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QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#738205#9622. 有限小数huo_hua_ya#TL 0ms3592kbC++231.9kb2024-11-12 18:15:352024-11-12 18:15:36

Judging History

你现在查看的是最新测评结果

  • [2024-11-12 18:15:36]
  • 评测
  • 测评结果:TL
  • 用时:0ms
  • 内存:3592kb
  • [2024-11-12 18:15:35]
  • 提交

answer

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const int N = 1e6 + 7;
const int mod = 998244353;
#define ll __int128
//求解不定方程 ax+by=c 的最小整数解 x
ll exgcd(ll a, ll b, ll &x, ll &y)
{
    if (!b) {x = 1; y = 0; return a;}
    ll ans = exgcd(b, a % b, x, y);
    ll tmp = x;
    x = y;
    y = tmp - a / b * y;
    return ans;
}
ll x, y;
ll cal(ll a, ll b, ll c)
{
    x = 0, y = 0;
    ll ans = exgcd(a, b, x, y);
    if (c % ans)return -1;
    x *= c / ans; b /= ans;
    // y *= c / ans;
    if (b < 0)b = -b;
    x = (x % b + b) % b;
    return x;
}
void solve()
{
    int a, b;
    cin >> a >> b;
    ll p = b, k = 1;
    while (p % 2 == 0) {
        p /= 2;
        k *= 2;
    }
    while (p % 5 == 0) {
        p /= 5;
        k *= 5;
    }
    long long c = 1e18, t = 0;
    auto check = [&](ll id) {
        c = cal(k, a, p * id);
        // cerr << c << "\n";
        t = (id*p - 1ll * k * c) / a;
        return t >= 1;
    };
    ll l = 1, r = 1e18;
    while (l < r) {
        ll mid = (l + r) >> 1;
        if (check(mid))r = mid;
        else l = mid + 1;
    }
    check(l);
    auto cb = [&](ll x){
        while(x % 2 == 0){
            x /= 2;
        }
        while(x%5==0){
            x/=5;
        }
        return x == 1;
    };
    // cerr << (long long)l <<'\n';
    long long cx = c,tx = t;
    for(int i=1;i<=3000;i++){
        check(l + i);
        // cerr <<c <<'\n';
        // if(c == 0)break;
        if(cx > c&&t*p<=1000000000ll&&cb(t)){
            cx = c;
            tx = t;
        }
    }
    long long d = tx * p;
    // assert(d<=1000000000&&d>=1);
    cout << cx << " " << d << '\n';
}
int main()
{
    ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
    int _ = 1;
    cin >> _;
    while (_--)
        solve();
    return 0;
}

Details

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Test #1:

score: 100
Accepted
time: 0ms
memory: 3592kb

input:

4
1 2
2 3
3 7
19 79

output:

0 1
1 3
1 14
3 316

result:

ok 4 case(s)

Test #2:

score: -100
Time Limit Exceeded

input:

10000
11 12
28 53
17 60
2 35
17 181
80 123
68 141
79 163
71 99
13 64
33 61
15 32
16 61
11 86
33 74
128 143
40 53
7 23
30 31
5 6
86 181
73 91
13 23
71 81
1 2
7 38
117 160
33 83
129 151
88 153
25 58
16 19
19 141
95 124
43 96
71 139
11 59
106 109
93 152
34 43
17 99
1 57
20 159
16 25
5 73
159 170
172 17...

output:

1 12
1 54272
0 27
1 7
7 90500
23 3936
5 282
5 326
1 63360
0 40
1 31232
0 25
1 4880
1 10750
1 18500
7 1430
3 10600
1 2944
1 31
1 6
7 113125
9 186368
1 58880
1 51840
0 1
1 304
0 25
1 415
9 94375
5 156672
1 4640
1 608
1 72192
3 775
1 75
3 347500
1 944
1 43600
1 76
2 215
1 6336
0 228
11 795000
0 8
1 146...

result: