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杭电 3270 The Diophantine Equation
http://acm.hdu.edu.cn/showproblem.php?pid=3270
The Diophantine Equation
Time Limit: 1000/500 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 1146 Accepted Submission(s): 297
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. HINT: The first equation is true for x = 2, y = 2. So, we get, 2*2 + 3*2=10. Therefore, the output should be “Yes.”
一道很简单的题目,稍稍细心一些就能很快的AC,(我愚钝呀,弄了好久,后来想想觉得A出来之前大脑是短路状态,,这是为什么啊)需要注意的是输入,处理的话也不是很难。
AC代码:
#include<iostream> #include<cstdio> #include<cstring> #include<cmath> using namespace std; int qiujie(int a,int b,int c) { int x; for(x=0; x<=c/a; x++) //枚举x可取的所有可能 { if((c-a*x)%b==0) //判断是否存在正整数y { return 1; } } return 0; } int main() { int a,b,c,i,j; char s1[16],s2[16],ch,cj; while(cin>>s1>>ch>>s2>>cj>>c) { a=b=0; for(i=0; i<strlen(s1)-1; i++) { if(s1[i]!='x') { a+=s1[i]-'0'; if(s1[i+1]!='x') a*=10; } /* a*=10; a+=s1[i]-'0';*/ } for(j=0; j<strlen(s2)-1; j++) { if(s2[j]!='y') { b+=s2[j]-'0'; if(s2[j+1]!='y') b*=10; } /* b*=10; b+=s2[j]-'0';*/ } if(s1[0]=='x')a=1; if(s2[0]=='y')b=1; if(qiujie(a,b,c)==1) printf("Yes.\n\n"); else printf("No.\n\n"); } return 0; }
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