(中等) HDU 4069 Squiggly Sudoku , DLX+精确覆盖。

　　Description

　　Today we play a squiggly sudoku, The objective is to fill a 9*9 grid with digits so that each column, each row, and each of the nine Connecting-sub-grids that compose the grid contains all of the digits from 1 to 9.
Left figure is the puzzle and right figure is one solution.

#include<iostream>
#include<cstring>
#include<cstdio>
#include<queue>

using namespace std;

const int MaxN=800;
const int MaxM=350;
const int MaxNode=MaxN*MaxM;

int map1[10][10];

struct DLX
{
int U[MaxNode],D[MaxNode],L[MaxNode],R[MaxNode],col[MaxNode],row[MaxNode];
int size,n,m;
int H[MaxN],S[MaxM];
int ans[100],ans1[100],anst[100];
int ansnum,depth;

void init(int _n,int _m)
{
ansnum=0;

n=_n;
m=_m;

for(int i=0;i<=m;++i)
{
U[i]=D[i]=i;
L[i]=i-1;
R[i]=i+1;
row[i]=0;

S[i]=0;
}
L[0]=m;
R[m]=0;

size=m;

for(int i=1;i<=n;++i)
H[i]=-1;
}

void Link(int r,int c)
{
col[++size]=c;
row[size]=r;
++S[c];

U[size]=U[c];
D[size]=c;
D[U[c]]=size;
U[c]=size;

if(H[r]==-1)
H[r]=L[size]=R[size]=size;
else
{
L[size]=L[H[r]];
R[size]=H[r];
R[L[H[r]]]=size;
L[H[r]]=size;
}
}

void remove(int c)
{
L[R[c]]=L[c];
R[L[c]]=R[c];

for(int i=D[c];i!=c;i=D[i])
for(int j=R[i];j!=i;j=R[j])
{
U[D[j]]=U[j];
D[U[j]]=D[j];
--S[col[j]];
}
}

void resume(int c)
{
for(int i=U[c];i!=c;i=U[i])
for(int j=L[i];j!=i;j=L[j])
{
U[D[j]]=j;
D[U[j]]=j;
++S[col[j]];
}

L[R[c]]=R[L[c]]=c;
}

void showans()
{
for(int i=0;i<depth;++i)
ans1[(anst[i]-1)/9+1]=(anst[i]-1)%9+1;

for(int i=1;i<=81;++i)
{
cout<<ans1[i];

if(i%9==0)
cout<<endl;
}
}

void copyans()
{
for(int i=0;i<100;++i)
anst[i]=ans[i];
}

bool Dance(int d)
{
if(R[0]==0)
{
depth=d;

if(ansnum)
{
++ansnum;
return 1;
}

++ansnum;

copyans();

return 0;
}

int c=R[0];

for(int i=R[0];i!=0;i=R[i])
if(S[i]<S[c])
c=i;

remove(c);

for(int i=D[c];i!=c;i=D[i])
{
ans[d]=row[i];

for(int j=R[i];j!=i;j=R[j])
remove(col[j]);

if(Dance(d+1))
return 1;

for(int j=L[i];j!=i;j=L[j])
resume(col[j]);
}

resume(c);

return 0;
}

void display()
{
for(int i=R[0];i!=0;i=R[i])
{
cout<<i<<' ';
for(int j=D[i];j!=i;j=D[j])
cout<<'('<<j<<','<<(row[j]-1)%9+1<<')'<<' ';

cout<<endl;
}
}
};

DLX dlx;
int s[100];

void getchange(int &r,int &c1,int &c2,int &c3,int &c4,int i,int j,int k)
{
r=(i*9+j)*9+k;
c1=i*9+j+1;
c2=i*9+k+81;
c3=j*9+k+162;
c4=map1[i][j]*9+k+243;
}

void slove()
{
int r,c1,c2,c3,c4;

dlx.init(729,324);

for(int i=0;i<9;++i)
for(int j=0;j<9;++j)
for(int k=1;k<=9;++k)
if(s[i*9+j]==0 || s[i*9+j]==k)
{
getchange(r,c1,c2,c3,c4,i,j,k);

dlx.Link(r,c1);
dlx.Link(r,c2);
dlx.Link(r,c3);
dlx.Link(r,c4);
}

/*    for(int i=1;i<=81;++i)
for(int j=1;j<=9;++j)
dlx.Link(j+(i-1)*9,i);

for(int i=1;i<=81;++i)
for(int j=1;j<=9;++j)
dlx.Link(9*(j-1)+(i-1)%9+1+81*((i-1)/9),i+81);

for(int i=1;i<=81;++i)
for(int j=1;j<=9;++j)
dlx.Link((j-1)*81+i,i+162);

for(int i=1;i<=3;++i)
for(int j=1;j<=3;++j)
for(int k=1;k<=9;++k)
for(int l=1;l<=3;++l)
for(int m=1;m<=3;++m)
dlx.Link((i-1)*243+(j-1)*27+k+(l-1)*81+(m-1)*9,(i-1)*27+(j-1)*9+k+243);

for(int i=0;i<81;++i)
if(s[i]!='.')
{
dlx.ans1[i+1]=s[i]-'0';

dlx.remove(i+1);

for(int j=dlx.D[i+1];j!=i+1;j=dlx.D[j])
{
if((dlx.row[j]-1)%9+1==s[i]-'0')
{
for(int k=dlx.R[j];k!=j;k=dlx.R[k])
dlx.remove(dlx.col[k]);

break;
}
}
}
*/

dlx.Dance(0);

int temp=dlx.ansnum;

if(temp==0)
cout<<"No solution"<<endl;
else if(temp==2)
cout<<"Multiple Solutions"<<endl;
else
dlx.showans();
}

const int step[4][2]={{-1,0},{0,1},{1,0},{0,-1}};
int kcou;
int lu[10][10][4];

void bfs(int num,int x,int y)
{
queue <int> que;
int temp,t1,t2;

que.push(x*10+y);
map1[x][y]=num;

while(!que.empty())
{
temp=que.front();
que.pop();

t1=temp/10;
t2=temp%10;

for(int k=0;k<4;++k)
if(lu[t1][t2][k] && map1[t1+step[k][0]][t2+step[k][1]]==-1)
{
que.push((t1+step[k][0])*10+t2+step[k][1]);
map1[t1+step[k][0]][t2+step[k][1]]=num;
}
}
}

void getmap()
{
int cou=0;

for(int i=0;i<9;++i)
for(int j=0;j<9;++j)
if(map1[i][j]==-1)
bfs(cou++,i,j);
}

int main()
{
ios::sync_with_stdio(false);

int T,t;
int fang[4];
cin>>T;

for(int cas=1;cas<=T;++cas)
{
memset(map1,-1,sizeof(map1));
memset(s,0,sizeof(s));
memset(lu,0,sizeof(lu));
kcou=0;

for(int i=0;i<9;++i)
for(int j=0;j<9;++j)
{
cin>>t;

for(int k=0;k<4;++k)
if(((t>>(4+k))&1)==0)
lu[i][j][k]=1;

s[i*9+j]=t&15;
}

getmap();

cout<<"Case "<<cas<<':'<<endl;

slove();
}

return 0;
}

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