HDU4592 Boring Game (2013 ACM-ICPC南京賽區全國邀請賽) 高斯消元

題目連結：http://acm.hdu.edu.cn/showproblem.php?pid=4592

分析：

本題的資料量特別大，所以要對高斯消元儘可能多的優化。

因為n的範圍比較小為1~8 ，因此我們可以將係數陣的逆給求出來 然後根據逆來判斷有沒有解 ，

有解的情況下 直接用A^(-1)*B=X; 求解,但是由於係數陣是0,1的 相當於二進位制， 我們可以將其改成10進位制 

然後進行運算的時候就快一點了 ，然後統計解中1的個數 直接列舉即可

程式碼如下：

#include <iostream>
#include <cstring>
#include <cstdio>
//#define debug
using namespace std;

int a[30][30];
int x[80],n,equ,var;

void init()
{
    memset(a,0,sizeof(a));
    memset(x,0,sizeof(x[0])*30);
    equ=n*n;
    var=equ;
    for(int i=0; i<n; i++)
    {
        for(int j=0; j<n; j++)
        {
            if(i!=0) a[i*n+j][(i-1)*n+j]=1;
            if(i!=n-1) a[i*n+j][(i+1)*n+j]=1;
            if(j!=0) a[i*n+j][i*n+j-1]=1;
            if(j!=n-1) a[i*n+j][i*n+j+1]=1;
            a[i*n+j][i*n+j]=1;
        }
    }
}

int Gauss()
{
    int k,col,max_r;

    for(k=0,col=0; k<equ&&col<var; k++,col++)
    {
        if(a[k][col]==0)
        {
            max_r=k;
            for(int i=k+1; i<equ; i++)
                if(a[i][col]>a[max_r][col])
                {
                    max_r=i;
                    break;
                }
            if(max_r!=k)
                for(int i=0; i<=var; i++)
                    swap(a[max_r][i],a[k][i]);
        }
        if(a[k][col]==0)
        {
            k--;
            continue;
        }
        for(int i=k+1; i<equ; i++)
        {
            if(a[i][col])
                for(int j=col; j<=var; j++)
                    a[i][j]=a[i][j]^a[k][j];
        }
    }
    for(int i=k; i<equ; i++)
        if(a[i][var]) return -1;

    int lim=(1<<(var-k)),ans=100000;
    for(int i=0; i<lim; i++)
    {
        int temp=i,sum=0;
        for(int j=var-1; j>=k; j--)
        {
            x[j]=temp&1;
            temp>>=1;
        }
        for(int j=k-1; j>=0; j--)
        {
            x[j]=a[j][var]&1;
            for(int r=j+1; r<var; r++)
                x[j]=x[j]^(a[j][r]&x[r]);
        }
        for(int j=0; j<var; j++)
            sum+=x[j];
        ans=min(ans,sum);
    }
    return ans;
}
int n2[4][2]=
{
    3,2,3,1,2,3,1,3
};
int n3[9][3]=
{
    5,1,6,0,2,7,5,4,3,1,3,1,
    2,7,2,
    4,6,4,
    6,1,5,
    7,2,0,
    3,4,5
};
int n6[36][6]=
{
    43,8,55,10,44,40,
    3,20,53,17,14,4,
    44,42,7,32,55,34,
    13,21,56,1,59,17,
    48,10,43,34,28,8,
    53,4,59,20,13,5,
    8,28,2,27,34,44,
    20,54,5,59,21,14,
    42,43,10,48,2,55,
    21,53,20,3,16,59,
    10,27,40,55,42,28,
    4,14,16,54,17,13,
    55,2,48,42,27,10,
    53,5,56,1,59,17,
    7,10,28,40,48,32,
    56,20,14,5,3,1,
    43,40,7,32,55,34,
    59,16,3,21,54,20,
    10,27,42,48,2,55,
    17,59,1,56,5,53,
    32,48,40,28,10,7,
    1,3,5,14,20,56,
    34,55,32,7,40,43,
    20,54,21,3,16,59,
    44,34,27,2,28,8,
    14,21,59,5,54,20,
    55,2,48,10,43,42,
    59,16,3,20,53,21,
    28,42,55,40,27,10,
    13,17,54,16,14,4,
    40,44,10,55,8,43,
    4,14,17,53,20,3,
    34,55,32,7,42,44,
    17,59,1,56,21,13,
    8,28,34,43,10,48,
    5,13,20,59,4,53
};
int n7[49][7]=
{
    109,65,14,84,88,16,96,
    108,34,27,2,28,40,112,
    3,20,53,81,110,84,56,
    107,0,107,8,119,42,28,
    96,20,86,69,59,21,14,
    27,34,108,32,28,10,7,
    91,65,56,21,13,4,3,
    65,99,21,86,68,56,16,
    34,119,32,7,42,108,40,
    20,54,69,91,5,86,84,
    0,0,8,28,34,107,42,
    20,54,81,109,80,53,21,
    34,119,2,112,42,27,10,
    65,99,84,53,17,14,4,
    14,21,59,5,54,68,88,
    27,32,107,8,119,42,28,
    53,69,88,17,99,5,110,
    107,8,119,34,0,34,119,
    86,81,13,68,99,80,59,
    108,2,107,8,119,42,28,
    56,84,110,80,54,17,13,
    84,86,5,91,5,86,84,
    2,7,8,27,8,7,2,
    81,91,17,96,17,91,81,
    8,28,34,107,34,28,8,
    69,109,68,3,68,109,69,
    32,112,8,108,8,112,32,
    21,53,80,109,80,53,21,
    88,68,54,5,59,21,14,
    28,42,119,8,107,32,27,
    110,5,99,17,88,69,53,
    119,34,0,34,119,8,107,
    59,80,99,68,13,81,86,
    28,42,119,8,107,2,108,
    13,17,54,80,110,84,56,
    16,56,68,86,21,99,65,
    40,108,42,7,32,119,34,
    84,86,5,91,69,54,20,
    42,107,34,28,8,0,0,
    21,53,80,109,81,54,20,
    10,27,42,112,2,119,34,
    4,14,17,53,84,99,65,
    96,16,88,84,14,65,109,
    112,40,28,2,27,34,108,
    56,84,110,81,53,20,3,
    28,42,119,8,107,0,107,
    14,21,59,69,86,20,96,
    7,10,28,32,108,34,27,
    3,4,13,21,56,65,91
};
int n8[64][8]=
{
    220,138,7,128,199,170,108,40,
    214,81,13,64,237,1,238,68,27,0,27,32,107,168,199,130,237,81,54,16,14,5,3,1,183,138,108,8,112,160,192,128,216,0,216,4,214,21,227,65,107,138,176,2,183,128,119,34,
    59,81,224,1,227,85,54,20,138,219,10,192,42,171,130,108,81,219,17,224,65,3,69,238,0,0,32,112,136,172,42,199,81,219,65,56,21,13,4,3,138,219,130,28,168,176,32,192,0,0,4,14,17,53,84,227,138,219,136,7,130,192,162,119,
    81,219,80,3,84,213,65,54,
    7,10,28,160,172,2,171,170,
    13,17,54,16,14,5,3,1,
    27,32,107,136,183,10,172,168,
    54,65,213,68,59,20,13,5,
    108,130,171,34,220,40,176,160,
    216,4,214,17,237,80,53,21,
    176,136,108,8,112,160,192,128,
    224,80,56,5,53,64,213,85,
    128,192,160,112,136,172,42,199,
    64,224,16,216,84,14,65,237,
    32,112,136,172,10,183,136,107,
    16,56,68,214,69,59,21,14,
    8,28,34,107,162,220,168,112,
    4,14,17,53,80,237,17,214,
    2,7,8,27,42,112,130,183,
    1,3,5,14,17,53,84,227,
    199,42,172,136,112,160,192,128,
    237,65,14,84,216,16,224,64,
    107,136,183,10,172,136,112,32,
    14,21,59,69,214,68,56,16,
    112,168,220,162,107,34,28,8,
    214,17,237,80,53,17,14,4,
    183,130,112,42,27,8,7,2,
    227,84,53,17,14,5,3,1,
    170,171,2,172,160,28,10,7,
    1,3,5,14,16,54,17,13,
    168,172,10,183,136,107,32,27,
    5,13,20,59,68,213,65,54,
    160,176,40,220,34,171,130,108,
    21,53,80,237,17,214,4,216,
    128,192,160,112,8,108,136,176,
    85,213,64,53,5,56,80,224,
    108,130,171,42,192,10,219,138,
    238,69,3,65,224,17,219,81,
    199,42,172,136,112,32,0,0,
    3,4,13,21,56,65,219,81,
    192,32,176,168,28,130,219,138,
    227,84,53,17,14,4,0,0,
    119,162,192,130,7,136,219,138,
    54,65,213,84,3,80,219,81,
    40,108,170,199,128,7,138,220,
    68,238,1,237,64,13,81,214,
    130,199,168,107,32,27,0,27,
    1,3,5,14,16,54,81,237,
    128,192,160,112,8,108,138,183,
    65,227,21,214,4,216,0,216,
    34,119,128,183,2,176,138,107,
    20,54,85,227,1,224,81,59
};



int ans[80];
int b[10];
int main()
{
    int cas;
    scanf("%d",&cas);
    while(cas--)
    {
        scanf("%d",&n);
        int sum=0;
        for(int i=0; i<n; i++)
            scanf("%d",&b[i]);
        if(n==4||n==5)
        {
            init();
            for(int i=0; i<n; i++)
            {
                int r=(i+1)*n-1,l=i*n;
                while(r>=l)
                {
                    a[r][var]=b[i]&1;
                    b[i]>>=1;
                    r--;
                }
            }
            int ans=Gauss();
            printf("%d\n",ans);
            continue;
        }
        if(n==1)
        {
            printf("%d\n",b[0]);
            continue;
        }
        equ=n*n;
        memset(ans,0,sizeof(ans[0])*(equ+4));
        if(n==2)
        {
            for(int j=0; j<n; j++)
                if(b[j])
                {
                    for(int i=0; i<equ; i++)
                        ans[i]=ans[i]^(n2[i][j]&b[j]);
                }
        }
        else if(n==3)
        {
            for(int j=0; j<n; j++)
                if(b[j])
                {
                    for(int i=0; i<equ; i++)
                        ans[i]=ans[i]^(n3[i][j]&b[j]);
                }
        }
        else if(n==6)
        {
            for(int j=0; j<n; j++)
                if(b[j])
                {
                    for(int i=0; i<equ; i++)
                        ans[i]=ans[i]^(n6[i][j]&b[j]);
                }
        }
        else if(n==7)
        {
            for(int j=0; j<n; j++)
                if(b[j])
                {
                    for(int i=0; i<equ; i++)
                        ans[i]=ans[i]^(n7[i][j]&b[j]);
                }
        }
        else if(n==8)
        {
            for(int j=0; j<n; j++)
                if(b[j])
                {
                    for(int i=0; i<equ; i++)
                        ans[i]=ans[i]^(n8[i][j]&b[j]);
                }
        }
        for(int i=0; i<equ; i++)
        {
            int cnt=0;
            while(ans[i])
            {
                cnt^=(ans[i]&1);
                ans[i]>>=1;
            }
            sum+=cnt;
        }
        printf("%d\n",sum);
    }
    return 0;
}