Submission #644497

#	Time	Username	Problem	Language	Result	Execution time	Memory
644497		GusterGoose27	Strongbox (POI11_sej)	C++11	77 / 100	171 ms	35064 KiB

sej

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef pair<int, int> pii;

const ll MAXN = 1e14;
const int MAXK = 25e4;
const int MAXF = 1e5;

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]);
	for (int i = 0; i < k; i++) {
		if (elems[i] == 0) elems[i] = 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];
	}
	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)

sej.cpp: In function 'void factorize(ll)':
sej.cpp:43:20: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   43 |  for (int i = 0; i < primes.size() && target > 1; i++) {
      |                  ~~^~~~~~~~~~~~~~~
sej.cpp: In function 'void factorize(ll, std::vector<int>&)':
sej.cpp:59:20: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::pair<int, int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   59 |  for (int i = 0; i < kfactored.size(); i++) {
      |                  ~~^~~~~~~~~~~~~~~~~~
sej.cpp: In function 'void make_coeffs()':
sej.cpp:71:20: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::pair<int, int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   71 |  for (int i = 0; i < kfactored.size(); i++) {
      |                  ~~^~~~~~~~~~~~~~~~~~
sej.cpp: In function 'int hsh(std::vector<int>&)':
sej.cpp:79:20: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   79 |  for (int i = 0; i < factored.size(); i++) {
      |                  ~~^~~~~~~~~~~~~~~~~
sej.cpp: In function 'int hsh(std::vector<std::pair<int, int> >&)':
sej.cpp:88:20: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::pair<int, int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   88 |  for (int i = 0; i < factored.size(); i++) {
      |                  ~~^~~~~~~~~~~~~~~~~
sej.cpp: In function 'int main()':
sej.cpp:121:21: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::pair<int, int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  121 |   for (int p = 0; p < kfactored.size(); p++) {
      |                   ~~^~~~~~~~~~~~~~~~~~

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