扩展欧几里得 exGCD

Elementary Number Theory - Extended Euclid Algorithm

Time Limit : 1 sec, Memory Limit : 65536 KB 
Japanese version is here

Extended Euclid Algorithm

Given positive integers a and b, find the integer solution (x, y) to ax+by=gcd(a,b), where gcd(a,b) is the greatest common divisor of a and b.

Input

a b

Two positive integers a and b are given separated by a space in a line.

Output

Print two integers x and y separated by a space. If there are several pairs of such x and y, print that pair for which |x|+|y| is the minimal (primarily) and x ≤ y (secondarily).

Constraints

• 1 ≤ a, b ≤ 109

Sample Input 1

4 12

Sample Output 1

1 0

Sample Input 2

3 8

Sample Output 2

3 -1

 #include <bits/stdc++.h>

 #define fread_siz 1024

 inline int get_c(void)
 {
     static char buf[fread_siz];
     static char *head = buf + fread_siz;
     static char *tail = buf + fread_siz;

     if (head == tail)
         fread(head = buf, , fread_siz, stdin);

     return *head++;
 }

 inline int get_i(void)
 {
     register int ret = ;
     register int neg = false;
     register int bit = get_c();

     for (; bit < ; bit = get_c())
         if (bit == '-')neg ^= true;

     for (; bit > ; bit = get_c())
         ret = ret *  + bit - ;

     return neg ? -ret : ret;
 }

 int exgcd(int a, int b, int &x, int &y)
 {
     if (!b)
     {
         x = ;
         y = ;
         return a;
     }
     int ret = exgcd(b, a%b, y, x);
     y = y - x * (a / b);
     return ret;
 }

 signed main(void)
 {
     int x, y;
     int a = get_i();
     int b = get_i();
     exgcd(a, b, x, y);
     printf("%d %d\n", x, y);
 }

@Author: YouSiki