Exact cover
Special Judge Time Limit: 15 Sec Memory Limit: 128 MB Submissions: 5179 Solved: 2748Description
There is an N*M matrix with only 0s and 1s, (1 <= N,M <= 1000). An exact cover is a selection of rows such that every column has a 1 in exactly one of the selected rows. Try to find out the selected rows.
Input
There are multiply test cases. First line: two integers N, M; The following N lines: Every line first comes an integer C(1 <= C <= 100), represents the number of 1s in this row, then comes C integers: the index of the columns whose value is 1 in this row.
Output
First output the number of rows in the selection, then output the index of the selected rows. If there are multiply selections, you should just output any of them. If there are no selection, just output "NO".
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
HINT
Source
dupeng
1 #include<iostream> 2 #include<cstdio> 3 #include<cstring> 4 5 using namespace std; 6 7 const int N=1010; 8 const int V=1000010; 9 10 int U[V],D[V]; 11 int L[V],R[V]; 12 int C[V]; 13 int H[N],S[N],mark[V]; 14 int size,n,m,vis[N],flag; 15 16 void Link(int r,int c){ 17 S[c]++;C[size]=c; 18 U[size]=U[c];D[U[c]]=size; 19 D[size]=c;U[c]=size; 20 if(H[r]==-1) 21 H[r]=L[size]=R[size]=size; 22 else{ 23 L[size]=L[H[r]]; R[L[H[r]]]=size; 24 R[size]=H[r]; L[H[r]]=size; 25 } 26 mark[size]=r; 27 size++; 28 } 29 30 void remove(int c){ //删除列 31 L[R[c]]=L[c]; 32 R[L[c]]=R[c]; 33 int i,j; 34 for(i=D[c];i!=c;i=D[i]) 35 for(j=R[i];j!=i;j=R[j]){ 36 U[D[j]]=U[j],D[U[j]]=D[j]; 37 S[C[j]]--; 38 } 39 } 40 41 void resume(int c){ 42 int i,j; 43 for(i=U[c];i!=c;i=U[i]) 44 for(j=L[i];j!=i;j=L[j]){ 45 U[D[j]]=j,D[U[j]]=j; 46 S[C[j]]++; 47 } 48 L[R[c]]=c; 49 R[L[c]]=c; 50 } 51 52 void Dance(int k){ 53 int i,j,min,c; 54 if(!R[0]){ 55 flag=1; 56 printf("%d",k); 57 for(i=0;i<k;i++) 58 printf(" %d",mark[vis[i]]); 59 printf("\n"); 60 return ; 61 } 62 for(min=N,i=R[0];i;i=R[i]) 63 if(S[i]<min){ 64 min=S[i]; 65 c=i; 66 } 67 remove(c); 68 for(i=D[c];i!=c;i=D[i]){ 69 vis[k]=i; 70 for(j=R[i];j!=i;j=R[j]) 71 remove(C[j]); 72 Dance(k+1); 73 if(flag) 74 return ; 75 for(j=L[i];j!=i;j=L[j]) 76 resume(C[j]); 77 78 } 79 resume(c); 80 } 81 82 int main(){ 83 84 freopen("input.txt","r",stdin); 85 86 while(~scanf("%d%d",&n,&m)){ 87 int i; 88 for(i=0;i<=m;i++){ 89 S[i]=0; 90 D[i]=U[i]=i; 91 L[i+1]=i;R[i]=i+1; 92 } 93 R[m]=0; 94 size=m+1; 95 memset(H,-1,sizeof(H)); 96 memset(mark,0,sizeof(mark)); 97 int k,j; 98 for(i=1;i<=n;i++){ 99 scanf("%d",&k); 100 while(k--){ 101 scanf("%d",&j); 102 Link(i,j); 103 } 104 } 105 flag=0; 106 Dance(0); 107 if(!flag) 108 printf("NO\n"); 109 } 110 return 0; 111 }