結果
| 問題 |
No.1019 最小格子三角形
|
| ユーザー |
 yosupot
|
| 提出日時 | 2020-04-03 23:10:25 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 1,332 ms / 2,000 ms |
| コード長 | 6,897 bytes |
| コンパイル時間 | 1,283 ms |
| コンパイル使用メモリ | 117,056 KB |
| 最終ジャッジ日時 | 2025-01-09 13:40:43 |
|
ジャッジサーバーID （参考情報） |
judge1 / judge4 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 24 |
ソースコード
//#pragma GCC optimize("Ofast")
//#pragma GCC target("avx")
//#undef LOCAL
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <complex>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <vector>
using namespace std;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }
template <class T> using V = vector<T>;
template <class T> using VV = V<V<T>>;
struct Scanner {
FILE* fp = nullptr;
char line[(1 << 15) + 1];
size_t st = 0, ed = 0;
void reread() {
memmove(line, line + st, ed - st);
ed -= st;
st = 0;
ed += fread(line + ed, 1, (1 << 15) - ed, fp);
line[ed] = '\0';
}
bool succ() {
while (true) {
if (st == ed) {
reread();
if (st == ed) return false;
}
while (st != ed && isspace(line[st])) st++;
if (st != ed) break;
}
if (ed - st <= 50) reread();
return true;
}
template <class T, enable_if_t<is_same<T, string>::value, int> = 0>
bool read_single(T& ref) {
if (!succ()) return false;
while (true) {
size_t sz = 0;
while (st + sz < ed && !isspace(line[st + sz])) sz++;
ref.append(line + st, sz);
st += sz;
if (!sz || st != ed) break;
reread();
}
return true;
}
template <class T, enable_if_t<is_integral<T>::value, int> = 0>
bool read_single(T& ref) {
if (!succ()) return false;
bool neg = false;
if (line[st] == '-') {
neg = true;
st++;
}
ref = T(0);
while (isdigit(line[st])) {
ref = 10 * ref + (line[st++] - '0');
}
if (neg) ref = -ref;
return true;
}
template <class T> bool read_single(V<T>& ref) {
for (auto& d : ref) {
if (!read_single(d)) return false;
}
return true;
}
void read() {}
template <class H, class... T> void read(H& h, T&... t) {
bool f = read_single(h);
assert(f);
read(t...);
}
Scanner(FILE* _fp) : fp(_fp) {}
};
struct Printer {
public:
template <bool F = false> void write() {}
template <bool F = false, class H, class... T>
void write(const H& h, const T&... t) {
if (F) write_single(' ');
write_single(h);
write<true>(t...);
}
template <class... T> void writeln(const T&... t) {
write(t...);
write_single('\n');
}
Printer(FILE* _fp) : fp(_fp) {}
~Printer() { flush(); }
private:
static constexpr size_t SIZE = 1 << 15;
FILE* fp;
char line[SIZE], small[50];
size_t pos = 0;
void flush() {
fwrite(line, 1, pos, fp);
pos = 0;
}
void write_single(const char& val) {
if (pos == SIZE) flush();
line[pos++] = val;
}
template <class T, enable_if_t<is_integral<T>::value, int> = 0>
void write_single(T val) {
if (pos > (1 << 15) - 50) flush();
if (val == 0) {
write_single('0');
return;
}
if (val < 0) {
write_single('-');
val = -val; // todo min
}
size_t len = 0;
while (val) {
small[len++] = char('0' + (val % 10));
val /= 10;
}
for (size_t i = 0; i < len; i++) {
line[pos + i] = small[len - 1 - i];
}
pos += len;
}
void write_single(const string& s) {
for (char c : s) write_single(c);
}
void write_single(const char* s) {
size_t len = strlen(s);
for (size_t i = 0; i < len; i++) write_single(s[i]);
}
template <class T> void write_single(const V<T>& val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) write_single(' ');
write_single(val[i]);
}
}
};
Scanner sc = Scanner(stdin);
Printer pr = Printer(stdout);
ll gcd(ll a, ll b) {
if (b == 0) return a;
return gcd(b, a % b);
}
const int MX = TEN(6) + 100;
VV<ll> prs(MX);
void init() {
V<ll> used(MX, false);
for (ll i = 2; i < MX; i++) {
if (used[i]) continue;
for (ll j = i; j < MX; j += i) {
prs[j].push_back(i);
used[j] = true;
}
}
}
const ll MOD = 998244353;
int main() {
init();
ll n;
sc.read(n);
/* using P = pair<ll, ll>;
const ll B = ll(sqrt(n) + 10);
V<P> pots;
for (ll p1 = -B; p1 <= B; p1++) {
for (ll p2 = -B; p2 <= B; p2++) {
if (p1 * p1 + p2 * p2 <= n) {
pots.push_back({p1, p2});
}
}
}
VV<ll> mp(2 * B + 1, V<ll>(2 * B + 1));
for (auto p: pots) {
for (auto q: pots) {
if (p.first * q.second - p.second * q.first == 1) {
mp[B+p.first][B+p.second]++;
mp[B+q.first][B+q.second]++;
}
}
}
ll sum = 0;
for (ll p1 = -B; p1 <= B; p1++) {
for (ll p2 = -B; p2 <= B; p2++) {
ll u = mp[B+p1][B+p2];
if (u) printf("%3lld ", u);
else if (p1 == 0 && p2 == 0) printf(" + ");
else printf(" ");
sum += u * (abs(p1) + abs(p2));
}
cout << endl;
}
cout << sum << endl;
ll sum2 = 8;
for (ll p1 = 1; p1 <= B; p1++) {
for (ll p2 = 1; p2 <= B; p2++) {
if (p1 * p1 + p2 * p2 <= n) {
if (gcd(p1, p2) == 1) {
sum2 += (p1 + p2) * 24;
}
}
}
}
cout << sum2 << endl;*/
ll ans = 8;
for (ll p1 = 1; p1 * p1 <= n; p1++) {
// p1 * p1 + p2 * p2 <= n
// p2 * p2 <= n - p1 * p1
ll up2 = ll(sqrt(n - p1 * p1) + 10);
while (p1 * p1 + up2 * up2 > n) up2--;
/* ll naive_cnt = 0;
for (ll p2 = 1; p2 <= up2; p2++) {
if (gcd(p1, p2) == 1) {
naive_cnt++;
}
}*/
ll cnt = 0;
// gcd(p1, p2) == 1, 1 <= p2 <= up2
int m = int(prs[p1].size());
for (int f = 0; f < (1 << m); f++) {
ll z = 1;
int freq = 1;
for (int i = 0; i < m; i++) {
if (f & (1 << i)) {
z *= prs[p1][i];
freq *= -1;
}
}
cnt += freq * (up2 / z) % MOD;
}
// assert(cnt == naive_cnt);
ans += (48 * p1 * cnt) % MOD;
ans = (ans + MOD) % MOD;
}
pr.writeln(ans);
return 0;
}