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Submission #644508

# Submission time Handle Problem Language Result Execution time Memory
644508 2022-09-24T18:30:20 Z GusterGoose27 Strongbox (POI11_sej) C++11
84 / 100
 176 ms 35048 KB 
#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 = 2e4;

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

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<long long 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<long long 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<long long int, int> >&)':
sej.cpp:88:20: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::pair<long long 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:120:21: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::pair<long long int, int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  120 |   for (int p = 0; p < kfactored.size(); p++) {
      |                   ~~^~~~~~~~~~~~~~~~~~

Subtask #1
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 7380 KB Output is correct
2 Correct 4 ms 7380 KB Output is correct
3 Correct 3 ms 7380 KB Output is correct
4 Correct 3 ms 7380 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 7428 KB Output is correct
2 Correct 4 ms 7380 KB Output is correct
3 Correct 4 ms 7380 KB Output is correct

Subtask #3
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 7380 KB Output is correct
2 Correct 4 ms 7380 KB Output is correct
3 Correct 4 ms 7380 KB Output is correct

Subtask #4
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 7508 KB Output is correct
2 Correct 5 ms 7636 KB Output is correct
3 Correct 4 ms 7508 KB Output is correct

Subtask #5
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 11 ms 8584 KB Output is correct
2 Correct 10 ms 8532 KB Output is correct
3 Correct 10 ms 8480 KB Output is correct
4 Correct 11 ms 8580 KB Output is correct

Subtask #6
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 27 ms 11588 KB Output is correct
2 Correct 43 ms 11640 KB Output is correct
3 Correct 56 ms 15728 KB Output is correct
4 Correct 46 ms 11632 KB Output is correct

Subtask #7
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 17 ms 9604 KB Output is correct
2 Correct 46 ms 15756 KB Output is correct
3 Correct 62 ms 15680 KB Output is correct
4 Correct 39 ms 11616 KB Output is correct

Subtask #8
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 47 ms 11644 KB Output is correct
2 Correct 54 ms 15732 KB Output is correct
3 Correct 60 ms 15732 KB Output is correct
4 Correct 44 ms 11668 KB Output is correct

Subtask #9
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 47 ms 15728 KB Output is correct
2 Correct 55 ms 15732 KB Output is correct
3 Correct 66 ms 15720 KB Output is correct
4 Correct 58 ms 15732 KB Output is correct

Subtask #10
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 40 ms 11588 KB Output is correct
2 Correct 59 ms 15736 KB Output is correct
3 Correct 65 ms 15764 KB Output is correct
4 Correct 65 ms 15784 KB Output is correct

Subtask #11
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 79 ms 16496 KB Output is correct
2 Correct 94 ms 18364 KB Output is correct
3 Correct 97 ms 21624 KB Output is correct
4 Correct 134 ms 26148 KB Output is correct
5 Correct 103 ms 21732 KB Output is correct

Subtask #12
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 102 ms 18992 KB Output is correct
2 Correct 150 ms 24220 KB Output is correct
3 Correct 114 ms 28816 KB Output is correct
4 Correct 109 ms 25900 KB Output is correct
5 Correct 135 ms 30388 KB Output is correct

Subtask #13
0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 109 ms 20544 KB Output is correct
2 Correct 174 ms 27240 KB Output is correct
3 Runtime error 149 ms 34420 KB Memory limit exceeded
4 Halted 0 ms 0 KB -

Subtask #14
0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 136 ms 22972 KB Output is correct
2 Correct 176 ms 27300 KB Output is correct
3 Runtime error 150 ms 35048 KB Memory limit exceeded
4 Halted 0 ms 0 KB -