• <ins id="pjuwb"></ins>
    <blockquote id="pjuwb"><pre id="pjuwb"></pre></blockquote>
    <noscript id="pjuwb"></noscript>
          <sup id="pjuwb"><pre id="pjuwb"></pre></sup>
            <dd id="pjuwb"></dd>
            <abbr id="pjuwb"></abbr>
            posts - 7,comments - 3,trackbacks - 0
            Slim Span
            Time Limit: 5000MSMemory Limit: 65536K
            Total Submissions: 4023Accepted: 2116

            Description

            Given an undirected weighted graph G, you should find one of spanning trees specified as follows.

            The graph G is an ordered pair (VE), where V is a set of vertices {v1v2, …, vn} and E is a set of undirected edges {e1e2, …, em}. Each edge e ∈ E has its weight w(e).

            A spanning tree T is a tree (a connected subgraph without cycles) which connects all the n vertices with n − 1 edges. The slimness of a spanning tree T is defined as the difference between the largest weight and the smallest weight among the n − 1 edges of T.


            Figure 5: A graph G and the weights of the edges

            For example, a graph G in Figure 5(a) has four vertices {v1v2v3v4} and five undirected edges {e1e2e3e4e5}. The weights of the edges are w(e1) = 3, w(e2) = 5, w(e3) = 6, w(e4) = 6, w(e5) = 7 as shown in Figure 5(b).


            Figure 6: Examples of the spanning trees of G

            There are several spanning trees for G. Four of them are depicted in Figure 6(a)~(d). The spanning tree Ta in Figure 6(a) has three edges whose weights are 3, 6 and 7. The largest weight is 7 and the smallest weight is 3 so that the slimness of the tree Ta is 4. The slimnesses of spanning trees TbTc and Td shown in Figure 6(b), (c) and (d) are 3, 2 and 1, respectively. You can easily see the slimness of any other spanning tree is greater than or equal to 1, thus the spanning tree Td in Figure 6(d) is one of the slimmest spanning trees whose slimness is 1.

            Your job is to write a program that computes the smallest slimness.

            Input

            The input consists of multiple datasets, followed by a line containing two zeros separated by a space. Each dataset has the following format.

            nm
            a1b1w1
            ambmwm

            Every input item in a dataset is a non-negative integer. Items in a line are separated by a space. n is the number of the vertices and m the number of the edges. You can assume 2 ≤ n ≤ 100 and 0 ≤ m ≤ n(n − 1)/2. ak and bk (k = 1, …, m) are positive integers less than or equal to n, which represent the two vertices vak and vbk connected by the kth edge ekwk is a positive integer less than or equal to 10000, which indicates the weight of ek. You can assume that the graph G = (VE) is simple, that is, there are no self-loops (that connect the same vertex) nor parallel edges (that are two or more edges whose both ends are the same two vertices).

            Output

            For each dataset, if the graph has spanning trees, the smallest slimness among them should be printed. Otherwise, −1 should be printed. An output should not contain extra characters.

            Sample Input

            4 5
            1 2 3
            1 3 5
            1 4 6
            2 4 6
            3 4 7
            4 6
            1 2 10
            1 3 100
            1 4 90
            2 3 20
            2 4 80
            3 4 40
            2 1
            1 2 1
            3 0
            3 1
            1 2 1
            3 3
            1 2 2
            2 3 5
            1 3 6
            5 10
            1 2 110
            1 3 120
            1 4 130
            1 5 120
            2 3 110
            2 4 120
            2 5 130
            3 4 120
            3 5 110
            4 5 120
            5 10
            1 2 9384
            1 3 887
            1 4 2778
            1 5 6916
            2 3 7794
            2 4 8336
            2 5 5387
            3 4 493
            3 5 6650
            4 5 1422
            5 8
            1 2 1
            2 3 100
            3 4 100
            4 5 100
            1 5 50
            2 5 50
            3 5 50
            4 1 150
            0 0

            Sample Output

            1
            20
            0
            -1
            -1
            1
            0
            1686
            50

            Source



            題目就是生成一棵樹,要求邊權最大減最小的差最小。
            根據Kruskal思想,把邊排序,之后枚舉一下就行了。

            代碼:

            #include <cmath>
            #include 
            <cstdio>
            #include 
            <cstdlib>
            #include 
            <cstring>
            #include 
            <iostream>
            #include 
            <algorithm>
            using namespace std;

            const int M = 5005;
            const int INF = 1 << 29;

            struct edge
            {
                
            int st, ed, w;
                
            bool operator < (edge a) const
                {
                    
            return w < a.w;
                }
            } e[M];

            int n, m, ans, num, temp;
            int f[105], rank[105];

            void makeset()
            {
                
            for (int i = 1; i <= n; ++i)
                    f[i] 
            = i;
                memset(rank, 
            0sizeof(rank));
            }

            int find(int x)
            {
                
            while (f[x] != x) x = f[x];
                
            return x;
            }

            void unionset(int a, int b)
            {
                
            int p = find(a);
                
            int q = find(b);
                
            if (rank[p] > rank[q])
                    f[q] 
            = p;
                
            else
                
            if (rank[p] < rank[q])
                    f[p] 
            = q;
                
            else
                {
                    f[p] 
            = q;
                    rank[q]
            ++;
                }
            }

            void kruskal()
            {
                ans 
            = INF;
                
            for (int i = 0; i < m - n + 2++i)
                {
                    makeset();
                    temp 
            = -1;
                    num 
            = 0;
                    
            for (int j = i; j < m; ++j)
                    {
                        
            if (find(e[j].st) != find(e[j].ed))
                        {
                            num
            ++;
                            unionset(e[j].st, e[j].ed);
                            
            if (num == n - 1)
                            {
                                temp 
            = e[j].w - e[i].w;
                                
            break;
                            }
                        }
                    }
                    
            if (temp == -1break;
                    
            if (temp != -1 && temp < ans) ans = temp;
                }
                
            if (ans >= INF) printf("-1\n");
                
            else printf("%d\n", ans);
            }

            int main()
            {
                
            while (scanf("%d%d"&n, &m), n || m)
                {
                    
            for (int i = 0; i < m; ++i)
                        scanf(
            "%d%d%d"&e[i].st, &e[i].ed, &e[i].w);
                    sort(e, e 
            + m);
                    kruskal();
                }
                
            return 0;
            }
            posted on 2011-10-17 15:54 LLawliet 閱讀(364) 評論(0)  編輯 收藏 引用 所屬分類: 圖論
            人妻久久久一区二区三区| 天天做夜夜做久久做狠狠| 色8久久人人97超碰香蕉987| 久久精品中文字幕无码绿巨人| 91精品日韩人妻无码久久不卡| 久久se精品一区二区影院| 久久综合色老色| 狠狠人妻久久久久久综合| 人妻少妇久久中文字幕| 国产精品成人精品久久久| 熟妇人妻久久中文字幕| 久久高潮一级毛片免费| 国产精品久久国产精麻豆99网站| 久久人人爽人人爽AV片| 久久精品国产一区| 乱亲女H秽乱长久久久| 久久婷婷是五月综合色狠狠| 精品久久无码中文字幕| 久久婷婷五月综合国产尤物app| 国产激情久久久久影院老熟女| 久久久婷婷五月亚洲97号色| 九九精品久久久久久噜噜| 久久久久久久综合日本| 国产三级精品久久| 99久久精品免费看国产一区二区三区 | 久久久精品视频免费观看| 久久精品国产亚洲AV无码偷窥 | 久久精品综合网| 亚洲精品NV久久久久久久久久| 国产成人99久久亚洲综合精品 | 亚洲综合熟女久久久30p| 久久av免费天堂小草播放| 99久久国产主播综合精品| 久久夜色tv网站| 四虎国产精品免费久久久| 青青草原综合久久大伊人精品| 久久Av无码精品人妻系列| 久久久国产精品福利免费| 99久久夜色精品国产网站| 一本大道久久a久久精品综合| 7国产欧美日韩综合天堂中文久久久久 |