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HUDJ 3270 The Diophantine Equation
The Diophantine Equation
Time Limit: 1000/500 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 1133 Accepted Submission(s): 292
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?
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.
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; }
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