hdu 3829 最大独立集

思路：很显然，让某一个孩子happy是一定可以做到的，但是同时有可能会让别的孩子unhappy，所以每一对这样的两个孩子之间存在”冲突”，如果在存在“冲突”的孩子之间建边的话，我们的问题就转化成了求二分图的最大独立集。具体为什么是二分图，博主也没有想明白...

 1 #include <iostream>

 2 #include <cstring>

 3 #include <cstdio>

 4 using namespace std;

 5 

 6 const int N = 501;

 7 const int M = N * N;

 8 const int L = 11;

 9 bool visit[N];

10 int head[N];

11 int mark[N];

12 int n, m, p, e;

13 

14 struct Edge

15 {

16     int v, next;

17 } edge[M];

18 

19 struct Hobby

20 {

21     char like[L], dislike[L];

22 } hobby[N];

23 

24 void init()

25 {

26     e = 0;

27     memset( head, -1, sizeof(head) );

28 }

29 

30 void addEdge( int u, int v )

31 {

32     edge[e].v = v;

33     edge[e].next = head[u];

34     head[u] = e++;

35 }

36 

37 int dfs( int u )

38 {

39     for ( int i = head[u]; i != -1; i = edge[i].next )

40     {

41         int v = edge[i].v;

42         if ( !visit[v] )

43         {

44             visit[v] = true;

45             if ( mark[v] == -1 || dfs( mark[v] ) )

46             {

47                 mark[v] = u;

48                 mark[u] = v;

49                 return 1;

50             }

51         }

52     }

53     return 0;

54 }

55 

56 int hunagry()

57 {

58     memset( mark, -1, sizeof(mark) );

59     int res = p;

60     for ( int i = 1; i <= p; i++ )

61     {

62         if ( mark[i] != -1 ) continue;

63         memset( visit, 0, sizeof(visit) );

64         res -= dfs(i);

65     }

66     return res;

67 }

68 

69 int main()

70 {

71     while ( scanf("%d%d%d", &n, &m, &p) != EOF )

72     {

73         init();

74         for ( int i = 1; i <= p; i++ )

75         {

76             scanf("%s%s", hobby[i].like, hobby[i].dislike);

77             for ( int j = i - 1; j > 0; j-- )

78             {

79                 if ( strcmp( hobby[i].like, hobby[j].dislike ) == 0

80                 ||   strcmp( hobby[j].like, hobby[i].dislike ) == 0 )

81                 {

82                     addEdge( i, j );

83                     addEdge( j, i );

84                 }

85             }

86         }

87         printf("%d\n", hunagry());

88     }

89     return 0;

90 }