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  • Codeforces Round #406 (Div. 2) A MONSTER

    A. The Monster
    time limit per test
    1 second
    memory limit per test
    256 megabytes
    input
    standard input
    output
    standard output

    A monster is chasing after Rick and Morty on another planet. They're so frightened that sometimes they scream. More accurately, Rick screams at times b, b + a, b + 2a, b + 3a, ...and Morty screams at times d, d + c, d + 2c, d + 3c, ....

    The Monster will catch them if at any point they scream at the same time, so it wants to know when it will catch them (the first time they scream at the same time) or that they will never scream at the same time.

    Input

    The first line of input contains two integers a and b (1 ≤ a, b ≤ 100).

    The second line contains two integers c and d (1 ≤ c, d ≤ 100).

    Output

    Print the first time Rick and Morty will scream at the same time, or  - 1 if they will never scream at the same time.

    Examples
    input
    20 2
    9 19
    output
    82
    input
    2 1
    16 12
    output
    -1
    和蓝桥杯凑包子数目是一个类型的题目
    先介绍一下扩展欧几里德定理
    对于不完全为 0 的整数 a,b,gcd(a,b)表示 a,b 的最大公约数。那么一定存在整
    数 x,y 使得 gcd(a,b)=ax+by。
    对于这道题目 我们可以整理出 b+x*a=d+y*c    那么就有 ax+(-yc)=d-b
    那么可不可达 我们就看d-b能否为gcd(a,c)的倍数了
    上代码
     
    #include <iostream>
    #include <cstdio>
    #include <cstring>
    #include <vector>
    #include <map>
    #include <stack>
    #include <algorithm>
    #include <queue>
    #include <string>
    #include <cmath>
    #include <cstdlib>
    using namespace std;
    int gcd(int x,int y)
    {
        if(y==0) return x;
        else return gcd(y,x%y);
    }
    // 是否可达的理解
    int main()
    {
        int a,b,c,d;
        cin>>a>>b>>c>>d;
        int pos=(d-b);
        if(pos%gcd(a,c)!=0)  cout<<-1<<endl;
        else
        {
            while(b!=d)
            {
                if(b < d) b+=a;
                else d+=c;
            }
            cout<<b<<endl;
        }
        return 0;
    }
    

      

     
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  • 原文地址:https://www.cnblogs.com/z1141000271/p/6830879.html
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