HDU 1301 Jungle Roads (最小生成树)

Jungle Roads

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 5037    Accepted Submission(s): 3656

Problem Description

The Head Elder of the tropical island of Lagrishan has a problem. A burst of foreign aid money was spent on extra roads between villages some years ago. But the jungle overtakes roads relentlessly, so the large road network is too expensive to maintain. The Council of Elders must choose to stop maintaining some roads. The map above on the left shows all the roads in use now and the cost in aacms per month to maintain them. Of course there needs to be some way to get between all the villages on maintained roads, even if the route is not as short as before. The Chief Elder would like to tell the Council of Elders what would be the smallest amount they could spend in aacms per month to maintain roads that would connect all the villages. The villages are labeled A through I in the maps above. The map on the right shows the roads that could be maintained most cheaply, for 216 aacms per month. Your task is to write a program that will solve such problems. 

The input consists of one to 100 data sets, followed by a final line containing only 0. Each data set starts with a line containing only a number n, which is the number of villages, 1 < n < 27, and the villages are labeled with the first n letters of the alphabet, capitalized. Each data set is completed with n-1 lines that start with village labels in alphabetical order. There is no line for the last village. Each line for a village starts with the village label followed by a number, k, of roads from this village to villages with labels later in the alphabet. If k is greater than 0, the line continues with data for each of the k roads. The data for each road is the village label for the other end of the road followed by the monthly maintenance cost in aacms for the road. Maintenance costs will be positive integers less than 100. All data fields in the row are separated by single blanks. The road network will always allow travel between all the villages. The network will never have more than 75 roads. No village will have more than 15 roads going to other villages (before or after in the alphabet). In the sample input below, the first data set goes with the map above. 

The output is one integer per line for each data set: the minimum cost in aacms per month to maintain a road system that connect all the villages. Caution: A brute force solution that examines every possible set of roads will not finish within the one minute time limit. 

 

 

Sample Input

9 A 2 B 12 I 25 B 3 C 10 H 40 I 8 C 2 D 18 G 55 D 1 E 44 E 2 F 60 G 38 F 0 G 1 H 35 H 1 I 35 3 A 2 B 10 C 40 B 1 C 20 0

 

 

Sample Output

216 30

 

 

 

最小生成树模板题，奇怪的是这题在POJ上交不了。

 1 #include <iostream>

 2 #include <cstdio>

 3 #include <string>

 4 #include <queue>

 5 #include <vector>

 6 #include <map>

 7 #include <algorithm>

 8 #include <cstring>

 9 #include <cctype>

10 #include <cstdlib>

11 #include <cmath>

12 #include <ctime>

13 using    namespace    std;

14 

15 const    int    SIZE = 30;

16 bool    VIS[SIZE];

17 int    N;

18 struct    Node

19 {

20     int    vec,cost;

21     bool    operator <(const Node & r) const

22     {

23         return    cost > r.cost;

24     }

25 };

26 vector<Node>    G[SIZE];

27 

28 int    prime(void);

29 int    main(void)

30 {

31     char    ch;

32     int    from,to,cost,k;

33     Node    temp;

34 

35     while(scanf("%d",&N) != EOF && N)

36     {

37         for(int i = 0;i < N;i ++)

38             G[i].clear();

39         for(int i = 0;i < N - 1;i ++)

40         {

41             scanf(" %c%d",&ch,&k);

42             from = ch - 'A';

43             while(k --)

44             {

45                 scanf(" %c%d",&ch,&cost);

46                 to = ch - 'A';

47                 temp.vec = to;

48                 temp.cost = cost;

49                 G[from].push_back(temp);

50                 temp.vec = from;

51                 G[to].push_back(temp);

52             }

53         }

54         printf("%d\n",prime());

55     }

56 

57     return    0;

58 }

59 

60 int    prime(void)

61 {

62     int    ans = 0;

63     int    num = 0;

64     Node    temp;

65     priority_queue<Node>    que;

66     temp.vec = temp.cost = 0;

67     que.push(temp);

68     fill(VIS,VIS + N,false);

69 

70     while(!que.empty())

71     {

72         Node    cur = que.top();

73         que.pop();

74         if(VIS[cur.vec])

75             continue;

76         ans += cur.cost;

77         num ++;

78         VIS[cur.vec] = true;

79         if(num == N)

80             break;

81 

82         for(int i = 0;i < G[cur.vec].size();i ++)

83             if(!VIS[G[cur.vec][i].vec])

84                 que.push(G[cur.vec][i]);

85     }

86 

87     return    ans;

88 }

Prime

#include <iostream>

#include <cstdio>

#include <string>

#include <queue>

#include <vector>

#include <map>

#include <algorithm>

#include <cstring>

#include <cctype>

#include <cstdlib>

#include <cmath>

#include <ctime>

using    namespace    std;



const    int    SIZE = 30;

int    FATHER[SIZE],N,NUM;

struct    Node

{

    int    from,to,cost;

}G[100];



void    ini(void);

int    find_father(int);

void    unite(int,int);

bool    same(int,int);

int    kruskal(void);

bool    comp(const Node &,const Node &);

int    main(void)

{

    char    ch;

    int    from,to,cost,k;



    while(scanf("%d",&N) && N)

    {

        ini();

        for(int i = 0;i < N - 1;i ++)

        {

            scanf(" %c%d",&ch,&k);

            from = ch - 'A';

            while(k --)

            {

                scanf(" %c%d",&ch,&cost);

                to = ch - 'A';

                G[NUM].from = from;

                G[NUM].to = to;

                G[NUM].cost = cost;

                NUM ++;

            }

        }

        printf("%d\n",kruskal());

    }



    return    0;

}



void    ini(void)

{

    NUM = 0;

    for(int i = 0;i <= N;i ++)

        FATHER[i] = i;

}



int    find_father(int n)

{

    if(n == FATHER[n])

        return    n;

    return    FATHER[n] = find_father(FATHER[n]);

}



void    unite(int x,int y)

{

    x = find_father(x);

    y = find_father(y);



    if(x == y)

        return    ;

    FATHER[x] = y;

}



bool    same(int x,int y)

{

    return    find_father(x) == find_father(y);

}



bool    comp(const Node & a,const Node & b)

{

    return    a.cost < b.cost;

}



int    kruskal(void)

{

    int    count = 0;

    int    ans = 0;



    sort(G,G + NUM,comp);

    for(int i = 0;i < NUM;i ++)

        if(!same(G[i].from,G[i].to))

        {

            unite(G[i].from,G[i].to);

            ans += G[i].cost;

            count ++;

            if(count == N - 1)

                break;

        }

    return    ans;

}

Kruskal