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답안 #644486

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
644486 2022-09-24T17:54:07 Z GusterGoose27 Strongbox (POI11_sej) C++11
70 / 100
 180 ms 43244 KB 
#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;
vector<ll> nprimes;
bitset<(int) sqrt(MAXN)+1> is_prime;
vector<pii> factorizations[MAXK];
int state[MAXF]; // 0 unvisited, 2 descended from k, 1 blocked
ll val[MAXF];
int hshs[MAXK];
int coeffs[MAXK];
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, vector<pii> &factored) { // 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) {
			factored.push_back(pii(primes[i], c));
			nprimes.push_back(primes[i]);
		}
	}
	if (target != 1) {
		nprimes.push_back(target);
		factored.push_back(pii(target, 1));
	}
}

void factorize2(ll target, vector<pii> &factored) { // prime
	for (int i = 0; i < nprimes.size(); i++) {
		int c = 0;
		while (target % nprimes[i] == 0) {
			target /= nprimes[i];
			c++;
		}
		factored.push_back(pii(nprimes[i], c));
	}
}

void make_coeffs() {
	int mult = 1;
	for (int i = 0; i < nprimes.size(); i++) {
		coeffs[i] = mult;
		mult *= (factorizations[k-1][i].second+1);
	}
}

int hsh(vector<pii> &factored) {
	int r = 0;
	for (int i = 0; i < nprimes.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], factorizations[k-1]);
	make_coeffs();
	hshs[k-1] = hsh(factorizations[k-1]);
	state[hshs[k-1]] = 2;
	val[hshs[k-1]] = elems[k-1];
	for (int i = 0; i < k-1; i++) {
		factorize2(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 < nprimes.size(); p++) {
			int v = i/coeffs[p];
			if (v % (factorizations[k-1][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]/nprimes[p];
			state[nxt] = state[i];
		}
	}
	assert(ans > 0);
	cout << ans << "\n";
}

Compilation message

sej.cpp: In function 'void factorize(ll, std::vector<std::pair<int, int> >&)':
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 factorize2(ll, std::vector<std::pair<int, int> >&)':
sej.cpp:61:20: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   61 |  for (int i = 0; i < nprimes.size(); i++) {
      |                  ~~^~~~~~~~~~~~~~~~
sej.cpp: In function 'void make_coeffs()':
sej.cpp:73:20: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   73 |  for (int i = 0; i < nprimes.size(); i++) {
      |                  ~~^~~~~~~~~~~~~~~~
sej.cpp: In function 'int hsh(std::vector<std::pair<int, int> >&)':
sej.cpp:81:20: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   81 |  for (int i = 0; i < nprimes.size(); i++) {
      |                  ~~^~~~~~~~~~~~~~~~
sej.cpp: In function 'int main()':
sej.cpp:114:21: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  114 |   for (int p = 0; p < nprimes.size(); p++) {
      |                   ~~^~~~~~~~~~~~~~~~

Subtask #1
7.0 / 7.0

# 결과 실행 시간 메모리 Grader output
1 Correct 3 ms 7380 KB Output is correct
2 Correct 4 ms 7380 KB Output is correct
3 Correct 5 ms 7380 KB Output is correct
4 Correct 4 ms 7380 KB Output is correct

Subtask #2
7.0 / 7.0

# 결과 실행 시간 메모리 Grader output
1 Correct 4 ms 7380 KB Output is correct
2 Correct 3 ms 7380 KB Output is correct
3 Correct 4 ms 7380 KB Output is correct

Subtask #3
7.0 / 7.0

# 결과 실행 시간 메모리 Grader output
1 Correct 4 ms 7380 KB Output is correct
2 Correct 3 ms 7380 KB Output is correct
3 Correct 4 ms 7380 KB Output is correct

Subtask #4
7.0 / 7.0

# 결과 실행 시간 메모리 Grader output
1 Correct 4 ms 7636 KB Output is correct
2 Correct 4 ms 7636 KB Output is correct
3 Correct 4 ms 7508 KB Output is correct

Subtask #5
7.0 / 7.0

# 결과 실행 시간 메모리 Grader output
1 Correct 10 ms 8532 KB Output is correct
2 Correct 9 ms 8532 KB Output is correct
3 Correct 9 ms 8580 KB Output is correct
4 Correct 10 ms 8532 KB Output is correct

Subtask #6
7.0 / 7.0

# 결과 실행 시간 메모리 Grader output
1 Correct 27 ms 11660 KB Output is correct
2 Correct 43 ms 11652 KB Output is correct
3 Correct 55 ms 15680 KB Output is correct
4 Correct 43 ms 11628 KB Output is correct

Subtask #7
7.0 / 7.0

# 결과 실행 시간 메모리 Grader output
1 Correct 17 ms 9608 KB Output is correct
2 Correct 46 ms 15736 KB Output is correct
3 Correct 62 ms 15680 KB Output is correct
4 Correct 38 ms 11648 KB Output is correct

Subtask #8
7.0 / 7.0

# 결과 실행 시간 메모리 Grader output
1 Correct 47 ms 11588 KB Output is correct
2 Correct 53 ms 15680 KB Output is correct
3 Correct 62 ms 15744 KB Output is correct
4 Correct 45 ms 11712 KB Output is correct

Subtask #9
7.0 / 7.0

# 결과 실행 시간 메모리 Grader output
1 Correct 47 ms 15784 KB Output is correct
2 Correct 54 ms 15756 KB Output is correct
3 Correct 59 ms 15780 KB Output is correct
4 Correct 57 ms 15740 KB Output is correct

Subtask #10
7.0 / 7.0

# 결과 실행 시간 메모리 Grader output
1 Correct 39 ms 11636 KB Output is correct
2 Correct 59 ms 15744 KB Output is correct
3 Correct 63 ms 15680 KB Output is correct
4 Correct 61 ms 15732 KB Output is correct

Subtask #11
0 / 7.0

# 결과 실행 시간 메모리 Grader output
1 Correct 83 ms 16448 KB Output is correct
2 Correct 102 ms 21536 KB Output is correct
3 Correct 102 ms 27880 KB Output is correct
4 Runtime error 124 ms 37128 KB Memory limit exceeded
5 Halted 0 ms 0 KB -

Subtask #12
0 / 7.0

# 결과 실행 시간 메모리 Grader output
1 Correct 106 ms 22140 KB Output is correct
2 Correct 155 ms 30684 KB Output is correct
3 Runtime error 127 ms 43244 KB Memory limit exceeded
4 Halted 0 ms 0 KB -

Subtask #13
0 / 8.0

# 결과 실행 시간 메모리 Grader output
1 Correct 100 ms 20412 KB Output is correct
2 Runtime error 180 ms 35068 KB Memory limit exceeded
3 Halted 0 ms 0 KB -

Subtask #14
0 / 8.0

# 결과 실행 시간 메모리 Grader output
1 Correct 141 ms 26936 KB Output is correct
2 Runtime error 177 ms 38652 KB Memory limit exceeded
3 Halted 0 ms 0 KB -