QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#696122 | #8336. Indeterminate Equation | DHMOzzz | AC ✓ | 1ms | 4096kb | C++20 | 3.9kb | 2024-10-31 21:35:46 | 2024-10-31 21:35:47 |
Judging History
This is a historical verdict posted at 2024-10-31 21:35:47.
- [2024-11-06 12:52:58]
- hack成功,自动添加数据
- (/hack/1138)
- [2024-10-31 21:35:46]
- Submitted
answer
#include<bits/stdc++.h>
using namespace std;
using i32 = int;
using ll = __int128;
#define int long long
const int N = 1000;
int cntp; //质数的个数
int prime[168]; //从0开始
int vis[N]; //存最小质因数
void euler(int n) {
for (int i = 2; i <= n; i++) {
if (!vis[i]) {
vis[i] = i;
prime[cntp++] = i;
}
for (int j = 0; j < cntp; j++) {
if (i * prime[j] > n) break;
vis[i * prime[j]] = prime[j];
if (i % prime[j] == 0) break;
}
}
}
int mul(int a, int b, int m) {
int r = a * b - m * (int) (1.L / m * a * b);
return r - m * (r >= m) + m * (r < 0);
}
int B[] = {2, 3, 5, 7, 11, 13, 17, 19, 23};
bool isPrime(int n) {
if (n <= 1) return 0;
for (int p: B) {
if (n == p) return 1;
if (n % p == 0) return 0;
}
auto mypow = [](int a, int n, int m) -> int {
int res = 1;
while (n) {
if (n & 1) res = mul(res, a, m);
a = mul(a, a, m);
n >>= 1;
}
return res;
};
int m = (n - 1) >> __builtin_ctz(n - 1);
for (int p: B) {
int t = m, a = mypow(p, m, n);
while (t != n - 1 && a != 1 && a != n - 1) {
a = mul(a, a, n);
t *= 2;
}
if (a != n - 1 && t % 2 == 0) return 0;
}
return 1;
}
int pollard_rho(int n) {
for (int p: B) {
if (n % p == 0) return p;
}
auto f = [&](int x) -> int {
x = mul(x, x, n) + 1;
return x >= n ? x - n : x;
};
int x = 0, y = 0, tot = 0, p = 1, q, g;
for (int i = 0; (i & 255) || (g = gcd(p, n)) == 1; i++, x = f(x), y = f(f(y))) {
if (x == y) {
x = tot++;
y = f(x);
}
q = mul(p, abs(x - y), n);
if (q) p = q;
}
return g;
}
unordered_map<int, int> factor(int n) {
unordered_map<int, int> ans;
vector<int> stk;
for (auto p: prime) {
while (n % p == 0) {
ans[p]++;
n /= p;
}
}
if (n == 1) return ans;
stk.push_back(n);
while (!stk.empty()) {
int b = stk.back();
stk.pop_back();
if (isPrime(b)) {
ans[b]++;
continue;
}
int c = b;
while (c >= b) c = pollard_rho(b);
stk.push_back(c);
stk.push_back(b / c);
}
return ans;
}
vector<int> divisors_by_pf(unordered_map<int, int> &pf) {
vector<int> div = {1};
for (auto &&[p, e]: pf) {
int n = div.size();
int pp = 1;
for (int i = 1; i <= e; i++) {
pp *= p;
for (int j = 0; j < n; j++) div.push_back(div[j] * pp);
}
}
return div;
}
//分解因数
vector<int> divisors(int n) {
auto pf = factor(n); //分解质因数
return divisors_by_pf(pf);
}
ll power(ll a, int n) {
ll res = 1;
while (n) {
if (n & 1) res = res * a;
a = a * a;
n >>= 1;
}
return res;
}
void solve() {
int n, k;
cin >> n >> k;
auto check = [&](int dt, int b) -> bool {
return power(dt + b, k) - power(b, k) <= n;
};
int ans = 0;
vector<int> div = divisors(n);
for (int dt: div) {
int l = 1, r = (int) pow(n / dt, 1.0 / (k - 1));
while (l + 1 < r) {
int mid = (l + r) >> 1;
if (check(dt, mid)) l = mid;
else r = mid;
}
if (power(dt + l, k) - power(l, k) == n) ans++;
}
cout << ans << "\n";
}
signed main() {
#ifdef ONLINE_JUDGE
#else
freopen("in.txt", "r", stdin);
freopen("out.txt", "w", stdout);
#endif
int Tcase = 1;
ios::sync_with_stdio(0), cin.tie(0);
euler(1000);
cin >> Tcase;
while (Tcase--) {
solve();
}
return 0;
}
这程序好像有点Bug,我给组数据试试?
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 0ms
memory: 3848kb
input:
3 7 3 15 4 31 5
output:
1 1 1
result:
ok 3 number(s): "1 1 1"
Test #2:
score: 0
Accepted
time: 1ms
memory: 3764kb
input:
20 409013310800583799 32 70368744177663 46 592570256192463681 4 360020145419649 5 357385021818058297 3 950227088646484702 56 127 7 718303642731669822 3 651621023623339377 45 405657994164855469 3 4095 12 288230376151711743 58 224251587219143167 5 2221626677255791 3 2953488086475199 4 6672460861685157...
output:
0 1 1 1 1 0 1 0 0 1 1 1 1 1 1 1 0 1 0 0
result:
ok 20 numbers
Test #3:
score: 0
Accepted
time: 1ms
memory: 3824kb
input:
20 299663213308337404 3 789663530028185253 15 899102550518872677 5 908651241968426417 38 10161731698203367 3 172563904510845597 3 24904219972305241 3 72057594037927935 56 900135928346130972 6 63 6 32370674179164127 3 638119226609365944 62 67108863 26 257821881508336320 3 815804918211865461 12 910411...
output:
1 0 1 0 1 1 1 1 0 1 1 0 1 1 0 0 1 1 1 1
result:
ok 20 numbers
Test #4:
score: 0
Accepted
time: 1ms
memory: 3876kb
input:
20 987212517904356866 10 625343233082041 3 281474976710655 48 35184372088831 45 8191 13 33554431 25 387412204026720769 3 109355953976006437 3 2198205420145 4 47103092714538256 21 448246606222334791 7 99826963551194419 3 417720736167446718 26 9007199254740991 53 130481423309676535 8 2251799813685247 ...
output:
0 1 1 1 1 1 1 1 1 0 0 1 0 1 0 1 1 1 1 1
result:
ok 20 numbers
Test #5:
score: 0
Accepted
time: 1ms
memory: 4080kb
input:
20 369621295427910453 63 829540864429248940 50 328188506235593452 38 801208558894131272 13 872695838727528838 3 1073741823 30 252424883748225843 19 276360191653207583 13 23680201591411597 3 605336327501498607 29 3368576601423011 5 541099690642302715 3 110139179543268157 3 1073741823 30 5091219638745...
output:
0 0 0 0 1 1 0 0 1 0 1 1 1 1 0 1 1 1 1 1
result:
ok 20 numbers
Test #6:
score: 0
Accepted
time: 1ms
memory: 3796kb
input:
20 8191 13 58185299844488917 3 946219666221344402 19 199313544345127719 42 305224472569938018 6 274877906943 38 8191 13 4398046511103 42 181275224823960757 3 26525260926988201 3 562949953421311 49 4464847706965471 3 457186927518156860 5 158117286447030969 46 549755813887 39 555307613261368 5 4401772...
output:
1 1 0 0 0 1 1 1 1 1 1 1 0 0 1 1 1 0 0 0
result:
ok 20 numbers
Test #7:
score: 0
Accepted
time: 1ms
memory: 3892kb
input:
20 4398046511103 42 833253453410579766 62 409534938012033754 63 72057594037927935 56 536870911 29 34951725759140191 3 90835460846790978 13 16777215 24 2251799813685247 51 699719950959624759 54 248653563296585041 3 421715905914046949 3 605636896545987345 4 524287 19 241759398856733802 6 4935421722667...
output:
1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 1 1 1 0
result:
ok 20 numbers
Test #8:
score: 0
Accepted
time: 1ms
memory: 4012kb
input:
20 106552237922246881 3 412052866942149907 3 2147483647 31 796082436742414414 24 408359486510009476 12 63 6 17592186044415 44 118509271529004788 9 3979116231690817 3 262143 18 70368744177663 46 42768140446560097 3 8589934591 33 386734487134757674 12 4503599627370495 52 536870911 29 28823037615171174...
output:
1 1 1 0 0 1 1 0 1 1 1 1 1 0 1 1 1 1 0 1
result:
ok 20 numbers
Test #9:
score: 0
Accepted
time: 1ms
memory: 4096kb
input:
20 134217727 27 83420139097331842 62 274135990917964800 5 434500257687581785 35 501744216766405008 15 451335986349193 5 868853355445748320 13 301001412129614 5 67108863 26 953222376692677434 25 1886006831138137 3 15857519990553792 5 69764165614656105 63 81798613090978231 3 989051271211163304 41 1867...
output:
1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 1 1
result:
ok 20 numbers
Test #10:
score: 0
Accepted
time: 1ms
memory: 4024kb
input:
20 290234946576194630 24 324991611316950487 3 377254568067887797 3 199176477432292800 5 481817525933591580 44 306179318310704225 5 184460035325889819 5 96166909590250592 3 69908027519627596 3 7371051187969 3 562949953421311 49 513570208984730028 6 180646903364861467 3 622083445561687933 56 145588025...
output:
0 1 1 1 0 1 1 1 1 1 1 0 1 0 1 1 1 1 0 1
result:
ok 20 numbers
Test #11:
score: 0
Accepted
time: 1ms
memory: 4012kb
input:
20 70368744177663 46 137438953471 37 72057594037927935 56 1898262015327215 4 593117722299956521 62 81438002329886371 3 399674414175214669 3 215867547011594871 32 584844110936591318 53 159843794446621357 3 54115722785729521 3 278593973273873791 3 741200008753001294 5 62103974292968851 3 7521806114753...
output:
1 1 1 1 0 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1
result:
ok 20 numbers
Test #12:
score: 0
Accepted
time: 1ms
memory: 3952kb
input:
20 15 4 639325486456928631 24 367160239938275019 3 35135369151859768 5 134217727 27 162403073577381280 4 4398046511103 42 849266064473374657 22 467964515935413061 3 8388607 23 137438953471 37 215086822275193505 3 305420275067478247 3 103789388695665446 18 215568298601022841 3 4503599627370495 52 469...
output:
1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 0 1
result:
ok 20 numbers
Test #13:
score: 0
Accepted
time: 1ms
memory: 4084kb
input:
20 137438953471 37 4503599627370495 52 360622068085547772 10 210287245019037702 35 74711655323394929 56 98155419968374287 21 102533060809494095 4 140737488355327 47 933243045575014403 11 72057594037927935 56 149720681727843610 57 1073741823 30 591686942125381888 31 119086672276608015 4 3477271960851...
output:
1 1 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 0 1 1
result:
ok 20 numbers
Test #14:
score: 0
Accepted
time: 1ms
memory: 3824kb
input:
20 819477969526523940 9 997198472969039861 35 233055230837054597 53 746904402177708777 27 67108863 26 4194303 22 390095551418097427 3 927752109611997442 48 32767 15 390318061363802287 3 686611024540234609 12 20402267600069161 3 698884614026798317 52 562949953421311 49 1550940349430625 4 511 9 759139...
output:
0 0 0 0 1 1 1 0 1 1 0 1 0 1 1 1 0 1 1 0
result:
ok 20 numbers
Test #15:
score: 0
Accepted
time: 1ms
memory: 3780kb
input:
20 347092101157932621 55 523357334205590686 31 686906733435643515 60 120007640497588865 3 347422310624045419 3 301665674749200847 3 866910816105601352 30 5127183360 4 68719476735 36 4194303 22 483964008794649279 18 234063663878120671 3 123845819701080601 3 285423692080282687 3 3912628851220100 5 310...
output:
0 0 0 1 1 1 0 1 1 1 0 1 1 1 1 1 1 0 0 0
result:
ok 20 numbers
Test #16:
score: 0
Accepted
time: 1ms
memory: 3828kb
input:
20 33554431 25 528392007319786400 31 16482551564781760 4 838990357775672509 32 942785412798517385 38 439170874733624419 3 29596780167767827 3 83285573011773301 3 950527866918480 4 2251799813685247 51 4095 12 273991306079656475 5 616699112264653214 52 51492842248899972 25 18785737008450461 15 9959774...
output:
1 0 1 0 0 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1
result:
ok 20 numbers
Test #17:
score: 0
Accepted
time: 1ms
memory: 3876kb
input:
20 2097151 21 3400566422153238 3 631760588083252674 28 167808767206605768 3 323394699435360469 3 335695376290788387 17 35345259238590038 23 39661511301666151 3 102003212137599169 3 131071 17 6017133684009169 3 810416549631456806 61 78371917503410782 3 255 8 292354900238725376 47 394542618557932158 1...
output:
1 1 0 1 1 0 0 1 1 1 1 0 0 1 0 0 1 1 0 1
result:
ok 20 numbers
Test #18:
score: 0
Accepted
time: 1ms
memory: 3944kb
input:
20 8191 13 34450976592326175 39 115992634653776988 30 30841490245990321 3 730558013031329906 56 69661494843438160 4 193199298983587 3 745954000719453413 3 14062568319648604 3 310197905349117863 26 323849701457243377 12 127287856421571104 3 2857372929472969 3 348006386420030269 3 16383 14 524287 19 1...
output:
1 0 0 1 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1
result:
ok 20 numbers
Test #19:
score: 0
Accepted
time: 1ms
memory: 3984kb
input:
20 328331949339594705 4 440018735280441037 3 651726196698130641 25 35184372088831 45 560815166864882104 3 1665749740436467 3 725187027841738697 10 97742833161599557 3 628708937360761 3 144115188075855871 57 45246298445492401 3 897305684378354416 4 435615967025653155 62 51390152812182661 3 5497558138...
output:
1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1
result:
ok 20 numbers
Test #20:
score: 0
Accepted
time: 1ms
memory: 3888kb
input:
20 10287757755011200 5 75165632304477787 3 208610838312868531 3 17592186044415 44 262143 18 472628059236086465 33 274441644154738406 14 63 6 70368744177663 46 9120350170569787 3 68931120362029927 3 244281394805637637 3 616071809801248136 44 36284940549244431 3 518603065311042205 31 4294967295 32 650...
output:
1 1 1 1 1 0 0 1 1 1 1 1 0 1 0 1 0 0 0 0
result:
ok 20 numbers
Test #21:
score: 0
Accepted
time: 1ms
memory: 3948kb
input:
20 951043950767860780 64 72057594037927935 56 4398046511103 42 268435455 28 984744214330259561 54 536393574249559831 3 134217727 27 779206543455963934 53 441797261073316237 3 10900408805331694 5 16383 14 755235903449005803 3 235576685499319964 3 4398046511103 42 16992310045669219 3 536870911 29 3180...
output:
0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 0 1
result:
ok 20 numbers
Extra Test:
score: 0
Extra Test Passed