USACO 3.2.4 Feed Ratios (枚举+克莱姆法则)

USACO 3.2.4 Feed Ratios (枚举+克莱姆法则)

其实就是解线性方程.

用克莱姆法则求解, 求解过程要判断是否是分数解或者负解。

Ax = k*B   枚举B, 从1到100.

/**/ /*
ID: lorelei3
TASK: ratios
LANG: C++
*/

#include  < fstream >

using   namespace  std;

int  A[ 4 ][ 4 ];
int  B[ 4 ], b[ 4 ];
int  x[ 4 ];
int  D;

int  det() {
    return    A[1][1]*(A[2][2]*A[3][3]-A[3][2]*A[2][3])-
            A[1][2]*(A[2][1]*A[3][3]-A[3][1]*A[2][3])+
            A[1][3]*(A[2][1]*A[3][2]-A[3][1]*A[2][2]);
}


int  Cramer() {
    int i,j;
    int tmp[4];
    for(i=1; i<=3; ++i){

        for(j=1; j<=3; ++j){
            tmp[j] = A[j][i];
            A[j][i] = B[j];
        }

        int Di = det();

        for(j=1; j<=3; ++j)
            A[j][i] = tmp[j];

        if(Di%D != 0)
            return -1;

        x[i] = Di/D;

        if(x[i]<0)
            return -1;        
    }
    return 1;
}

int  main() {
    int i,j,k;

    ifstream fin("ratios.in");
    ofstream fout("ratios.out");

    for(i=1; i<=3; ++i)
        fin>>b[i];

    for(i=1; i<=3; ++i)
        for(j=1; j<=3; ++j)
            fin>>A[j][i];

    D=det();
    
    for(k=1; k<=100; ++k){
        for(i=1; i<=3; ++i)
            B[i] = k*b[i];

        if(Cramer()==1){
            for(i=1; i<=3; ++i)
                fout<<x[i]<<" ";
            fout<<k<<endl;
            return 0;
        }
    }
    
    fout<<"NONE"<<endl;
    return 0;
}