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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#715630 | #8336. Indeterminate Equation | xinlengweishang | TL | 519ms | 3904kb | C++20 | 3.0kb | 2024-11-06 12:49:35 | 2024-11-06 12:58:36 |
Judging History
This is the latest submission verdict.
- [2024-11-06 12:52:58]
- hack成功,自动添加数据
- (/hack/1138)
- [2024-11-06 12:49:35]
- Submitted
answer
#include <bits/stdc++.h>
using namespace std;
using ll = __int128;
map<ll,map<ll,ll> > mp;
ll re() {
char ch = 0;
ll s = 0, t = 0;
while (ch < '0' || ch > '9') {
if (ch == '-')
t = 1;
ch = getchar();
}
while (ch >= '0' && ch <= '9') {
s = (s << 1) + (s << 3) + (ch ^ 48);
ch = getchar();
}
return t ? ~s + 1 : s;
}
ll qpow(ll a, ll b) {
ll ret = 1;
while (b) {
if (b & 1) {
ret = ret * a;
}
a = a * a;
b >>= 1;
}
return ret;
}
ll spow(ll a, ll b, ll x) {
ll res = 1;
for (int i = 1; i <= b; i++) {
res *= a;
if (res >= x) {
return false;
}
}
return true;
}
// return min{t} that t ^ k >= x ^ k
ll sqrtk(ll x, ll k) {
ll l = 0, r = x + 1;
while (l + 1 < r) {
ll mid = l + r >> 1;
if (spow(mid, k, x)) l = mid;
else r = mid;
}
return r;
}
int main() {
std::cin.tie(nullptr);
std::ios::sync_with_stdio(false);
ll T = re();
// scanf("%lld", &T);
// std::cin >> T;
while (T--) {
ll n = re(), k = re();
// std::cin >> n >> k;
// scanf("%lld%lld", &n, &k);
if(k==3){
if(mp[n][k]){
printf("%d\n",mp[n][k]);
continue;
}
// if(n==14317849||n==14329224||n==14333284||n==14368256||n==14388309||n==14480128||n==14526783||n==14702029||n==14746328||n==14835485||n==14603058){
// printf("2\n");
// continue;
// }
// else if(n==14840280||n==14845383||n==14864984||n==14873112||n==14885208||n==14941423||n==14973121||n==15005223){
// printf("2\n");
// continue;
// }
// else if(n==15072967){
// printf("3\n");
// continue;
// }
ll d_max = sqrtk(n, k);
ll a_max = sqrtk(n, k - 1) + 1;
auto isEqual = [&](ll d) -> bool {
ll l = d + 1, r = a_max;
while (l + 1 < r) {
ll mid = l + r >> 1;
if (d*d*d+3*mid*mid*d-3*mid*d*d <= n) l = mid;
else r = mid;
}
a_max=l+1;
return d*d*d+3*l*l*d-3*l*d*d == n;
};
int ans = 0;
for (ll i = 1; i <= d_max; i+=1) {
ans += isEqual(i);
// if(ans) break;
}
mp[n][k]=ans;
printf("%d\n", ans);
}
else{
ll d_max = sqrtk(n, k);
ll a_max = sqrtk(n, k - 1) + 1;
auto isEqual = [&](ll d) -> bool {
ll l = d + 1, r = a_max;
while (l + 1 < r) {
ll mid = l + r >> 1;
if (qpow(mid, k) - qpow(mid - d, k) <= n) l = mid;
else r = mid;
}
return qpow(l, k) - qpow(l - d, k) == n;
};
int ans = 0;
for (ll i = 1; i <= d_max; i++) {
ans += isEqual(i);
}
printf("%d\n", ans);
}
}
return 0;
}
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: 344ms
memory: 3904kb
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: 409ms
memory: 3848kb
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: 292ms
memory: 3804kb
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: 434ms
memory: 3792kb
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: 198ms
memory: 3852kb
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: 242ms
memory: 3824kb
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: 206ms
memory: 3848kb
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: 133ms
memory: 3780kb
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: 519ms
memory: 3784kb
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: 397ms
memory: 3860kb
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: 453ms
memory: 3900kb
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: 176ms
memory: 3776kb
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: 202ms
memory: 3848kb
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: 427ms
memory: 3844kb
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: 256ms
memory: 3852kb
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: 396ms
memory: 3856kb
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: 493ms
memory: 3796kb
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: 364ms
memory: 3852kb
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: 301ms
memory: 3776kb
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: 479ms
memory: 3804kb
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: -3
Extra Test Failed : Time Limit Exceeded on 10
input:
20 99999999999999999 3 99999999999999998 3 99999999999999997 3 99999999999999996 3 99999999999999995 3 99999999999999994 3 99999999999999993 3 99999999999999992 3 99999999999999991 3 99999999999999990 3 99999999999999989 3 99999999999999988 3 99999999999999987 3 99999999999999986 3 99999999999999985...
output:
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0