• <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
            久久精品国产亚洲精品2020| 午夜精品久久久久久久| 久久国产精品久久国产精品| 久久91综合国产91久久精品| 精品国产乱码久久久久久浪潮 | 久久天天躁狠狠躁夜夜躁2014| 波多野结衣久久精品| 久久综合九色综合欧美狠狠| 亚洲综合久久夜AV | 久久国产精品成人影院| 亚洲国产天堂久久久久久| 久久久久久夜精品精品免费啦| 久久国产香蕉一区精品| 香蕉久久夜色精品升级完成| 久久久久人妻一区精品| 精品久久久久久中文字幕| 久久久久久国产精品美女 | 久久久这里有精品| 国产一区二区三区久久| 久久精品国产久精国产果冻传媒| 91精品无码久久久久久五月天| 狠狠色综合网站久久久久久久高清 | 久久精品国产99国产精品| 亚洲中文字幕无码久久2020| 色综合久久中文色婷婷| 久久青青草视频| 久久国产香蕉一区精品| 69久久夜色精品国产69| 青青草原综合久久大伊人| 久久综合综合久久97色| 精品久久久久久成人AV| 精品无码久久久久国产| 国产亚洲精品自在久久| 俺来也俺去啦久久综合网| 亚洲国产精品久久电影欧美| 精品久久久久久久久免费影院| 狠狠色丁香婷婷综合久久来来去| 国产日韩久久久精品影院首页| 品成人欧美大片久久国产欧美...| 国产一区二区精品久久| 国产午夜精品久久久久九九|