The Diophantine Equation

Time Limit: 1000/500 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)

Problem Description

We will consider a linear Diaphonic equation here and you are to find out whether the equation is solvable in non-negative integers or not.

Easy, is not it?

Input

There will be multiple cases. Each case will consist of a single line expressing the Diophantine equation we want to solve. The equation will be in the form ax + by = c. Here a and b are two positive integers expressing the co-efficient
of two variables x and y.

There are spaces between:

1. “ax” and ‘+’

2. ‘+’ and “by”

3. “by” and ‘=’

4. ‘=’ and “c”

c is another integer that express the result of ax + by. -1000000<c<1000000. All other integers are positive and less than 100000. Note that, if a=1 then ‘ax’ will be represented as ‘x’ and same for by.

Output

You should output a single line containing either the word “Yes.” or “No.” for each input cases resulting either the equation is solvable in non-negative integers or not. An equation is solvable in non-negative integers if for non-negative
integer value of x and y the equation is true. There should be a blank line after each test cases. Please have a look at the sample input-output for further clarification.

Sample Input

2x + 3y = 10
15x + 35y = 67
x + y = 0

Sample Output

Yes.

No.

Yes.

注意输入就行了：

#include<cstring>
#include<iostream>
using namespace std;

int main()
{
    char s1[20],s2[20];char q,w;
    int k;
    while(cin>>s1>>q>>s2>>w>>k)
    {
        int n,m,i,j;
        n=m=0;
        for(i=0;i<strlen(s1)-1;i++)
            n*=10,n+=s1[i]-'0';
        for(j=0;j<strlen(s2)-1;j++)
            m*=10,m+=s2[j]-'0';

        if(n==0)  n=1;
        if(m==0)  m=1;
        //printf("%d    %d\n",n,m);
        int sum,flag;
        sum=flag=0;
        for(i=0;i<=k;i+=n)
            if((k-i)%m==0)
            {
                flag=1;
                break;
            }

        if(flag) cout<<"Yes.\n\n";
        else     cout<<"No.\n\n";
    }

    return 0;
}

HUDJ 3270 The Diophantine Equation