# | Time | Username | Problem | Language | Result | Execution time | Memory |
---|---|---|---|---|---|---|---|
644509 | GusterGoose27 | Strongbox (POI11_sej) | C++11 | 174 ms | 29384 KiB |
This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll, int> pii;
const ll MAXN = 1e14;
const int MAXK = 25e4;
const int MAXF = 1e4;
ll n;
int k;
ll elems[MAXK];
ll gcd(ll a, ll b) {
if (a > b) return gcd(b, a);
if (a == 0) return b;
return gcd(b%a, a);
}
vector<ll> primes;
bitset<(int) sqrt(MAXN)+1> is_prime;
vector<pii> kfactored;
vector<int> factorizations[MAXK-1];
int state[MAXF]; // 0 unvisited, 2 descended from k, 1 blocked
ll val[MAXF];
int hshs[MAXK];
vector<int> coeffs;
int mxh = 0;
ll ans = 0;
void make_primes(ll mx) {
is_prime.set();
for (int i = 2; i <= mx; i++) {
if (!is_prime[i]) continue;
primes.push_back(i);
for (int j = 2*i; j <= mx; j+= i) is_prime[j] = 0;
}
}
void factorize(ll target) { // prime
for (int i = 0; i < primes.size() && target > 1; i++) {
int c = 0;
while (target % primes[i] == 0) {
target /= primes[i];
c++;
}
if (c) {
kfactored.push_back(pii(primes[i], c));
}
}
if (target != 1) {
kfactored.push_back(pii(target, 1));
}
}
void factorize(ll target, vector<int> &factored) { // prime
for (int i = 0; i < kfactored.size(); i++) {
int c = 0;
while (target % kfactored[i].first == 0) {
target /= kfactored[i].first;
c++;
}
factored.push_back(c);
}
}
void make_coeffs() {
int mult = 1;
for (int i = 0; i < kfactored.size(); i++) {
coeffs.push_back(mult);
mult *= (kfactored[i].second+1);
}
}
int hsh(vector<int> &factored) {
int r = 0;
for (int i = 0; i < factored.size(); i++) {
r += factored[i]*coeffs[i];
}
mxh = max(mxh, r);
return r;
}
int hsh(vector<pii> &factored) {
int r = 0;
for (int i = 0; i < factored.size(); i++) {
r += factored[i].second*coeffs[i];
}
mxh = max(mxh, r);
return r;
}
int main() {
ios_base::sync_with_stdio(false); cin.tie(NULL);
cin >> n >> k;
for (int i = 0; i < k; i++) {
cin >> elems[i];
}
elems[k-1] = gcd(elems[k-1], n);
for (int i = 0; i < k-1; i++) elems[i] = gcd(elems[i], elems[k-1]);
if (elems[k-1] == 0) elems[k-1] = n;
make_primes((int) sqrt(n));
factorize(elems[k-1]);
make_coeffs();
hshs[k-1] = hsh(kfactored);
state[hshs[k-1]] = 2;
val[hshs[k-1]] = elems[k-1];
for (int i = 0; i < k-1; i++) {
factorize(elems[i], factorizations[i]);
hshs[i] = hsh(factorizations[i]);
state[hshs[i]] = 1;
val[hshs[i]] = elems[i];
}
assert(mxh < MAXF);
for (int i = mxh; i >= 0; i--) {
if (state[i] == 0) continue;
if (state[i] == 2) ans = max(ans, n/val[i]);
for (int p = 0; p < kfactored.size(); p++) {
int v = i/coeffs[p];
if (v % (kfactored[p].second+1) == 0) continue;
int nxt = i-coeffs[p];
if (state[nxt] == 1 || (state[nxt] == 2 && state[i] == 2)) continue;
val[nxt] = val[i]/kfactored[p].first;
state[nxt] = state[i];
}
}
assert(ans > 0);
cout << ans << "\n";
}
Compilation message (stderr)
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