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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#746310 | #9622. 有限小数 | Yurily | TL | 1ms | 3776kb | C++20 | 2.4kb | 2024-11-14 14:11:22 | 2024-11-14 14:11:29 |
Judging History
answer
#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
#define LL __int128
using namespace std;
const LL e9 = 1e9;
const LL e18 = 1e36;
LL a, b, k;
LL b2, b5;
LL gcd(LL a, LL b){
LL r = a % b;
while(r > 0){
a = b;
b = r;
r = a % b;
}
return b;
}
LL div_ceil(LL x,LL y){
if(x>=0){
if(x%y)
return x/y+1;
return x/y;
}
else{
return -((-x)/y);
}
}
void extend_gcd(LL a,LL b,LL &x,LL &y){
if(b==0){
x=1;
y=0;
return;
}
extend_gcd(b,a%b,x,y);
LL tmp=x;
x=y;
y=tmp-(a/b)*y;
}
LL getf(LL a, LL b, LL c){
LL g=gcd(a,b);
LL aa=a/g,bb=b/g,cc=c/g;
LL xx,yy;
extend_gcd(aa,bb,xx,yy);
LL x0=xx*cc;
LL t=div_ceil(-x0,bb);
return x0+bb*t;
}
void sol(){
long long tmpa,tmpb;
scanf("%lld%lld", &tmpa, &tmpb);
a=tmpa,b=tmpb;
k = b;
b2 = b5 = 0;
while(k > 0 && k % 2 == 0){
b2++;
k /= 2;
}
while(k > 0 && k % 5 == 0){
b5++;
k /= 5;
}
if(k == 1){
printf("0 1\n");
return ;
}
LL minc = e18, mind = e18;
LL x, y, t, c, d, g;
for(x = 1; x <= e18 && b * x <= e18; x *= 2){
for(y = 1; y <= e18 && b * x * y <= e18; y *= 5){
t = k - (a * x * y % k);
c = t;
d = b * x * y;
g = gcd(c, d);
c /= g;
d /= g;
if(c < minc && d <= e9){
minc = c;
mind = d;
}
}
}
for(LL xi = 0, x = 1; xi <= b2; xi++, x *= 2){
for(LL yi = 0, y = 1; yi <= b5; yi++, y *= 5){
LL p = x * y;
LL q = k - a % k;
//p * x1 + k * y1 === q
//t = min(x1)
t = getf(p, k, q);
c = t;
d = b / p;
g = gcd(c, d);
c /= g;
d /= g;
if(c < minc){
minc = c;
mind = d;
}
}
}
printf("%lld %lld\n", (long long)minc, (long long)mind);
}
int main(){
// freopen("in.txt", "r", stdin);
// freopen("out.txt", "w", stdout);
int T;
scanf("%d", &T);
while(T--)
sol();
return 0;
}
Details
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Test #1:
score: 100
Accepted
time: 1ms
memory: 3776kb
input:
4 1 2 2 3 3 7 19 79
output:
0 1 1 3 1 4375 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 828125000 1 60 1 7 1 231680000 23 960937500 1 36096000 5 326 1 63360 0 1 1 61000 0 1 1 4880 1 10750 1 18500 1 11714560 1 331250 1 898437500 1 31 1 6 1 289600000 1 455000 1 115000000 1 1265625 0 1 1 1484375 0 1 1 415 1 235937500 1 765000000 1 181250 1 2968750 1 4406250 3 775 1 48 3 347500 1 94...