結果

問題 No.1917 LCMST
ユーザー rniyarniya
提出日時 2022-04-29 22:37:15
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 541 ms / 4,000 ms
コード長 10,789 bytes
コンパイル時間 2,498 ms
コンパイル使用メモリ 215,052 KB
最終ジャッジ日時 2025-01-28 23:25:35
ジャッジサーバーID
(参考情報)
judge3 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 42
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#define LOCAL
#include <bits/stdc++.h>
using namespace std;
#pragma region Macros
typedef long long ll;
typedef __int128_t i128;
typedef unsigned int uint;
typedef unsigned long long ull;
#define ALL(x) (x).begin(), (x).end()
template <typename T> istream& operator>>(istream& is, vector<T>& v) {
for (T& x : v) is >> x;
return is;
}
template <typename T> ostream& operator<<(ostream& os, const vector<T>& v) {
for (size_t i = 0; i < v.size(); i++) {
os << v[i] << (i + 1 == v.size() ? "" : " ");
}
return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const pair<T, U>& p) {
os << '(' << p.first << ',' << p.second << ')';
return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const map<T, U>& m) {
os << '{';
for (auto itr = m.begin(); itr != m.end();) {
os << '(' << itr->first << ',' << itr->second << ')';
if (++itr != m.end()) os << ',';
}
os << '}';
return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const unordered_map<T, U>& m) {
os << '{';
for (auto itr = m.begin(); itr != m.end();) {
os << '(' << itr->first << ',' << itr->second << ')';
if (++itr != m.end()) os << ',';
}
os << '}';
return os;
}
template <typename T> ostream& operator<<(ostream& os, const set<T>& s) {
os << '{';
for (auto itr = s.begin(); itr != s.end();) {
os << *itr;
if (++itr != s.end()) os << ',';
}
os << '}';
return os;
}
template <typename T> ostream& operator<<(ostream& os, const multiset<T>& s) {
os << '{';
for (auto itr = s.begin(); itr != s.end();) {
os << *itr;
if (++itr != s.end()) os << ',';
}
os << '}';
return os;
}
template <typename T> ostream& operator<<(ostream& os, const unordered_set<T>& s) {
os << '{';
for (auto itr = s.begin(); itr != s.end();) {
os << *itr;
if (++itr != s.end()) os << ',';
}
os << '}';
return os;
}
template <typename T> ostream& operator<<(ostream& os, const deque<T>& v) {
for (size_t i = 0; i < v.size(); i++) {
os << v[i] << (i + 1 == v.size() ? "" : " ");
}
return os;
}
template <typename T, size_t N> ostream& operator<<(ostream& os, const array<T, N>& v) {
for (size_t i = 0; i < N; i++) {
os << v[i] << (i + 1 == N ? "" : " ");
}
return os;
}
template <int i, typename T> void print_tuple(ostream&, const T&) {}
template <int i, typename T, typename H, class... Args> void print_tuple(ostream& os, const T& t) {
if (i) os << ',';
os << get<i>(t);
print_tuple<i + 1, T, Args...>(os, t);
}
template <typename... Args> ostream& operator<<(ostream& os, const tuple<Args...>& t) {
os << '{';
print_tuple<0, tuple<Args...>, Args...>(os, t);
return os << '}';
}
void debug_out() { cerr << '\n'; }
template <class Head, class... Tail> void debug_out(Head&& head, Tail&&... tail) {
cerr << head;
if (sizeof...(Tail) > 0) cerr << ", ";
debug_out(move(tail)...);
}
#ifdef LOCAL
#define debug(...) \
cerr << " "; \
cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n'; \
cerr << " "; \
debug_out(__VA_ARGS__)
#else
#define debug(...) void(0)
#endif
template <typename T> T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; }
template <typename T> T lcm(T x, T y) { return x / gcd(x, y) * y; }
int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
int topbit(long long t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
int botbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); }
int botbit(long long a) { return a == 0 ? 64 : __builtin_ctzll(a); }
int popcount(signed t) { return __builtin_popcount(t); }
int popcount(long long t) { return __builtin_popcountll(t); }
bool ispow2(int i) { return i && (i & -i) == i; }
long long MSK(int n) { return (1LL << n) - 1; }
template <class T> T ceil(T x, T y) {
assert(y >= 1);
return (x > 0 ? (x + y - 1) / y : x / y);
}
template <class T> T floor(T x, T y) {
assert(y >= 1);
return (x > 0 ? x / y : (x - y + 1) / y);
}
template <class T1, class T2> inline bool chmin(T1& a, T2 b) {
if (a > b) {
a = b;
return true;
}
return false;
}
template <class T1, class T2> inline bool chmax(T1& a, T2 b) {
if (a < b) {
a = b;
return true;
}
return false;
}
template <typename T> void mkuni(vector<T>& v) {
sort(v.begin(), v.end());
v.erase(unique(v.begin(), v.end()), v.end());
}
template <typename T> int lwb(const vector<T>& v, const T& x) { return lower_bound(v.begin(), v.end(), x) - v.begin(); }
#pragma endregion
#include <algorithm>
#include <cassert>
#include <vector>
struct UnionFind {
UnionFind(int n) : n(n), num(n), data(n, -1) {}
int find(int x) {
assert(0 <= x && x < n);
return data[x] < 0 ? x : data[x] = find(data[x]);
}
bool merge(int x, int y) {
assert(0 <= x && x < n);
assert(0 <= y && y < n);
if ((x = find(x)) == (y = find(y))) return false;
if (-data[x] < -data[y]) std::swap(x, y);
data[x] += data[y];
data[y] = x;
num--;
return true;
}
bool same(int x, int y) {
assert(0 <= x && x < n);
assert(0 <= y && y < n);
return find(x) == find(y);
}
int size(int x) {
assert(0 <= x && x < n);
return -data[find(x)];
}
int count() const { return num; }
std::vector<std::vector<int>> groups() {
std::vector<std::vector<int>> res(n);
for (int i = 0; i < n; i++) res[find(i)].emplace_back(i);
res.erase(std::remove_if(res.begin(), res.end(), [&](const std::vector<int>& v) { return v.empty(); }));
return res;
}
int operator[](int x) { return find(x); }
private:
int n, num;
// root node : -1 * component size
// otherwise : parent
std::vector<int> data;
};
#include <numeric>
#include <vector>
namespace elementary_math {
template <typename T> std::vector<T> divisor(T n) {
std::vector<T> res;
for (T i = 1; i * i <= n; i++) {
if (n % i == 0) {
res.emplace_back(i);
if (i * i != n) res.emplace_back(n / i);
}
}
return res;
}
template <typename T> std::vector<std::pair<T, int>> prime_factor(T n) {
std::vector<std::pair<T, int>> res;
for (T p = 2; p * p <= n; p++) {
if (n % p == 0) {
res.emplace_back(p, 0);
while (n % p == 0) {
res.back().second++;
n /= p;
}
}
}
if (n > 1) res.emplace_back(n, 1);
return res;
}
std::vector<int> osa_k(int n) {
std::vector<int> min_factor(n + 1, 0);
for (int i = 2; i <= n; i++) {
if (min_factor[i]) continue;
for (int j = i; j <= n; j += i) {
if (!min_factor[j]) {
min_factor[j] = i;
}
}
}
return min_factor;
}
std::vector<int> prime_factor(const std::vector<int>& min_factor, int n) {
std::vector<int> res;
while (n > 1) {
res.emplace_back(min_factor[n]);
n /= min_factor[n];
}
return res;
}
long long modpow(long long x, long long n, long long mod) {
assert(0 <= n && 1 <= mod && mod < (1LL << 31));
if (mod == 1) return 0;
x %= mod;
long long res = 1;
while (n > 0) {
if (n & 1) res = res * x % mod;
x = x * x % mod;
n >>= 1;
}
return res;
}
long long extgcd(long long a, long long b, long long& x, long long& y) {
long long d = a;
if (b != 0) {
d = extgcd(b, a % b, y, x);
y -= (a / b) * x;
} else
x = 1, y = 0;
return d;
}
long long inv_mod(long long a, long long mod) {
assert(1 <= mod);
long long x, y;
if (extgcd(a, mod, x, y) != 1) return -1;
return (mod + x % mod) % mod;
}
template <typename T> T euler_phi(T n) {
auto pf = prime_factor(n);
T res = n;
for (const auto& p : pf) {
res /= p.first;
res *= p.first - 1;
}
return res;
}
std::vector<int> euler_phi_table(int n) {
std::vector<int> res(n + 1, 0);
iota(res.begin(), res.end(), 0);
for (int i = 2; i <= n; i++) {
if (res[i] != i) continue;
for (int j = i; j <= n; j += i) res[j] = res[j] / i * (i - 1);
}
return res;
}
// minimum i > 0 s.t. x^i \equiv 1 \pmod{m}
template <typename T> T order(T x, T m) {
T n = euler_phi(m);
auto cand = divisor(n);
sort(cand.begin(), cand.end());
for (auto& i : cand) {
if (modpow(x, i, m) == 1) {
return i;
}
}
return -1;
}
} // namespace elementary_math
const int INF = 1e9;
const long long IINF = 1e18;
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const char dir[4] = {'D', 'R', 'U', 'L'};
const long long MOD = 1000000007;
// const long long MOD = 998244353;
const int MAX_A = 100010;
int main() {
cin.tie(0);
ios::sync_with_stdio(false);
int N;
cin >> N;
vector<int> A(N);
cin >> A;
vector<int> cnt(MAX_A, 0);
vector<int> cand;
for (int& x : A) cnt[x]++;
ll ans = 0;
for (int i = 1; i < MAX_A; i++) {
if (cnt[i] == 0) continue;
ans += 1LL * i * (cnt[i] - 1);
cand.emplace_back(i);
}
int n = cand.size();
UnionFind UF(n);
vector<deque<pair<ll, int>>> div(MAX_A);
for (int i = 0; i < n; i++) {
auto d = elementary_math::divisor(cand[i]);
for (int& y : d) div[y].emplace_back(cand[i], i);
}
priority_queue<pair<ll, int>> pq;
for (int i = 1; i < MAX_A; i++) {
if (div[i].size() < 2) continue;
pq.emplace(-div[i][0].first * div[i][1].first / i, i);
}
auto UPDATE = [&](int x) {
auto p = div[x].front();
div[x].pop_front();
while (!div[x].empty() and UF.same(div[x].front().second, p.second)) div[x].pop_front();
div[x].emplace_front(p);
if (div[x].size() < 2) return;
pq.emplace(-div[x][0].first * div[x][1].first / x, x);
};
auto MERGE = [&](int x) {
if (!UF.merge(div[x][0].second, div[x][1].second)) {
UPDATE(x);
return;
}
ans += div[x][0].first * div[x][1].first / x;
auto p = div[x].front();
div[x].pop_front();
div[x].emplace_front(p);
UPDATE(x);
};
while (UF.count() > 1) {
auto p = pq.top();
pq.pop();
MERGE(p.second);
}
cout << ans << '\n';
return 0;
}
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