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#514083#9167. Coprime Arrayucup-team1134#AC ✓0ms3832kbC++235.8kb2024-08-10 21:40:452024-08-10 21:40:45

Judging History

你现在查看的是测评时间为 2024-08-10 21:40:45 的历史记录

  • [2024-10-14 07:52:26]
  • 管理员手动重测本题所有获得100分的提交记录
  • 测评结果:AC
  • 用时:1ms
  • 内存:3820kb
  • [2024-08-11 17:38:28]
  • hack成功,自动添加数据
  • (/hack/775)
  • [2024-08-10 21:40:45]
  • 评测
  • 测评结果:100
  • 用时:0ms
  • 内存:3832kb
  • [2024-08-10 21:40:45]
  • 提交

answer

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return true; } return false; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return true; } return false; }
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second
#define mp make_pair
#define si(x) int(x.size())
const int mod=998244353,MAX=300005,INF=15<<26;

/**
 * Author: chilli, Ramchandra Apte, Noam527, Simon Lindholm
 * Date: 2019-04-24
 * License: CC0
 * Source: https://github.com/RamchandraApte/OmniTemplate/blob/master/modulo.hpp…
 * Description: Calculate $a\cdot b\bmod c$ (or $a^b \bmod c$) for $0 \le a, b \le c \le 7.2\cdot 10^{18}$.
 * Time: O(1) for \texttt{modmul}, O(\log b) for \texttt{modpow}
 * Status: stress-tested, proven correct
 * Details:
 * This runs ~2x faster than the naive (__int128_t)a * b % M.
 * A proof of correctness is in doc/modmul-proof.tex. An earlier version of the proof,
 * from when the code used a * b / (long double)M, is in doc/modmul-proof.md.
 * The proof assumes that long doubles are implemented as x87 80-bit floats; if they
 * are 64-bit, as on e.g. MSVC, the implementation is only valid for
 * $0 \le a, b \le c < 2^{52} \approx 4.5 \cdot 10^{15}$.
 */
#pragma once

typedef unsigned long long ull;
ull modmul(ull a, ull b, ull M) {
ll ret = a * b - M * ull(1.L / M * a * b);
return ret + M * (ret < 0) - M * (ret >= (ll)M);
}
ull modpow(ull b, ull e, ull mod) {
ull ans = 1;
for (; e; b = modmul(b, b, mod), e /= 2)
if (e & 1) ans = modmul(ans, b, mod);
return ans;
}

/**
 * Author: chilli, SJTU, pajenegod
 * Date: 2020-03-04
 * License: CC0
 * Source: own
 * Description: Pollard-rho randomized factorization algorithm. Returns prime
 * factors of a number, in arbitrary order (e.g. 2299 -> \{11, 19, 11\}).
 * Time: $O(n^{1/4})$, less for numbers with small factors.
 * Status: stress-tested
 *
 * Details: This implementation uses the improvement described here
 * (https://en.wikipedia.org/wiki/Pollard%27s_rho_algorithm#Variants…), where
 * one can accumulate gcd calls by some factor (40 chosen here through
 * exhaustive testing). This improves performance by approximately 6-10x
 * depending on the inputs and speed of gcd. Benchmark found here:
 * (https://ideone.com/nGGD9T)
 *
 * GCD can be improved by a factor of 1.75x using Binary GCD
 * (https://lemire.me/blog/2013/12/26/fastest-way-to-compute-the-greatest-common-divisor/…).
 * However, with the gcd accumulation the bottleneck moves from the gcd calls
 * to the modmul. As GCD only constitutes ~12% of runtime, speeding it up
 * doesn't matter so much.
 *
 * This code can probably be sped up by using a faster mod mul - potentially
 * montgomery reduction on 128 bit integers.
 * Alternatively, one can use a quadratic sieve for an asymptotic improvement,
 * which starts being faster in practice around 1e13.
 *
 * Brent's cycle finding algorithm was tested, but doesn't reduce modmul calls
 * significantly.
 *
 * Subtle implementation notes:
 * - we operate on residues in [1, n]; modmul can be proven to work for those
 * - prd starts off as 2 to handle the case n = 4; it's harmless for other n
 *   since we're guaranteed that n > 2. (Pollard rho has problems with prime
 *   powers in general, but all larger ones happen to work.)
 * - t starts off as 30 to make the first gcd check come earlier, as an
 *   optimization for small numbers.
 */
#pragma once

/**
 * Author: chilli, c1729, Simon Lindholm
 * Date: 2019-03-28
 * License: CC0
 * Source: Wikipedia, https://miller-rabin.appspot.com
 * Description: Deterministic Miller-Rabin primality test.
 * Guaranteed to work for numbers up to $7 \cdot 10^{18}$; for larger numbers, use Python and extend A randomly.
 * Time: 7 times the complexity of $a^b \mod c$.
 * Status: Stress-tested
 */
#pragma once

bool isPrime(ull n) {
if (n < 2 || n % 6 % 4 != 1) return (n | 1) == 3;
ull A[] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022},
    s = __builtin_ctzll(n-1), d = n >> s;
for (ull a : A) {   // ^ count trailing zeroes
ull p = modpow(a%n, d, n), i = s;
while (p != 1 && p != n - 1 && a % n && i--)
p = modmul(p, p, n);
if (p != n-1 && i != s) return 0;
}
return 1;
}

ull pollard(ull n) {
auto f = [n](ull x) { return modmul(x, x, n) + 1; };
ull x = 0, y = 0, t = 30, prd = 2, i = 1, q;
while (t++ % 40 || __gcd(prd, n) == 1) {
if (x == y) x = ++i, y = f(x);
if ((q = modmul(prd, max(x,y) - min(x,y), n))) prd = q;
x = f(x), y = f(f(y));
}
return __gcd(prd, n);
}
vector<ull> factor(ull n) {
if (n == 1) return {};
if (isPrime(n)) return {n};
ull x = pollard(n);
auto l = factor(x), r = factor(n / x);
l.insert(l.end(), all(r));
return l;
}

mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());

vector<ll> solve(ll S,ll X){
    if(gcd(S,X)==1) return {S};
    
    if(gcd(S,X)%2==0||X&1){
        for(ll d=0;;d++){
            ll a=S/2+d,b=S-a;
            if(gcd(a,X)==1&&gcd(b,X)==1){
                return {a,b};
            }
        }
    }
    if(gcd(S+2,X)==1){
        return {S+2,-1,-1};
    }else if(gcd(S-2,X)==1){
        return {S-2,1,1};
    }else{
        while(1){
            ll a=rng()%mod-500000000;
            if(gcd(abs(a),X)>1) continue;
            ll b=rng()%mod-500000000;
            if(gcd(abs(b),X)>1) continue;
            ll c=S-a-b;
            if(gcd(abs(c),X)>1) continue;
            return {a,b,c};
        }
    }
    return {};
}

int main(){
    
    std::ifstream in("text.txt");
    std::cin.rdbuf(in.rdbuf());
    cin.tie(0);
    ios::sync_with_stdio(false);
    
    ll S,X;cin>>S>>X;
    auto res=solve(S,X);
    cout<<si(res)<<"\n";
    for(ll x:res) cout<<x<<" ";
    cout<<endl;
}

这程序好像有点Bug,我给组数据试试?

详细

Test #1:

score: 100
Accepted
time: 0ms
memory: 3612kb

input:

9 6

output:

3
11 -1 -1 

result:

ok Correct

Test #2:

score: 0
Accepted
time: 0ms
memory: 3828kb

input:

14 34

output:

2
7 7 

result:

ok Correct

Test #3:

score: 0
Accepted
time: 0ms
memory: 3672kb

input:

1000000000 223092870

output:

2
500000021 499999979 

result:

ok Correct

Test #4:

score: 0
Accepted
time: 0ms
memory: 3588kb

input:

2 1000000000

output:

2
1 1 

result:

ok Correct

Test #5:

score: 0
Accepted
time: 0ms
memory: 3828kb

input:

649557664 933437700

output:

2
324778841 324778823 

result:

ok Correct

Test #6:

score: 0
Accepted
time: 0ms
memory: 3812kb

input:

33396678 777360870

output:

2
16698349 16698329 

result:

ok Correct

Test #7:

score: 0
Accepted
time: 0ms
memory: 3616kb

input:

48205845 903124530

output:

3
48205847 -1 -1 

result:

ok Correct

Test #8:

score: 0
Accepted
time: 0ms
memory: 3660kb

input:

251037078 505905400

output:

2
125518539 125518539 

result:

ok Correct

Test #9:

score: 0
Accepted
time: 0ms
memory: 3828kb

input:

30022920 172746860

output:

2
15011467 15011453 

result:

ok Correct

Test #10:

score: 0
Accepted
time: 0ms
memory: 3620kb

input:

63639298 808058790

output:

2
31819649 31819649 

result:

ok Correct

Test #11:

score: 0
Accepted
time: 0ms
memory: 3592kb

input:

76579017 362768406

output:

3
76579015 1 1 

result:

ok Correct

Test #12:

score: 0
Accepted
time: 0ms
memory: 3788kb

input:

40423669 121437778

output:

3
40423671 -1 -1 

result:

ok Correct

Test #13:

score: 0
Accepted
time: 0ms
memory: 3828kb

input:

449277309 720915195

output:

2
224638658 224638651 

result:

ok Correct

Test #14:

score: 0
Accepted
time: 0ms
memory: 3528kb

input:

81665969 919836918

output:

3
81665971 -1 -1 

result:

ok Correct

Test #15:

score: 0
Accepted
time: 0ms
memory: 3752kb

input:

470578680 280387800

output:

2
235289357 235289323 

result:

ok Correct

Test #16:

score: 0
Accepted
time: 0ms
memory: 3676kb

input:

58450340 803305503

output:

2
29225176 29225164 

result:

ok Correct

Test #17:

score: 0
Accepted
time: 0ms
memory: 3616kb

input:

125896113 323676210

output:

3
-337333643 201393187 261836569 

result:

ok Correct

Test #18:

score: 0
Accepted
time: 0ms
memory: 3616kb

input:

381905348 434752500

output:

2
190952689 190952659 

result:

ok Correct

Test #19:

score: 0
Accepted
time: 0ms
memory: 3596kb

input:

78916498 653897673

output:

1
78916498 

result:

ok Correct

Test #20:

score: 0
Accepted
time: 0ms
memory: 3832kb

input:

35787885 270845190

output:

3
35787883 1 1 

result:

ok Correct

Extra Test:

score: 0
Extra Test Passed