POJ C Looooops 2115 (扩展欧几里得)

C Looooops Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 23143   Accepted: 6357 Description A Compiler Mystery: We are given a C-language style for loop of type  for (variable = A; variable != B; variable += C) statement; I.e., a loop which starts by setting variable to value A and while variable is not equal to B, repeats statement followed by increasing the variable by C. We want to know how many times does the statement get executed for particular values of A, B and C, assuming that all arithmetics is calculated in a k-bit unsigned integer type (with values 0 <= x < 2k) modulo 2k.  Input The input consists of several instances. Each instance is described by a single line with four integers A, B, C, k separated by a single space. The integer k (1 <= k <= 32) is the number of bits of the control variable of the loop and A, B, C (0 <= A, B, C < 2k) are the parameters of the loop.  The input is finished by a line containing four zeros.  Output The output consists of several lines corresponding to the instances on the input. The i-th line contains either the number of executions of the statement in the i-th instance (a single integer number) or the word FOREVER if the loop does not terminate.  Sample Input 3 3 2 16 3 7 2 16 7 3 2 16 3 4 2 16 0 0 0 0 Sample Output 0 2 32766 FOREVER Source CTU Open 2004

题意：给出a,b,c,k,算(a+x*c)%2^k是否等于b
分析：扩展欧几里得最小整数解　可以把上面的方程转成　a*x + 2^k*y = b

如果没有整数解，则永远到不了，套模板，这里有模板点击打开链接

#include <stdio.h>
#include <string.h>
#include <algorithm>
#include <math.h>
#include <stdlib.h>
using namespace std;
long long x,y;
long long e_gcd(long long a,long long b,long long &x,long long &y)
{
if(b==0)
{
x=1;
y=0;
return a;
}
long long ans=e_gcd(b,a%b,x,y);
long long temp;
temp=x;
x=y;
y=temp-a/b*y;
return ans;
}
int main()
{
long long a,b,c,d,n,m,k,l;
while(~scanf("%lld%lld%lld%lld",&a,&b,&c,&k))
{
if(a==0 && b==0 && c==0 && k==0)
break;
n=c;
m=1LL<<k;
l=b-a;
d=e_gcd(n,m,x,y);
if(l%d!=0)
printf("FOREVER\n");
else
{
x=x*(l/d);
m=m/d;
printf("%lld\n",((x%m)+m)%m);
}
}
return 0;
}