1017 - Exact cover

时间限制：15秒 内存限制：128兆

自定评测 5584 次提交 2975 次通过

题目描述

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.

输入

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.

输出

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".

样例输入

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

样例输出

3 2 4 6

题目链接：http://acm.hust.edu.cn/problem/show/1017

精确覆盖入门题。

Dancing Links 就是一种加快搜索速度的方法，采用四向链表。

  1 /* ***********************************************

  2 Author        :kuangbin

  3 Created Time  :2014/5/25 22:55:25

  4 File Name     :E:\2014ACM\专题学习\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为递归深度

 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 }

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