POJ1061 青蛙的约会

Posted 2020-09-06 BBBob

 1 /*
 2  POJ1061 青蛙的约会
 3  http://poj.org/problem?id=1061
 4  扩展欧几里得
 5 
 6  原题为求t使得,存在l满足
 7     (x+mt)-(y+nt)=cl
 8     即求
 9     cl+(n-m)t=x-y
10  *
11  *
12  *
13  */
14 
15 #include <cstdio>
16 #include <cmath>
17 using namespace std;
18 long long ex_gcd(long long a,long long b,long long &x,long long &y)//solve x,y in a*x+b*y=ex_gcd(a,b,x,y)=gcd(a,b);
19 {
20     if(b==0LL)
21     {
22         x=1LL;
23         y=0LL;
24         return a;
25     }
26     long long ans=ex_gcd(b,a%b,x,y);
27     long long tmp=x;
28     x=y;
29     y=tmp-a/b*y;
30     return ans;
31     //x = x0 + (b/gcd)*t
32     //y = y0 – (a/gcd)*t
33      
34 }
35 int main()
36 {
37     long long x,y,m,n,l;
38     scanf("%lld%lld%lld%lld%lld",&x,&y,&m,&n,&l);
39     long long a=l,b=n-m;
40     l=x-y;
41     long long xx,yy;
42     long long gcd=ex_gcd(a,b,xx,yy);
43     if(l%gcd)
44     {
45         printf("Impossible\n");
46         return 0;
47     }
48 
49     long long r=l/gcd;
50     //while(xx<=0)
51     //{
52         //xx=xx+b/gcd;
53         //yy=yy-a/gcd;
54     //}
55     yy=yy*r;
56     a=a/gcd;
57     long long t=yy%a;
58     while(t<0)
59         t+=a;
60     printf("%lld\n",t);
61     return 0;
62 }