Red Huang

Red Huang

uva 10512

測試數據非常強大,一兩個錯誤就猛吃 WA

利用公式解可以解出這道題目,只要利用那兩條等式換來換去就可以得到 ay4+by2+c=0 這個等式

再套公式即可。

//====================================================================||  
// Name        : A Day in Math-land.cpp                                              ||  
// Date : 2013/7/18 下午11:20:06                                               ||  
// Author : GCA                                                       ||  
//                  6AE7EE02212D47DAD26C32C0FE829006                  ||  
//====================================================================||  
#include <iostream>  
#include <cstdio>  
#include <cstring>  
#include <algorithm>  
#include <cmath>  
#include <climits>  
#include <vector>  
#include <set>  
#include <map>  
#include <queue>  
#include <cctype>  
#include <utility>  
using namespace std;  
#ifdef ONLINE\_JUDGE  
#define ll "%lld"  
#else  
#define ll "%I64d"  
#endif  
typedef unsigned int uint;  
typedef long long int Int;  
#define Set(a,s) memset(a,s,sizeof(a))  
#define Write(w) freopen(w,"w",stdout)  
#define Read(r) freopen(r,"r",stdin)  
#define Pln() printf("\\n")  
#define I\_de(x,n)for(int i=0;i<n;i++)printf("%d ",x\[i\]);Pln()  
#define De(x)printf(#x"%d\\n",x)  
#define For(i,x)for(int i=0;i<x;i++)  
#define CON(x,y) x##y  
#define Pmz(dp,nx,ny)for(int hty=0;hty<ny;hty++){for(int htx=0;htx<nx;htx++){\\  
    printf("%d ",dp\[htx\]\[hty\]);}Pln();}  
#define M 10001  
#define PII pair<int,int\>  
#define PB push\_back  
#define oo (1LL<<62)  
#define Set\_oo 0x3f  
#define Is\_debug true  
#define debug(...) if(Is\_debug)printf("DEBUG: "),printf(\_\_VA\_ARGS\_\_)  
#define FOR(it,c) for(\_\_typeof((c).begin()) it=(c).begin();it!=(c).end();it++)  
#define eps 1e-6  
bool xdy(double x,double y){return x>y+eps;}  
bool xddy(double x,double y){return x>y-eps;}  
bool xcy(double x,double y){return x<y-eps;}  
bool xcdy(double x,double y){return x<y+eps;}  
int min3(int x,int y,int z){  
    int tmp=min(x,y);  
    return min(tmp,z);  
}  
int max3(int x,int y,int z){  
    int tmp=max(x,y);  
    return max(tmp,z);  
}  
Int p,q;  
inline Int sqr(Int x){  
    return x\*x;  
}  
inline bool isqrt(Int x,Int &ans){  
    if(x<0)return false;  
    ans=sqrt(x);  
    return ans\*ans==x;  
}  
void solve(){  
    Int d=sqr(p)+6LL\*p\*q+sqr(q);  
    Int y,x,tmp,t,ansx=oo,ansy;  
    bool is\=isqrt(d,t);  
    if(!is){  
        printf("Impossible.\\n");  
        return ;  
    }  
//    debug("%lld\\n",t);  
    if((3LL\*p+q+t)%4==0){  
        tmp=(3LL\*p+q+t)>>2LL;  
        is\=isqrt(tmp,y);  
        if(is){  
            bool fg=false;  
            if(y&&p%y==0){  
                x=p/y-y;  
                fg=true;  
            }else if(y==0){  
                fg=isqrt(q,x);  
            }  
            if(x>=y&&x<ansx&&fg){  
                ansx=x;  
                ansy=y;  
            }  
            fg=false;  
            y=-y;  
            if(y&&p%y==0){  
                x=p/y-y;  
                fg=true;  
            }else if(y==0){  
                fg=isqrt(q,x);  
            }  
            if(x>=y&&x<ansx&&fg){  
                ansx=x;  
                ansy=y;  
            }  
        }  
    }  
    if((3LL\*p+q-t)%4==0){  
        tmp=(3LL\*p+q-t)>>2LL;  
        is\=isqrt(tmp,y);  
        if(is){  
            bool fg=false;  
            if(y&&p%y==0){  
                x=p/y-y;  
                fg=true;  
            }else if(y==0){  
                fg=isqrt(q,x);  
            }  
            if(x>=y&&x<ansx&&fg){  
                ansx=x;  
                ansy=y;  
            }  
            fg=false;  
            y=-y;  
            if(y&&p%y==0){  
                x=p/y-y;  
                fg=true;  
            }else if(y==0){  
                fg=isqrt(q,x);  
            }  
            if(x>=y&&x<ansx&&fg){  
                ansx=x;  
                ansy=y;  
            }  
        }  
    }  
    if(ansx==oo)printf("Impossible.\\n");  
    else printf("%lld %lld\\n",ansx,ansy);  
}  
int main() {  
    ios\_base::sync\_with\_stdio(0);  
    int test;  
    scanf("%d",&test);  
    int ff=0;  
    while(test--){  
        scanf("%lld %lld",&p,&q);  
        printf("Case %d:\\n",++ff);  
        solve();  
  
    }  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
}  

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