hdu 4592（高斯消元好题）

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=4592；

题目分析：  本题其实就是一个普通的高斯消元题，但是本题数据范围巨大，所以不能用普通的高斯消元来写，只能采用求逆打表法，进行求解。只有满秩矩阵才能有逆元，通过消元可以看出，只有4,5时时多解的，所以其他就打表好了，但不能打0,1矩阵，还是会超时，最后打出的是十进制数就好办了。

代码如下：

#include <set>
#include <map>
#include <stack>
#include <queue>
#include <math.h>
#include <vector>
#include <string>
#include <utility>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <iostream>
#include <algorithm>
#include <functional>

using namespace std;
int A2[4][2]=
{
{3,2},{3,1},
{2,3},{1,3}
};

int A3[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 A6[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 A7[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 A8[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}
};
const int maxn=405;
int a[maxn][maxn*2+1],x[maxn];
int equ,var;
int free_num,ans=100000000;
void Debug(){
int i,j;
for(i=0;i<equ;i++){
for(j=0;j<var+1;j++)
cout<<a[i][j]<<" ";
cout<<endl;
}
cout<<endl;
}

int Gauss(){
int k,col=0;
for(k=0;k<equ&&col<var;++k,++col) {
int max_r=k;
for(int i=k+1;i<equ;++i)
if(a[i][col]>a[max_r][col])
max_r=i;
if(max_r!=k){
for(int i=k;i<var+1;++i)
swap(a[k][i],a[max_r][i]);
}
if(a[k][col]==0){
k--;
continue;
}
for(int i=k+1;i<equ;++i) {
if(a[i][col] != 0) {
for(int j=col;j<var+1;++j)
a[i][j]^=a[k][j];
}
}
}
for(int i=k;i<equ;++i)
if(a[i][col]!=0)return -1;
// Debug();
for(int i=0;i<equ;++i)
if(!a[i][i]) {
int j;
for(j=i+1;j<var;++j)
if(a[i][j]) break;
if(j==var) break;
for(int k=0;k<equ;++k)
swap(a[k][i],a[k][j]);
}
int sum=0x3f3f3f3f;
if (var-k>0){
for(int num=0;num<(1<<(var-k));num++){
int minn=0;
memset(x,0,sizeof(x));
for(int ans=0;ans<var-k;ans++){
if((1<<ans)&num){
x[var-ans-1]=1;
minn++;
}
}
for(int i=k-1;i>=0;--i)
{
int tmp=a[i][var];
for(int j=i+1;j<var;++j)
if(a[i][j]!=0)
tmp^=x[j];
x[i]=tmp;
minn+=x[i];
}
sum=min(minn,sum);
}
}
if (var-k==0){
sum=0;
for(int i=k-1;i>=0;--i)
{
int tmp=a[i][var];
for(int j=i+1;j<var;++j)
if(a[i][j]!=0)
tmp^=a[i][j]*x[j];
x[i]=tmp;
}
for(int i=0;i<var;i++)
sum+=x[i];
}
return sum;
}
void init(int n){
equ=n*n;
var=equ;
memset(a,0,sizeof(a));
memset(x,0,sizeof(x[0])*30);
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 main(){
int cas,n,X;
scanf("%d",&cas);
while(cas--){
scanf("%d",&n);
if(n==1){
scanf("%d",&X);
printf("%d\n",X);
continue;
}
if(n==4||n==5){
init(n);
for(int i=0;i<n;i++){
scanf("%d",&X);
int r=(i+1)*n-1,l=i*n;
while(r>=l){
a[r][var]=X&1;
X>>=1;
r--;
}
}
int ans=Gauss();
printf("%d\n",ans);
continue;
}
int ans=0;
int t[80];
for(int i=0; i<n; i++)
scanf("%d",&t[i]);
equ=n*n;
memset(x,0,sizeof(x[0])*(equ+4));
if(n==2)
for(int j=0; j<n; j++)
if(t[j])
for(int i=0; i<equ; i++)
x[i]=x[i]^(A2[i][j]&t[j]);
else if(n==3)
for(int j=0;j<n;j++)
if(t[j])
for(int i=0; i<equ; i++)
x[i]=x[i]^(A3[i][j]&t[j]);
else if(n==6)
for(int j=0; j<n; j++)
if(t[j])
for(int i=0; i<equ; i++)
x[i]=x[i]^(A6[i][j]&t[j]);
else if(n==7){
for(int j=0; j<n; j++)
if(t[j]){
for(int i=0; i<equ; i++)
x[i]=x[i]^(A7[i][j]&t[j]);
}
}
else if(n==8){
for(int j=0;j<n;j++)
if(t[j]){
for(int i=0; i<equ; i++){
x[i]=x[i]^(A8[i][j]&t[j]);
}
}
}
for(int i=0; i<equ; i++){
int t=0;
while(x[i]){
t^=(x[i]&1);
x[i]>>=1;
}
ans+=t;
}
printf("%d\n",ans);
}
return 0;
}