zoukankan      html  css  js  c++  java
  • POJ2115(扩展欧几里得)

    C Looooops

    Time Limit: 1000MS   Memory Limit: 65536K
    Total Submissions: 23700   Accepted: 6550

    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

     由题意易得(a+cx)%2^k==b,求x最小值。可得同余方程c*x=(b-a)mod2^k。

     1 //2016.8.17
     2 #include<iostream>
     3 #include<cstdio>
     4 #include<algorithm>
     5 #define ll long long 
     6 
     7 using namespace std;
     8 
     9 ll ex_gcd(ll a, ll b, ll& x, ll& y)//扩展欧几里得
    10 {
    11     if(b==0)
    12     {
    13         x = 1; 
    14         y = 0;
    15         return a;
    16     }
    17     ll ans = ex_gcd(b, a%b, x, y);
    18     ll tmp = x;
    19     x = y;
    20     y = tmp-(a/b)*y;
    21     return ans;
    22 }
    23 
    24 int main()
    25 {
    26     ll a, b, c, x, y, res, n;
    27     int k;
    28     while(scanf("%lld%lld%lld%d", &a, &b, &c, &k)!=EOF)
    29     {
    30         if(!a&&!b&&!c&&!k)
    31           break;
    32         n = (ll)1<<k;
    33         res = ex_gcd(c, n, x, y);
    34         cout<<res<<endl<<x<<endl;
    35         if((b-a)%res!=0)cout<<"FOREVER"<<endl;
    36         else 
    37         {
    38             x = x*(b-a)/res%n;//方程ax=b-a(mod n)的最小解
    39             ll tmp = n/res;
    40             x = (x%tmp+tmp)%tmp;//最小正数解
    41             printf("%lld
    ", x);
    42         }
    43     }
    44 
    45     return 0;
    46 }
     1 #include <iostream>
     2 #define ll long long
     3 
     4 using namespace std;
     5 
     6 ll ex_gcd(ll a, ll b, ll& x, ll& y){
     7     if(b == 0){
     8         x = 1;
     9         y = 0;
    10         return a;
    11     }
    12     ll ans = ex_gcd(b, a%b, x, y);
    13     ll tmpx = x;
    14     x = y;
    15     y = tmpx-a/b*y;
    16     return ans;
    17 }
    18 
    19 int main()
    20 {
    21     int a, b, c, k;
    22     while(cin>>a>>b>>c>>k){
    23         if(!a&&!b&&!c&&!k)break;
    24         ll x, y;
    25         ll A = c;
    26         ll B = b-a;
    27         ll n = 1LL<<k;
    28         ll gcd = ex_gcd(A, n, x, y);
    29         if(B%gcd != 0)
    30             cout<<"FOREVER"<<endl;
    31         else{
    32             x = (x*(B/gcd))%n;
    33             x = (x%(n/gcd)+n/gcd)%(n/gcd);
    34             cout<<x<<endl;
    35         }
    36     }
    37     return 0;
    38 }
  • 相关阅读:
    docker学习数据卷挂载方式
    接口自动化CIJenkins
    linux安装docker
    docker学习容器备份
    Python实现简易的ORM模型
    Python队列
    selenium实现绕过登录
    docker学习镜像常用操作命令
    docker学习容器常用命令
    把握趋势,成为赢家
  • 原文地址:https://www.cnblogs.com/Penn000/p/5779548.html
Copyright © 2011-2022 走看看