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ID | 题目 | 提交者 | 结果 | 用时 | 内存 | 语言 | 文件大小 | 提交时间 | 测评时间 |
---|---|---|---|---|---|---|---|---|---|
#419631 | #6566. Power of Divisors | ohiostatescarlet | AC ✓ | 5ms | 11556kb | C++17 | 3.4kb | 2024-05-24 04:59:19 | 2024-05-24 04:59:19 |
Judging History
answer
#include <bits/stdc++.h>
using namespace std;
#ifdef LOCAL
#include "templates/debug.h"
#else
#define dbg(x...)
#endif
// Always assume a problem requires no fancy algorithms, unless it's obvious.
// Visualize small example cases.
// Think about simpler variations.
// Notice interesting properties.
// Think: If you just had x, you could solve the problem. Can you get x?
using ll = long long;
namespace PollardRho {
mt19937 rnd(chrono::steady_clock::now().time_since_epoch().count());
const int P = 1e6 + 9;
ll seq[P];
int primes[P], spf[P];
inline ll add_mod(ll x, ll y, ll m) {
return (x += y) < m ? x : x - m;
}
inline ll mul_mod(ll x, ll y, ll m) {
ll res = __int128(x) * y % m;
return res;
}
inline ll pow_mod(ll x, ll n, ll m) {
ll res = 1 % m;
for (; n; n >>= 1) {
if (n & 1) res = mul_mod(res, x, m);
x = mul_mod(x, x, m);
}
return res;
}
inline bool miller_rabin(ll n) {
if (n <= 2 || (n & 1 ^ 1)) return (n == 2);
if (n < P) return spf[n] == n;
ll c, d, s = 0, r = n - 1;
for (; !(r & 1); r >>= 1, s++) {}
for (int i = 0; primes[i] < n && primes[i] < 32; i++) {
c = pow_mod(primes[i], r, n);
for (int j = 0; j < s; j++) {
d = mul_mod(c, c, n);
if (d == 1 && c != 1 && c != (n - 1)) return false;
c = d;
}
if (c != 1) return false;
}
return true;
}
void init() {
int cnt = 0;
for (int i = 2; i < P; i++) {
if (!spf[i]) primes[cnt++] = spf[i] = i;
for (int j = 0, k; (k = i * primes[j]) < P; j++) {
spf[k] = primes[j];
if (spf[i] == spf[k]) break;
}
}
}
// returns O(n^(1/4))
ll pollard_rho(ll n) {
while (1) {
ll x = rnd() % n, y = x, c = rnd() % n, u = 1, v, t = 0;
ll *px = seq, *py = seq;
while (1) {
*py++ = y = add_mod(mul_mod(y, y, n), c, n);
*py++ = y = add_mod(mul_mod(y, y, n), c, n);
if ((x = *px++) == y) break;
v = u;
u = mul_mod(u, abs(y - x), n);
if (!u) return __gcd(v, n);
if (++t == 32) {
t = 0;
if ((u = __gcd(u, n)) > 1 && u < n) return u;
}
}
if (t && (u = __gcd(u, n)) > 1 && u < n) return u;
}
}
vector<ll> factorize(ll n) {
if (n == 1) return vector <ll>();
if (miller_rabin(n)) return vector<ll> {n};
vector <ll> v, w;
while (n > 1 && n < P) {
v.push_back(spf[n]);
n /= spf[n];
}
if (n >= P) {
ll x = pollard_rho(n);
v = factorize(x);
w = factorize(n / x);
v.insert(v.end(), w.begin(), w.end());
}
return v;
}
}
int main() {
cin.tie(0)->sync_with_stdio(0);
int64_t x; cin >> x;
if (x == 1) {
cout << "1\n";
return 0;
}
PollardRho::init();
map<int, int> cnt;
for (auto i : PollardRho::factorize(x)) {
cnt[i]++;
}
int64_t g = 0;
for (auto [a, b] : cnt) {
g = gcd(g, b);
}
vector<int> p;
for (int i = 1; i <= g; i++) {
if (g % i == 0) p.push_back(i);
}
for (auto power : p) {
int factors = 1;
int64_t ans = 1;
for (auto [a, b] : cnt) {
b /= power;
factors *= b + 1;
while (b--) ans *= a;
}
if (factors == power) {
cout << ans << '\n';
return 0;
}
}
cout << "-1\n";
}
詳細信息
Test #1:
score: 100
Accepted
time: 0ms
memory: 9920kb
input:
15625
output:
25
result:
ok single line: '25'
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score: 0
Accepted
time: 5ms
memory: 11060kb
input:
64000000
output:
20
result:
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score: 0
Accepted
time: 5ms
memory: 9588kb
input:
65536
output:
-1
result:
ok single line: '-1'
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score: 0
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time: 1ms
memory: 3624kb
input:
1
output:
1
result:
ok single line: '1'
Test #5:
score: 0
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time: 5ms
memory: 9876kb
input:
10
output:
-1
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ok single line: '-1'
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score: 0
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time: 0ms
memory: 9548kb
input:
100
output:
-1
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ok single line: '-1'
Test #7:
score: 0
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time: 4ms
memory: 9700kb
input:
10000
output:
10
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score: 0
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time: 5ms
memory: 11396kb
input:
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output:
100
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score: 0
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time: 4ms
memory: 10308kb
input:
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output:
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ok single line: '218089'
Test #10:
score: 0
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time: 5ms
memory: 11140kb
input:
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output:
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memory: 10908kb
input:
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output:
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memory: 10956kb
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32
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time: 5ms
memory: 9852kb
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time: 2ms
memory: 8660kb
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time: 4ms
memory: 9660kb
input:
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ok single line: '-1'
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time: 0ms
memory: 11012kb
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output:
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time: 5ms
memory: 9112kb
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time: 5ms
memory: 10828kb
input:
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score: 0
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time: 2ms
memory: 8500kb
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time: 5ms
memory: 11072kb
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score: 0
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time: 4ms
memory: 8600kb
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time: 2ms
memory: 10684kb
input:
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time: 5ms
memory: 11556kb
input:
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time: 2ms
memory: 9800kb
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memory: 10680kb
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time: 4ms
memory: 8088kb
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score: 0
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time: 5ms
memory: 8656kb
input:
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ok single line: '-1'
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score: 0
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time: 5ms
memory: 11276kb
input:
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output:
-1
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ok single line: '-1'
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score: 0
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time: 5ms
memory: 10408kb
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score: 0
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time: 2ms
memory: 8208kb
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-1
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ok single line: '-1'
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score: 0
Accepted
time: 4ms
memory: 9860kb
input:
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4
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score: 0
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time: 4ms
memory: 9964kb
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Test #36:
score: 0
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time: 4ms
memory: 8656kb
input:
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-1
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ok single line: '-1'
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score: 0
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time: 4ms
memory: 8264kb
input:
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score: 0
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time: 0ms
memory: 9944kb
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ok single line: '-1'
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score: 0
Accepted
time: 2ms
memory: 9620kb
input:
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score: 0
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time: 5ms
memory: 10836kb
input:
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Test #41:
score: 0
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time: 5ms
memory: 9836kb
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score: 0
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time: 4ms
memory: 10692kb
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score: 0
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time: 2ms
memory: 10280kb
input:
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score: 0
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time: 4ms
memory: 10804kb
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output:
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ok single line: '-1'
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score: 0
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memory: 10304kb
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memory: 10568kb
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score: 0
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memory: 10088kb
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score: 0
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memory: 9156kb
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ok single line: '-1'
Test #49:
score: 0
Accepted
time: 5ms
memory: 11456kb
input:
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output:
-1
result:
ok single line: '-1'