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            posts - 7,comments - 3,trackbacks - 0
            The Unique MST
            Time Limit: 1000MS
            Memory Limit: 10000K
            Total Submissions: 11943
            Accepted: 4112

            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

            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@P

            代碼:
            #include <iostream>
            #include 
            <cstdio>
            #include 
            <cstring>
            #include 
            <algorithm>
            using namespace std;

            typedef 
            struct
            {
                
            int x, y, w;
            } edge;

            edge s[
            10010];
            int top, t[10010];

            bool cmp(edge a, edge b)
            {
                
            return a.w < b.w;
            }

            int kru(int n, int m, int x)
            {
                
            int i, j, a, b, tag[110], tem, sum, k;
                
            for (i = 0; i < n; ++i)
                {
                    tag[i] 
            = i;
                }
                k 
            = 1, j = 0, sum = 0;
                
            while (k < n)
                {
                    a 
            = s[j].x - 1;
                    b 
            = s[j].y - 1;
                    
            if (j == x)
                    {
                        j
            ++;
                        
            continue;
                    }
                    
            if (tag[a] != tag[b])
                    {
                        
            if (x == -1)
                        {
                            t[top] 
            = j;
                            top
            ++;
                        }
                        tem 
            = tag[b];
                        k
            ++, sum += s[j].w;
                        
            for (i =  0; i < n; ++i)
                        {
                            
            if (tag[i] == tem)
                            {
                                tag[i] 
            = tag[a];
                            }
                        }
                    }
                    j
            ++;
                }
                
            return sum;
            }
            int main()
            {
                
            int p, n, m, cmin;
                scanf(
            "%d"&p);
                
            while (p--)
                {
                    
            int flag = 1;
                    scanf(
            "%d%d"&n, &m);
                    
            for (int i = 0; i < m; ++i)
                        scanf(
            "%d%d%d"&s[i].x, &s[i].y, &s[i].w);
                    sort(s, s 
            + m, cmp);
                    top 
            = 0;
                    
            int min = kru(n, m, -1);
                    
            int key = top;
                    
            for (int l = 0; l < key; ++l)
                    {
                        cmin 
            = kru(n, m, t[l]);
                        
            if (cmin == min)
                        {
                            flag 
            = 0;
                            printf(
            "Not Unique!\n");
                            
            break;
                        }
                    }
                    
            if (flag)
                    printf(
            "%d\n", min);
                }
                
            return 0;
            }
            posted on 2011-10-17 21:07 LLawliet 閱讀(254) 評論(0)  編輯 收藏 引用 所屬分類: 圖論
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