1017 - Exact cover

時間限制：15秒 記憶體限制：128兆

題目描述

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.

輸入

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.

輸出

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".

樣例輸入

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

樣例輸出

3 2 4 6

題目連結：http://acm.hust.edu.cn/problem/show/1017

精確覆蓋入門題。

Dancing Links 就是一種加快搜索速度的方法，採用四向連結串列。

  1 /* ***********************************************
  2 Author        :kuangbin
  3 Created Time  :2014/5/25 22:55:25
  4 File Name     :E:\2014ACM\專題學習\DLX\HUST1017.cpp
  5 ************************************************ */
  6 
  7 #include <stdio.h>
  8
 
 #include <string.h>
  9 #include <iostream>
 10 #include <algorithm>
 11 #include <vector>
 12 #include <queue>
 13 #include <set>
 14 #include <map>
 15 #include <string>
 16 #include <math.h>
 17 #include <stdlib.h>
 18 #include <time.h>
 19 using namespace std;
 20 const int maxnode = 100010;
 21 const int MaxM = 1010;
 22 const int MaxN = 1010;
 23 struct DLX
 24 {
 25     int n,m,size;
 26     int U[maxnode],D[maxnode],R[maxnode],L[maxnode],Row[maxnode],Col[maxnode];
 27     int H[MaxN], S[MaxM];
 28     int ansd, ans[MaxN];
 29     void init(int _n,int _m)
 30     {
 31         n = _n;
 32         m = _m;
 33         for(int i = 0;i <= m;i++)
 34         {
 35             S[i] = 0;
 36             U[i] = D[i] = i;
 37             L[i] = i-1;
 38             R[i] = i+1;
 39         }
 40         R[m] = 0; L[0] = m;
 41         size = m;
 42         for(int i = 1;i <= n;i++)
 43             H[i] = -1;
 44     }
 45     void Link(int r,int c)
 46     {
 47         ++S[Col[++size]=c];
 48         Row[size] = r;
 49         D[size] = D[c];
 50         U[D[c]] = size;
 51         U[size] = c;
 52         D[c] = size;
 53         if(H[r] < 0)H[r] = L[size] = R[size] = size;
 54         else
 55         {
 56             R[size] = R[H[r]];
 57             L[R[H[r]]] = size;
 58             L[size] = H[r];
 59             R[H[r]] = size;
 60         }
 61     }
 62     void remove(int c)
 63     {
 64         L[R[c]] = L[c]; R[L[c]] = R[c];
 65         for(int i = D[c];i != c;i = D[i])
 66             for(int j = R[i];j != i;j = R[j])
 67             {
 68                 U[D[j]] = U[j];
 69                 D[U[j]] = D[j];
 70                 --S[Col[j]];
 71             }
 72     }
 73     void resume(int c)
 74     {
 75         for(int i = U[c];i != c;i = U[i])
 76             for(int j = L[i];j != i;j = L[j])
 77                 ++S[Col[U[D[j]]=D[U[j]]=j]];
 78         L[R[c]] = R[L[c]] = c;
 79     }
 80     //d為遞迴深度
 81     bool Dance(int d)
 82     {
 83         if(R[0] == 0)
 84         {
 85             ansd = d;
 86             return true;
 87         }
 88         int c = R[0];
 89         for(int i = R[0];i != 0;i = R[i])
 90             if(S[i] < S[c])
 91                 c = i;
 92         remove(c);
 93         for(int i = D[c];i != c;i = D[i])
 94         {
 95             ans[d] = Row[i];
 96             for(int j = R[i]; j != i;j = R[j])remove(Col[j]);
 97             if(Dance(d+1))return true;
 98             for(int j = L[i]; j != i;j = L[j])resume(Col[j]);
 99         }
100         resume(c);
101         return false;
102     }
103 };
104 
105 DLX g;
106 int main()
107 {
108     //freopen("in.txt","r",stdin);
109     //freopen("out.txt","w",stdout);
110     int n,m;
111     while(scanf("%d%d",&n,&m) == 2)
112     {
113         g.init(n,m);
114         for(int i = 1;i <= n;i++)
115         {
116             int num,j;
117             scanf("%d",&num);
118             while(num--)
119             {
120                 scanf("%d",&j);
121                 g.Link(i,j);
122             }
123         }
124         if(!g.Dance(0))printf("NO\n");
125         else
126         {
127             printf("%d",g.ansd);
128             for(int i = 0;i < g.ansd;i++)
129                 printf(" %d",g.ans[i]);
130             printf("\n");
131         }
132     }
133     return 0;
134 }