Dance links algorithm

In fact Dance links is just a data structure, Dance links is an algorithm. Dacing links x is an efficient algorithm for solving this kind of problem, and this algorithm, based on the cross-cross-loop bidirectional

Linked list. The following are two-way cross-linked lists:

Here is a bare topic that uses this algorithm template:

Exact Cover

Description:

There is a n*m matrix with only 0s and 1s, (1 <= n,m <= 1000). An exact cover are a selection of rows such that every column have a 1 in exactly one of the selected rows. Try to find out the selected rows.

Sample Input:

6 7

3 1 4 7

2 1 4

3 4 5 7

3 3 5 6

4 2 3) 6 7

2 2 7

Sample Output:

3 2 4 6

Reference code:

1#include <stdio.h>2#include <iostream>3 using namespacestd;4 Const intMaxnode = +*Ten+Ten;5 Const intMAXN = ++Ten;6 Const intMAXM = ++Ten;7 8 structDLX {9     intN,m, size;//n rows, number of M columns, number of Szie nodesTen     intU[maxnode], D[maxnode], L[maxnode], R[maxnode], Col[maxnode], Row[maxnode]; One     intH[MAXN], S[MAXM];//H[i] First node of row I, s[j] number of nodes in column J A     intANSD, ANS[MAXN];//ANSD The number of rows contained in the solution, ans[] solution -  -     voidInitint_n,int_m)//Initialize the list of cross-links the     { -n =_n; -m =_m; -          for(inti =0; I <= m; i++) +         { -Col[i] = i; Row[i] =0; +U[i] = D[i] =i; AL[i] = i +1; R[i] = i-1; atS[i] =0; -         } -r[0] = m; L[M] =0; -Size =m; -          for(inti =1; I <= N; i++) -H[i] =-1; in     } -     voidLinkintRintC//Insert a node in row r, column C to {//note, here is the direction downward +size++; -Col[size] =C; theRow[size] =R; *s[c]++; $D[size] =D[c];Panax NotoginsengU[D[C]] =size; -U[size] =C; theD[C] =size; +         if(H[r] = =-1) AH[R] = r[size] = L[size] =size; the         Else +         { -R[size] =R[h[r]]; $L[r[h[r]] =size; $L[size] =H[r]; -R[h[r]] =size; -         } the     } -     voidRemoveintC//remove rows from column C and the nodes on the columnWuyi     { theL[R[C]] =L[c]; -R[L[C]] =R[c]; Wu          for(inti = d[c]; I! = C; i =D[i]) -              for(intj = L[i]; J! = i; j =L[j]) About             { $D[U[J]] =D[j]; -U[D[J]] =U[j]; ---S[col[j]]; -             } A     } +     voidResumeintC//restores the row in column C and the nodes on the column, just opposite to remove the     { -          for(inti = u[c];i! = C;i =U[i]) $              for(intj = R[i]; J! = i; j =R[j]) the             { the++S[col[j]]; theD[U[J]] =J; theU[D[J]] =J; -             } inL[R[C]] =C; theR[L[C]] =C; the     } About     BOOLDance (intD//d is the depth of the search the     { the         if(r[0] ==0) the         { +ANSD =D; -             return true; the         }Bayi         intc = r[0]; the          for(inti = r[0]; I! =0; i =R[i]) the             if(S[i] <S[c]) -c =i; - Remove (c); the          for(inti = d[c]; I! = C; i = D[i])//try individually the         { theANS[D] =Row[i]; the              for(intj = R[i]; J! = i; j =R[j]) - Remove (col[j]); the             if(Dance (d +1))return true; the              for(intj = L[i]; J! = i; j =L[j]) the Resume (col[j]);94         } theResume (c);//this dispensable, written just for completeness the         return false; the     }98 }; About  - DLX G;101 intMain ()102 {103     intN, M;104      the      while(SCANF ("%d%d", &n,&m) = =2)106     {107 g.init (n, m);108          for(inti =1; I <= N; i++)109         { the             intnum, J;111scanf"%d", &num); the              while(num--)113             { thescanf"%d", &j); the G.link (i, j); the             }117         }118         if(!g.dance (0))119printf"no\n"); -         Else121         {122printf"%d", G.ANSD);123              for(inti =0; i < G.ANSD; i++)124printf"%d", G.ans[i]); theprintf"\ n");126         }127     } -     return 0;129}

There is nothing wrong with the place, thank you for advice.

Dance links algorithm