sgu200 分类： sgu 2015-05-25 18:53 32人阅读 评论(0) 收藏

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对每个数分解质因数，然后对每个质因子有一个异或方程，
解异或方程，记其中自由元的个数为f，答案即为 2f−1。

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#include<cstdio>
#include<cstdlib>
#include<iostream>
#include<algorithm>

const int MAXN = 105, Nya = -1;
typedef int Array[MAXN][MAXN];
typedef int Seq[MAXN];
typedef int Array2[MAXN<<1][MAXN];

int t, m, ans;
Seq prime;int tot;
Seq b; Array a; 
Array2 u; Seq x;

void GetPrime()
{
    for(int i = 2; tot < t; i++)
    {
        bool tag = true;
        for(int j = 1; j <= tot && tag; j++)
            if(!(i % prime[j])) tag = false;
        if(tag) prime[++tot] = i;   
    }
}
void PrimeFactor(int px,int r[])
{
    for(int i = 1; i <= t && i <= px; i++)
        while(!(px % prime[i])) 
            px /= prime[i], r[i] ^= 1;  
}//r[i] x->prime[i]  
// XorSum(P[i]*a[i][j]) = 0

int Guass()
{
    int ret = 0;

    for(int i = 1; i <= m; i++)
    {
        int g = Nya;

        for(int q = i; q <= t; q++)
            if(u[q][i]) g = q;

        if(g != i)
        {
            if(g == Nya) g = ++t, ret++;
            for(int j = 1; j <= m; j++)
                std::swap(u[i][j],u[g][j]);
        }

        for(int q = i+1; q <= t; q++)
        {
            if(!u[q][i]) continue;
            for(int j = i; j <= m; j++)
                u[q][j] ^= u[i][j];     
        }
    } 
    for(int i = m; i >= 1; i--)
        for(int j = i + 1; j <= m; j++)
            x[i] ^= x[j] * u[i][j];

    for(int i = 1; i <= t; i++)
    {
        int calcu = 0;
        for(int j = 1; j <= m; j++)
            calcu ^= x[j] * u[i][j];    
        if(calcu) return -1;    
    }

    return ret;
}
struct BigNum
{
    int num[MAXN],l;
    void prt()
    {
        if(!l) {printf("0");return;}
        for(int i = l; i >= 1; i--)
            printf("%d",num[i]);
    }
}emp;

BigNum operator +(const BigNum &a,const BigNum &b)
{
    BigNum ret = emp;
    ret.l = std::max(a.l,b.l);
    for(int i = 1; i <= ret.l; i++)
        ret.num[i] = a.num[i] + b.num[i];
    for(int i = 1; i <= ret.l; i++)
        if(ret.num[i] >= 10) 
            ret.num[i] -= 10, ret.num[i+1] ++;
    if(ret.num[ret.l + 1]) ret.l++; 

    return ret;     
}

int main()
{
#ifndef ONLINE_JUDGE    
    freopen("sgu200.in","r",stdin);
    freopen("sgu200.out","w",stdout);
#endif  

    std::cin >> t >> m;

    GetPrime();

    for(int i = 1; i <= m; i++)
    {
        std::cin >> b[i];
        PrimeFactor(b[i],a[i]);
    }
    for(int i = 1; i <= t; i ++)
        for(int j = 1; j <= m; j++)
            u[i][j] = a[j][i]; 

    ans = Guass();

    if(ans == Nya) puts("0");
    else
    {
        BigNum s = emp, h = emp;
        h.num[1] = 1, h.l = 1; 
        for(int i = 1; i <= ans; i++)
            s = s + h, h = h + h;
        s.prt(); puts("");  
    }

#ifndef ONLINE_JUDGE    
    fclose(stdin);
    fclose(stdout);
#endif  
    return 0;
}

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