poj2115 C Looooops

C Looooops

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 29262		Accepted: 8441

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 < 2^k) modulo 2^k.

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 < 2^k) 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

大致题意：求在mod 2^k下的一个for循环要运行多少次.

分析：列出同余式，扩展欧几里得解决.

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
 
using namespace std;
 
typedef long long ll;
ll a,b,c,k,A,B,C,d;
 
ll qpow(ll b)
{
    ll res = ,x = ;
    while (b)
    {
        if (b & )
            res *= x;
        x *= x;
        b >>= ;
    }
    return res;
}
 
ll gcd(ll a,ll b)
{
    if (!b)
        return a;
    return gcd(b,a % b);
}
 
void exgcd(ll a,ll b,ll &x,ll &y)
{
    if (!b)
    {
        x = ;
        y = ;
        return;
    }
    exgcd(b,a % b,x,y);
    ll t = x;
    x = y;
    y = t - (a / b) * y;
}
 
int main()
{
    while (scanf("%lld%lld%lld%lld",&a,&b,&c,&k) == )
    {
        if (!a && !b && !c && !k)
            break;
        C = b - a;
        A = c;
        B = qpow(k);
        d = gcd(A,B);
        if (C % d !=  || (b >= B || a >= B || c >= B))
           printf("FOREVER\n");
        else
        {
            ll x,y;
            exgcd(A,B,x,y);
            x = x * C / d;
            B /= d;
            x = (x % B + B) % B;
            printf("%lld\n",x);
        }
    }
 
    return ;
}