
const Int ub = min(b, K);
if (lb < ub) {
dp[i] += (ub - lb) * dp[quo.indexOf(k)];
}
}
}
printf("%u\n", dp.back().x);
}
return 0;
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 1ms
memory: 3564kb
input:
1
output:
1
result:
ok 1 number(s): "1"
Test #2:
score: 0
Accepted
time: 1ms
memory: 3632kb
input:
2
output:
2
result:
ok 1 number(s): "2"
Test #3:
score: 0
Accepted
time: 1ms
memory: 3636kb
input:
100
output:
949
result:
ok 1 number(s): "949"
Test #4:
score: 0
Accepted
time: 1ms
memory: 3628kb
input:
10
output:
19
result:
ok 1 number(s): "19"
Test #5:
score: 0
Accepted
time: 1ms
memory: 3640kb
input:
1000
output:
48614
result:
ok 1 number(s): "48614"
Test #6:
score: 0
Accepted
time: 0ms
memory: 3636kb
input:
10000
output:
2602393
result:
ok 1 number(s): "2602393"
Test #7:
score: 0
Accepted
time: 0ms
memory: 3636kb
input:
100000
output:
139804054
result:
ok 1 number(s): "139804054"
Test #8:
score: 0
Accepted
time: 4ms
memory: 3680kb
input:
1000000
output:
521718285
result:
ok 1 number(s): "521718285"
Test #9:
score: 0
Accepted
time: 17ms
memory: 3708kb
input:
10000000
output:
503104917
result:
ok 1 number(s): "503104917"
Test #10:
score: 0
Accepted
time: 89ms
memory: 3664kb
input:
100000000
output:
198815604
result:
ok 1 number(s): "198815604"
Test #11:
score: 0
Accepted
time: 498ms
memory: 3632kb
input:
1000000000
output:
373787809
result:
ok 1 number(s): "373787809"
Test #12:
score: 0
Accepted
time: 498ms
memory: 3624kb
input:
999999999
output:
997616263
result:
ok 1 number(s): "997616263"
Test #13:
score: 0
Accepted
time: 494ms
memory: 3684kb
input:
999999990
output:
997615701
result:
ok 1 number(s): "997615701"
Test #14:
score: 0
Accepted
time: 498ms
memory: 3632kb
input:
999999900
output:
993928691
result:
ok 1 number(s): "993928691"
Test #15:
score: 0
Accepted
time: 498ms
memory: 3636kb
input:
999999000
output:
754532207
result:
ok 1 number(s): "754532207"
Test #16:
score: 0
Accepted
time: 498ms
memory: 3624kb
input:
999990000
output:
996592686
result:
ok 1 number(s): "996592686"
Test #17:
score: 0
Accepted
time: 498ms
memory: 3560kb
input:
999900000
output:
311678722
result:
ok 1 number(s): "311678722"
Test #18:
score: 0
Accepted
time: 497ms
memory: 3628kb
input:
999000000
output:
60462624
result:
ok 1 number(s): "60462624"
Test #19:
score: 0
Accepted
time: 490ms
memory: 3628kb
input:
990000000
output:
444576800
result:
ok 1 number(s): "444576800"
Test #20:
score: 0
Accepted
time: 456ms
memory: 3628kb
input:
900000000
output:
95615129
result:
ok 1 number(s): "95615129"
Test #21:
score: 0
Accepted
time: 4ms
memory: 3644kb
input:
1361956
output:
813433539
result:
ok 1 number(s): "813433539"
Test #22:
score: 0
Accepted
time: 14ms
memory: 3652kb
input:
7579013
output:
677659797
result:
ok 1 number(s): "677659797"
Test #23:
score: 0
Accepted
time: 11ms
memory: 3708kb
input:
8145517
output:
801509527
result:
ok 1 number(s): "801509527"
Test #24:
score: 0
Accepted
time: 12ms
memory: 3640kb
input:
6140463
output:
869023935
result:
ok 1 number(s): "869023935"
Test #25:
score: 0
Accepted
time: 5ms
memory: 3652kb
input:
3515281
output:
989091505
result:
ok 1 number(s): "989091505"
Test #26:
score: 0
Accepted
time: 13ms
memory: 3704kb
input:
6969586
output:
539840131
result:
ok 1 number(s): "539840131"