QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#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";
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 0ms
memory: 9920kb
input:
15625
output:
25
result:
ok single line: '25'
Test #2:
score: 0
Accepted
time: 5ms
memory: 11060kb
input:
64000000
output:
20
result:
ok single line: '20'
Test #3:
score: 0
Accepted
time: 5ms
memory: 9588kb
input:
65536
output:
-1
result:
ok single line: '-1'
Test #4:
score: 0
Accepted
time: 1ms
memory: 3624kb
input:
1
output:
1
result:
ok single line: '1'
Test #5:
score: 0
Accepted
time: 5ms
memory: 9876kb
input:
10
output:
-1
result:
ok single line: '-1'
Test #6:
score: 0
Accepted
time: 0ms
memory: 9548kb
input:
100
output:
-1
result:
ok single line: '-1'
Test #7:
score: 0
Accepted
time: 4ms
memory: 9700kb
input:
10000
output:
10
result:
ok single line: '10'
Test #8:
score: 0
Accepted
time: 5ms
memory: 11396kb
input:
1000000000000000000
output:
100
result:
ok single line: '100'
Test #9:
score: 0
Accepted
time: 4ms
memory: 10308kb
input:
10372926089038969
output:
218089
result:
ok single line: '218089'
Test #10:
score: 0
Accepted
time: 5ms
memory: 11140kb
input:
10642944803293201
output:
10157
result:
ok single line: '10157'
Test #11:
score: 0
Accepted
time: 0ms
memory: 10908kb
input:
10646534823110209
output:
103182047
result:
ok single line: '103182047'
Test #12:
score: 0
Accepted
time: 5ms
memory: 10956kb
input:
1073741824
output:
32
result:
ok single line: '32'
Test #13:
score: 0
Accepted
time: 5ms
memory: 9852kb
input:
121
output:
11
result:
ok single line: '11'
Test #14:
score: 0
Accepted
time: 2ms
memory: 8660kb
input:
1296
output:
6
result:
ok single line: '6'
Test #15:
score: 0
Accepted
time: 4ms
memory: 9660kb
input:
16
output:
-1
result:
ok single line: '-1'
Test #16:
score: 0
Accepted
time: 0ms
memory: 11012kb
input:
16277421889
output:
127583
result:
ok single line: '127583'
Test #17:
score: 0
Accepted
time: 5ms
memory: 9112kb
input:
169
output:
13
result:
ok single line: '13'
Test #18:
score: 0
Accepted
time: 5ms
memory: 10828kb
input:
1985984
output:
-1
result:
ok single line: '-1'
Test #19:
score: 0
Accepted
time: 2ms
memory: 8500kb
input:
2
output:
-1
result:
ok single line: '-1'
Test #20:
score: 0
Accepted
time: 5ms
memory: 11072kb
input:
205891132094649
output:
243
result:
ok single line: '243'
Test #21:
score: 0
Accepted
time: 4ms
memory: 8600kb
input:
25
output:
5
result:
ok single line: '5'
Test #22:
score: 0
Accepted
time: 2ms
memory: 10684kb
input:
2626114239841
output:
1273
result:
ok single line: '1273'
Test #23:
score: 0
Accepted
time: 5ms
memory: 11556kb
input:
26269395104446321
output:
12731
result:
ok single line: '12731'
Test #24:
score: 0
Accepted
time: 2ms
memory: 9800kb
input:
3
output:
-1
result:
ok single line: '-1'
Test #25:
score: 0
Accepted
time: 5ms
memory: 10680kb
input:
3596345248055296
output:
88
result:
ok single line: '88'
Test #26:
score: 0
Accepted
time: 0ms
memory: 8080kb
input:
36
output:
-1
result:
ok single line: '-1'
Test #27:
score: 0
Accepted
time: 4ms
memory: 8376kb
input:
4
output:
2
result:
ok single line: '2'
Test #28:
score: 0
Accepted
time: 4ms
memory: 8936kb
input:
4096
output:
8
result:
ok single line: '8'
Test #29:
score: 0
Accepted
time: 4ms
memory: 8088kb
input:
49
output:
7
result:
ok single line: '7'
Test #30:
score: 0
Accepted
time: 5ms
memory: 8656kb
input:
5
output:
-1
result:
ok single line: '-1'
Test #31:
score: 0
Accepted
time: 5ms
memory: 11276kb
input:
576460752303423488
output:
-1
result:
ok single line: '-1'
Test #32:
score: 0
Accepted
time: 5ms
memory: 10408kb
input:
581431415926321
output:
24112889
result:
ok single line: '24112889'
Test #33:
score: 0
Accepted
time: 2ms
memory: 8208kb
input:
6
output:
-1
result:
ok single line: '-1'
Test #34:
score: 0
Accepted
time: 4ms
memory: 9860kb
input:
64
output:
4
result:
ok single line: '4'
Test #35:
score: 0
Accepted
time: 4ms
memory: 9964kb
input:
656100000000
output:
30
result:
ok single line: '30'
Test #36:
score: 0
Accepted
time: 4ms
memory: 8656kb
input:
7
output:
-1
result:
ok single line: '-1'
Test #37:
score: 0
Accepted
time: 4ms
memory: 8264kb
input:
729
output:
9
result:
ok single line: '9'
Test #38:
score: 0
Accepted
time: 0ms
memory: 9944kb
input:
8
output:
-1
result:
ok single line: '-1'
Test #39:
score: 0
Accepted
time: 2ms
memory: 9620kb
input:
81
output:
-1
result:
ok single line: '-1'
Test #40:
score: 0
Accepted
time: 5ms
memory: 10836kb
input:
8527674378686464
output:
452
result:
ok single line: '452'
Test #41:
score: 0
Accepted
time: 5ms
memory: 9836kb
input:
9
output:
3
result:
ok single line: '3'
Test #42:
score: 0
Accepted
time: 4ms
memory: 10692kb
input:
982134461213542729
output:
994009
result:
ok single line: '994009'
Test #43:
score: 0
Accepted
time: 2ms
memory: 10280kb
input:
9992002399680016
output:
9998
result:
ok single line: '9998'
Test #44:
score: 0
Accepted
time: 4ms
memory: 10804kb
input:
999269311525198921
output:
-1
result:
ok single line: '-1'
Test #45:
score: 0
Accepted
time: 4ms
memory: 10304kb
input:
999949000866995087
output:
-1
result:
ok single line: '-1'
Test #46:
score: 0
Accepted
time: 0ms
memory: 10568kb
input:
999995482005103081
output:
-1
result:
ok single line: '-1'
Test #47:
score: 0
Accepted
time: 5ms
memory: 10088kb
input:
999999969999997921
output:
-1
result:
ok single line: '-1'
Test #48:
score: 0
Accepted
time: 5ms
memory: 9156kb
input:
999999999999999989
output:
-1
result:
ok single line: '-1'
Test #49:
score: 0
Accepted
time: 5ms
memory: 11456kb
input:
999999999999999999
output:
-1
result:
ok single line: '-1'