poj 3074(数独 Dancing Link精确覆盖)
| Time Limit: 1000MS | Memory Limit: 65536K | |
| Total Submissions: 5830 | Accepted: 1839 |
Description
In the game of Sudoku, you are given a large 9 × 9 grid divided into smaller 3 × 3 subgrids. For example,
| . | 2 | 7 | 3 | 8 | . | . | 1 | . |
| . | 1 | . | . | . | 6 | 7 | 3 | 5 |
| . | . | . | . | . | . | . | 2 | 9 |
| 3 | . | 5 | 6 | 9 | 2 | . | 8 | . |
| . | . | . | . | . | . | . | . | . |
| . | 6 | . | 1 | 7 | 4 | 5 | . | 3 |
| 6 | 4 | . | . | . | . | . | . | . |
| 9 | 5 | 1 | 8 | . | . | . | 7 | . |
| . | 8 | . | . | 6 | 5 | 3 | 4 | . |
Given some of the numbers in the grid, your goal is to determine the remaining numbers such that the numbers 1 through 9 appear exactly once in (1) each of nine 3 × 3 subgrids, (2) each of the nine rows, and (3) each of the nine columns.
Input
The input test file will contain multiple cases. Each test case consists of a single line containing 81 characters, which represent the 81 squares of the Sudoku grid, given one row at a time. Each character is either a digit (from 1 to 9) or a period (used to indicate an unfilled square). You may assume that each puzzle in the input will have exactly one solution. The end-of-file is denoted by a single line containing the word “end”.
Output
For each test case, print a line representing the completed Sudoku puzzle.
Sample Input
.2738..1..1...6735.......293.5692.8...........6.1745.364.......9518...7..8..6534. ......52..8.4......3...9...5.1...6..2..7........3.....6...1..........7.4.......3. end
Sample Output
527389416819426735436751829375692184194538267268174593643217958951843672782965341 416837529982465371735129468571298643293746185864351297647913852359682714128574936
Source
#include<cstdio>
using namespace std;
const int N=9;
const int mm=N*N*N*(N*N*4)+N;
const int mn=N*N*N+N;
int U[mm],D[mm],L[mm],R[mm],C[mm],X[mm];
int H[mn],S[mn],Q[mn];
bool v[mn];
char map[mn];
int size;
void prepare(int r,int c)
{
for(int i=0;i<=c;++i)
{
S[i]=0;
U[i]=D[i]=i;
L[i+1]=i;
R[i]=i+1;
}
R[size=c]=0;
while(r)H[r--]=-1;
}
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[C[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])
++S[C[U[D[j]]=D[U[j]]=j]];
L[R[c]]=R[L[c]]=c;
}
bool Dance(int k)
{
if(!R[0])
{
for(int i=0;i<k;++i)map[(X[Q[i]]-1)/9+1]=(X[Q[i]]-1)%9+1;
for(int i=1;i<=N*N;++i)printf("%d",map[i]);
puts("");
return 1;
}
int i,j,c,tmp=mm;
for(i=R[0];i;i=R[i])
if(S[i]<tmp)tmp=S[c=i];
remove(c);
for(i=D[c];i!=c;i=D[i])
{
Q[k]=i;
for(j=R[i];j!=i;j=R[j])remove(C[j]);
if(Dance(k+1))return 1;
for(j=L[i];j!=i;j=L[j])resume(C[j]);
}
resume(c);
return 0;
}
void Link(int r,int c)
{
++S[C[++size]=c];
X[size]=r;
D[size]=D[c];
U[D[c]]=size;
U[size]=c;
D[c]=size;
if(H[r]<0)H[r]=L[size]=R[size]=size;
else
{
R[size]=R[H[r]];
L[R[H[r]]]=size;
L[size]=H[r];
R[H[r]]=size;
}
}
void place(int &r,int &c1,int &c2,int &c3,int &c4,int i,int j,int k)
{
r=(i*N+j)*N+k,c1=i*N+j+1,c2=N*N+i*N+k,c3=N*N*2+j*N+k,c4=N*N*3+((i/3)*3+(j/3))*N+k;
}
int main()
{
int i,j,k,r,c1,c2,c3,c4;
while(scanf("%s",map),map[0]!='e')
{
prepare(mn,N*N*4);
for(i=1;i<=mn;++i)v[i]=0;
for(k=0,i=0;i<9;++i)
for(j=0;j<9;++j,++k)
if(map[k]>'0'&&map[k]<='9')
{
place(r,c1,c2,c3,c4,i,j,map[k]-'0');
Link(r,c1),Link(r,c2),Link(r,c3),Link(r,c4);
v[c2]=v[c3]=v[c4]=1;
}
for(i=0;i<9;++i)
for(j=0;j<9;++j)
for(k=1;k<=9;++k)
{
place(r,c1,c2,c3,c4,i,j,k);
if(v[c2]||v[c3]||v[c4])continue;
Link(r,c1),Link(r,c2),Link(r,c3),Link(r,c4);
}
Dance(0);
}
return 0;
}