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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#800643 | #9622. 有限小数 | CCSU_YZT | WA | 0ms | 3728kb | C++20 | 1.7kb | 2024-12-06 13:41:42 | 2024-12-06 13:41:43 |
Judging History
answer
#include <bits/stdc++.h>
using namespace std;
// 扩展欧几里得算法求逆元:在已知gcd(a,m)=1的情况下求a在模m下的逆元
long long extended_gcd(long long a, long long b, long long &x, long long &y) {
if (b == 0) {
x = 1; y = 0;
return a;
}
long long x1, y1;
long long g = extended_gcd(b, a % b, x1, y1);
x = y1;
y = x1 - (a / b)*y1;
return g;
}
long long modInverse(long long a, long long m) {
long long x, y;
long long g = extended_gcd(a, m, x, y);
// 假设g=1
x = (x % m + m) % m;
return x;
}
int main(){
ios::sync_with_stdio(false);
cin.tie(NULL);
int T; cin >> T;
while(T--){
long long a,b; cin >> a >> b;
// 因为gcd(a,b)=1
// 将b分解为q*s, q只包含2和5
// 提取b中的2因子
long long bb = b;
long long q = 1;
while (bb % 2 == 0) { q *= 2; bb /= 2; }
while (bb % 5 == 0) { q *= 5; bb /= 5; }
long long s = bb; // s为剩余因子部分
if (s == 1) {
// b本身只含2和5,a/b是有限小数
// 输出c=0,d=1即可
cout << 0 << " " << 1 << "\n";
} else {
// 我们选择d = s
// 要求 s | (a + c*q)
// 即 a + c*q ≡ 0 (mod s)
// c*q ≡ -a (mod s)
// 由于gcd(q,s)=1,可以求q的逆元
long long c;
long long q_inv = modInverse(q, s);
long long val = ((-a) % s + s) % s;
c = (val * q_inv) % s; // 最小非负解
cout << c << " " << s << "\n";
}
}
return 0;
}
Details
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Test #1:
score: 0
Wrong Answer
time: 0ms
memory: 3728kb
input:
4 1 2 2 3 3 7 19 79
output:
0 1 1 3 4 7 60 79
result:
wrong answer Jury found better answer than participant's 1 < 4 (Testcase 3)