【2016ACM/ICPC亚洲区大连站D】HDU - 5974 A Simple Math Problem 数论推公式

题意

x+y=a lcm(x,y)=b  求x,y

12WCases +  b 10^9 + a 10^4

http://acm.hdu.edu.cn/showproblem.php?pid=5974

 

分析

数据范围知肯定不是枚举……肯定是公式题

 

代码

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
using namespace std;
typedef long long ll;
ll gcd(ll a,ll b)
{
    return b==0?a:gcd(b,a%b);
}
int main()
{
    ll a,b;
    while(scanf("%lld%lld",&a,&b)!=EOF){
        ll c=gcd(a,b);
        ll d=a*a-4*b*c;
        if(d<0){
            printf("No Solution\n");
            continue;
        }
        ll i=(a-sqrt(d))/2/c;
        ll j=a/c-i;
        ll x=c*i;
        ll y=c*j;
        if(x*y==b*c)
            printf("%lld %lld\n",x,y);
        else
            printf("No Solution\n");
    }
}