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QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#696122#8336. Indeterminate EquationDHMOzzzAC ✓1ms4096kbC++203.9kb2024-10-31 21:35:462024-10-31 21:35:47

Judging History

This is a historical verdict posted at 2024-10-31 21:35:47.

  • [2024-11-06 12:58:18]
  • 自动重测本题所有获得100分的提交记录
  • Verdict: AC
  • Time: 1ms
  • Memory: 4060kb
  • [2024-11-06 12:52:58]
  • hack成功,自动添加数据
  • (/hack/1138)
  • [2024-10-31 21:35:47]
  • Judged
  • Verdict: 100
  • Time: 1ms
  • Memory: 4096kb
  • [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