Extended GCD Codevs 1200 congruence equation

Codevs 1200 congruence equation

2012 Noip National League Improvement Group

time limit: 1 sspace limit: 128000 KBtitle level: Diamonds DiamondTitle Description Description

The minimum positive integer solution for ax≡1 (mod b) of the x congruence equation is obtained.

Enter a description Input Description

Enter only one row, containing two positive integers a, b, separated by a space.

Output description Output Description

The output has only one row containing a positive integer x0, or a minimum positive integer solution, and the input data guarantees there must be a solution.

Sample input Sample Input

3 10

Sample output Sample Output

7

Data range and Tips Data Size & Hint

"Data Range"
For 40% of data, 2≤b≤1,000;
For 60% of data, 2≤b≤50,000,000
For 100% of data, 2≤a, b≤2,000,000,000

Category labels Tags Click here to expandEuclidean theorem number theory Continental region NOIP National League increase Group 2012

1 /*ax≡1 (mod b) is ax=by+1, and x, y are integers, so ax mod b==1, for ax=by+1, with the extension GCD solution, and then find the right x output can be*/2#include <iostream>3 using namespacestd;4#include <cstdio>5 Long Longb;6 voidEXGCD (Long LongALong LongBLong Long&x,Long Long&y,Long Long&gcd)7 {8     if(b==0)9     {Tengcd=a;x=1; y=0; One       return; A     } -EXGCD (b,a%b,x,y,gcd); -     intt=x; thex=y; -Y=t-(A/b) *y; - } - intMain () + { -Cin>>a>>b; +     Long Longgcd,x,y; A EXGCD (A,B,X,Y,GCD); at     Long Longa0=a/gcd,b0=b/gcd; -     Long Longk=1/gcd; -x*=k;y*=K; -     if(x<=0) -     { -         intI=1; in          while(1) -         { to             if(A * (x+i*b0) +b* (y-i*a0) = =1) +             { -                 if(x+i*b0>0) the                 { *cout<< (x+i*b0) <<Endl; $                     return 0;Panax Notoginseng                 } -             } thei++; +         } A     } the     if(x>0) +     { -         inti=-1; $          while(1) $         { -             if(A * (x+i*b0) +b* (y-i*a0) = =1) -             { the                 if(x+i*b0<0) -                 {Wuyicout<<x<<Endl; the                     return 0; -                 } Wu             } -i--; About         } $     } -     return 0; -}

Extended GCD Codevs 1200 congruence equation