POJ 1679 The Unique MST

The Unique MST

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 19847		Accepted: 6959

Description

Given a connected undirected graph, tell if its minimum spanning tree is unique. 

Definition 1 (Spanning Tree): Consider a connected, undirected graph G = (V, E). A spanning tree of G is a subgraph of G, say T = (V', E'), with the following properties: 
1. V' = V. 
2. T is connected and acyclic. 

Definition 2 (Minimum Spanning Tree): Consider an edge-weighted, connected, undirected graph G = (V, E). The minimum spanning tree T = (V, E') of G is the spanning tree that has the smallest total cost. The total cost of T means the sum of the weights on all the edges in E'. 

Input

 1 #include <iostream>

 2 #include <cstring>

 3 #include <cstdio>

 4 #include <queue>

 5 #define INF 0x3f3f3f3f

 6 #define pii pair<int,int>

 7 using namespace std;

 8 const int maxn = 10000;

 9 struct arc {

10     int to,cost,next;

11     arc(int x = 0,int y = 0,int z = -1) {

12         to = x;

13         cost = y;

14         next = z;

15     }

16 };

17 arc e[maxn];

18 int head[maxn],d[maxn],p[maxn],n,m,tot;

19 bool used[maxn];

20 void add(int u,int v,int w) {

21     e[tot] = arc(v,w,head[u]);

22     head[u] = tot++;

23 }

24 int prim() {

25     priority_queue<pii,vector< pii >,greater< pii > >q;

26     for(int i = 1; i < maxn; ++i) {

27         d[i] = INF;

28         used[i] = false;

29         p[i] = -1;

30     }

31     d[1] = 0;

32     q.push(make_pair(d[1],1));

33     int ans = 0;

34     bool isUnique = true;

35     while(!q.empty()) {

36         pair<int,int>now = q.top();

37         q.pop();

38         if(used[now.second]) continue;

39         used[now.second] = true;

40         ans += now.first;

41         for(int i = head[now.second]; ~i; i = e[i].next) {

42             if(!used[e[i].to] && d[e[i].to] > e[i].cost) {

43                 d[e[i].to] = e[i].cost;

44                 p[e[i].to] = now.second;

45                 q.push(make_pair(d[e[i].to],e[i].to));

46             }

47             if(used[e[i].to] && p[now.second] != -1 && p[now.second] != e[i].to && e[i].cost == now.first) isUnique = false;

48         }

49     }

50     return isUnique?ans:-1;

51 }

52 int main() {

53     int kase;

54     scanf("%d",&kase);

55     while(kase--) {

56         scanf("%d %d",&n,&m);

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

58         for(int i = tot = 0; i < m; ++i) {

59             int u,v,w;

60             scanf("%d %d %d",&u,&v,&w);

61             add(u,v,w);

62             add(v,u,w);

63         }

64         int ans = prim();

65         ans == -1?puts("Not Unique!"):printf("%d\n",ans);

66     }

67     return 0;

68 }

69 /*

70 2

71 3 3

72 1 2 1

73 2 3 2

74 3 1 3

75 4 4

76 1 2 2

77 2 3 2

78 3 4 2

79 4 1 2

80 

81 */

View Code

 

 

 

The first line contains a single integer t (1 <= t <= 20), the number of test cases. Each case represents a graph. It begins with a line containing two integers n and m (1 <= n <= 100), the number of nodes and edges. Each of the following m lines contains a triple (xi, yi, wi), indicating that xi and yi are connected by an edge with weight = wi. For any two nodes, there is at most one edge connecting them.

Output

For each input, if the MST is unique, print the total cost of it, or otherwise print the string 'Not Unique!'.

Sample Input

2

3 3

1 2 1

2 3 2

3 1 3

4 4

1 2 2

2 3 2

3 4 2

4 1 2

Sample Output

3

Not Unique!

Source

POJ Monthly--2004.06.27 srbga@POJ

 

解题：测试数据好像有问题啊，大大的问题。。。下面写法貌似只能过这题

 

 1 #include <iostream>

 2 #include <cstdio>

 3 #include <cstring>

 4 #include <cstdlib>

 5 #include <vector>

 6 #include <climits>

 7 #include <algorithm>

 8 #include <cmath>

 9 #define LL long long

10 #define INF 0x3f3f3f

11 using namespace std;

12 int mp[101][101],d[101];

13 int n,m;

14 bool vis[101];

15 int prim(){

16     int i,j,k,temp,index,ans = 0;

17     for(i = 1; i <= n; i++) d[i] = INF;

18     d[1] = 0;

19     memset(vis,false,sizeof(vis));

20     for(i = 0; i < n; i++){

21         temp = INF;

22         for(j = 1; j <= n; j++)

23             if(!vis[j] && d[j] < temp) temp = d[index = j];

24         k = 0;

25         for(j = 1; j <= n; j++){

26             if(vis[j] && mp[index][j] == temp) k++;

27         }

28         if(k > 1) return -1;

29         vis[index] = true;

30         ans += temp;

31         for(j = 1; j <= n; j++){

32             if(!vis[j] && d[j] > mp[index][j]) d[j] = mp[index][j];

33         }

34     }

35     return ans;

36 }

37 int main(){

38     int ks,i,j,u,v,w;

39     scanf("%d",&ks);

40     while(ks--){

41         scanf("%d%d",&n,&m);

42         for(i = 0; i <= n; i++)

43             for(j = 0; j <= n; j++)

44             mp[i][j] = INF;

45         for(i = 0; i < m; i++){

46             scanf("%d%d%d",&u,&v,&w);

47             if(mp[u][v] > w){

48                 mp[u][v] = mp[v][u] = w;

49             }

50         }

51         w = prim();

52         if(w < 0) puts("Not Unique!");

53         else printf("%d\n",w);

54     }

55     return 0;

56 }

View Code

 

 

上面的代码有些许问题

 

完整的正确代码

 1 #include <iostream>

 2 #include <cstdio>

 3 #include <cstring>

 4 #include <cmath>

 5 #include <algorithm>

 6 #include <climits>

 7 #include <vector>

 8 #include <queue>

 9 #include <cstdlib>

10 #include <string>

11 #include <set>

12 #include <stack>

13 #define LL long long

14 #define pii pair<int,int>

15 #define INF 0x3f3f3f3f

16 using namespace std;

17 const int maxn = 110;

18 int g[maxn][maxn],d[maxn],p[maxn],maxv[maxn][maxn],used[maxn][maxn],n,m;

19 bool vis[maxn];

20 int prim() {

21     for(int i = 1; i <= n; ++i) {

22         d[i] = INF;

23         p[i] = -1;

24         vis[i] = false;

25     }

26     int sum = d[1] = 0;

27     for(int i = 1; i <= n; ++i) {

28         int minv = INF,index;

29         for(int j = 1; j <= n; ++j)

30             if(!vis[j] && d[j] < minv)

31                 minv = d[index = j];

32         if(p[index] > -1) {

33             used[index][p[index]] = used[p[index]][index] = 2;

34             for(int j = 1; j <= n; ++j)

35                 if(vis[j]) maxv[j][index] = maxv[index][j] = max(maxv[j][p[index]],minv);

36         }

37         sum += minv;

38         vis[index] = true;

39         for(int j = 1; j <= n; ++j)

40             if(!vis[j] && g[index][j] < INF && g[index][j] < d[j]) {

41                 d[j] = g[index][j];

42                 p[j] = index;

43             }

44     }

45     return sum;

46 }

47 int main() {

48     int t,u,v,w;

49     scanf("%d",&t);

50     while(t--) {

51         scanf("%d %d",&n,&m);

52         for(int i = 0; i <= n; ++i)

53             for(int j = 0; j <= n; ++j) {

54                 maxv[i][j] = 0;

55                 g[i][j] = INF;

56                 used[i][j] = 0;

57             }

58         for(int i = 0; i < m; ++i){

59             scanf("%d %d %d",&u,&v,&w);

60             if(g[u][v] > w){

61                 g[u][v] = g[v][u] = w;

62                 used[u][v] = used[v][u] = 1;

63             }

64         }

65         int ans = prim(),ans2 = INF;

66         for(int i = 1; i <= n; ++i)

67         for(int j = i + 1; j <= n; ++j){

68             if(used[i][j] == 1) ans2 = min(ans2,ans - maxv[i][j] + g[i][j]);

69         }

70         ans == ans2?puts("Not Unique!"):printf("%d\n",ans);

71     }

72     return 0;

73 }

View Code

 

不用求次小生成树，也能判断是否唯一，prim版