Linearization of the kernel functions in SVM

 

SVM（Support Vector Machine）is an important classification tool, which has a wide range of applications in cluster analysis, community division and so on. SVM The kernel functions used in SVM have many forms. Here we only discuss the function of the form f(x,y,z) = ax^2 + by^2 + cy^2 + dxy + eyz + fzx + gx + hy + iz + j. By introducing new variables p, q, r, u, v, w, the linearization of the function f(x,y,z) is realized by setting the correspondence x^2 <-> p, y^2 <-> q, z^2 <-> r, xy <-> u, yz <-> v, zx <-> w and the function f(x,y,z) = ax^2 + by^2 + cy^2 + dxy + eyz + fzx + gx + hy + iz + j can be written as g(p,q,r,u,v,w,x,y,z) = ap + bq + cr + du + ev + fw + gx + hy + iz + j, which is a linear function with 9 variables. 

Now your task is to write a program to change f into g.

InputThe input of the first line is an integer T, which is the number of test data (T<120). Then T data follows. For each data, there are 10 integer numbers on one line, which are the coefficients and constant a, b, c, d, e, f, g, h, i, j of the function f(x,y,z) = ax^2 + by^2 + cy^2 + dxy + eyz + fzx + gx + hy + iz + j.OutputFor each input function, print its correspondent linear function with 9 variables in conventional way on one line.Sample Input

2
0 46 3 4 -5 -22 -8 -32 24 27
2 31 -5 0 0 12 0 0 -49 12

Sample Output

46q+3r+4u-5v-22w-8x-32y+24z+27
2p+31q-5r+12w-49z+12

 

//注意前面数都为0，后面符号问题，1 -1没有1，第一个的符号问题

#include<stdio.h>
#include<string.h>
int main()
{
    char a[10]={'p','q','r','u','v','w','x','y','z'};
    int b[10],i,n;
    scanf("%d",&n);
    while(n--)
    {
        int m=0;
        for(i=0;i<=9;i++)
            scanf("%d",&b[i]);
        for(i=0;i<=9;i++)
        {
            if(b[i]==0)
                continue;
            if(m==0)
            {
                if(b[i]==1&&i!=9)
                    printf("%c",a[i]);
                else
                if(b[i]==-1&&i!=9)
                   printf("-%c",a[i]);
                else
                if(i!=9)
                   printf("%d%c",b[i],a[i]);
            }
            else
            {
                if(b[i]==1&&i!=9)
                    printf("+%c",a[i]),m++;
                else
                if(b[i]==-1&&i!=9)
                   printf("-%c",a[i]);
                else
                if(b[i]>0&&i!=9)
                   printf("+%d%c",b[i],a[i]);
                else
                if(b[i]<0&&i!=9)
                   printf("%d%c",b[i],a[i]);
            }
            if(i==9)
            {
                if(m==0)
                    printf("%d",b[i]);
                else
                {
                    if(b[i]>0)
                        printf("+");
                    printf("%d",b[i]);
                }
            }
            m++;
        }
        puts("");
    }
}