次小生成树学习: 顾名思义,次小生成树,就是将图的所有生成树排序后,权值第二小的生成树. 次小生成树的朴素求法是很好想的,即首先求出最小生成树,之后枚举最小生成树中的所有边,将当前枚举的边"禁止使用",在这基础之上再求最小生成树,将所有边枚举之后的结果取最小值,那就是次小生成树.这个算法简单暴力,但是可想而知的复杂度是比较大的,在图是稠密图的时候,复杂度接近O(n^3).在规模较大的时候不建议使用. 另一个推荐的求法:在添加最小生成树的边之外的边时,会形成环,这个时候,把在这个环中,且…

题目:poj 1679 The Unique MST 题意:给你一颗树,让你求最小生成树和次小生成树值是否相等. 分析:这个题目关键在于求解次小生成树. 方法是,依次枚举不在最小生成树上的边,然后加入到最小生成树上,然后把原树上加入了之后形成环的最长的边删去,知道一个最小的.就是次小生成树. 这些须要的都能够在求解最小生成树的时候处理出来. AC代码: #include <cstdio> #include <cstring> #include <iostream> #i…

题目地址:http://poj.org/problem?id=1679 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! 次小生成树学习博客:http://blog.csdn.net/niushuai666/article/details/6925258 分析:T组数据,每组n个节点m条边.计算一下,最小生成树是不是独一无二的,如果是就输出最小生成树的权值和,否则输出Not Unique…

题目连接 http://poj.org/problem?id=1679 The Unique MST 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…

http://poj.org/problem?id=1679 The Unique MST Time Limit: 1000MS   Memory Limit: 10000K Total Submissions: 17726   Accepted: 6150 Description Given a connected undirected graph, tell if its minimum spanning tree is unique. Definition 1 (Spanning Tree…

题目链接:http://poj.org/problem?id=1679 The Unique MST Time Limit: 1000MS   Memory Limit: 10000K Total Submissions: 29408   Accepted: 10520 Description Given a connected undirected graph, tell if its minimum spanning tree is unique. Definition 1 (Spannin…

题目链接:http://poj.org/problem?id=1679 有t组数据,给你n个点,m条边,求是否存在相同权值的最小生成树(次小生成树的权值大小等于最小生成树). 先求出最小生成树的大小,把最小生成树的边存起来.然后分别枚举最小生成树上的每条边,除了这条边,其他边是否能生成最小生成树,若生成树的权值等于原来最小生成树的权值,则不唯一,否则输出最小生成树的权值.这里我用kruskal比较方便. #include <iostream> #include <cstdio> #…

题目链接:http://poj.org/problem?id=1679 题意: 给你一个图,问你这个图的最小生成树是否唯一. 题解: 求这个图的最小生成树和次小生成树.如果相等,则说明不唯一. 次小生成树(倍增算法): maxn[k][i]:表示从节点i向上走2^k步,这一段中边权的最大值. 枚举每一条不在MST中的边,求出这条边两端点之间在MST上路径上的最大边权mx. 次小生成树(非严格) = max(MST - mx + len) AC Code: #include <iostream>…

题意:求解最小生成树的权值是否唯一,即要我们求次小生成树的权值两种方法求最小生成树,一种用prim算法, 一种用kruskal算法 一:用prim算法 对于给定的图,我们可以证明,次小生成树可以由最小生成树变换一边得到. 那么我们可以如下求给定图的次小生成树.首先,我们用prime算法求出图的最小生成树, 在这个过程中记录每条边是否用过,以及两个点之间最短路径上的最大权值F[i,j] F[i,j]可以如此求得,当加入点u的时候,并且u的父结点是v 那么对于已经在生成树中的节点x F[x,u] =…

The Unique MST Time Limit: 1000MS   Memory Limit: 10000K Total Submissions: 24034   Accepted: 8535 Description Given a connected undirected graph, tell if its minimum spanning tree is unique. Definition 1 (Spanning Tree): Consider a connected, undire…

题意:构成MST是否唯一 思路: 问最小生成树是否唯一.我们可以先用Prim找到一棵最小生成树,然后保存好MST中任意两个点i到j的这条路径中的最大边的权值Max[i][j],如果我们能找到一条边满足:他不是最小生成树中的边,并且它的权值等于Max[i][j],那么他就可以代替MST中的这条边,所以MST不唯一. 次小生成树总结 代码: #include<cmath> #include<stack> #include<queue> #include<string&…

题目链接 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 fol…

The Unique MST Time Limit: 1000MS   Memory Limit: 10000K Total Submissions: 22668   Accepted: 8038 Description Given a connected undirected graph, tell if its minimum spanning tree is unique. Definition 1 (Spanning Tree): Consider a connected, undire…

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…

题目链接: http://poj.org/problem?id=1679 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…

这题可以用次小生成树解,这里用Kruskal算法来做.每条边除维护u,v,w外,还维护: used:表示这条边是否加过 eq:表示有没有与这条边相等的边 del:删除标记,以便删边之用 如果对于一个最小生成树的的边A,有一条与之权值相等的边B,则考虑把A删掉,再求一次最小生成树,看求出的总权值是否与前一个最小生成树的总权值相等.如果相等,则不唯一,如果找遍了这些权值相等的边都没找到,就说明唯一(注意每次不相等的话要把A重新加进来). 代码: #include <iostream> #inclu…

The Unique MST 题目链接: http://acm.hust.edu.cn/vjudge/contest/124434#problem/J 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).…

求最小生成树是否唯一 求一遍最小生成树再求一遍次小生成树 看看值是否相等就可以 #include<cstdio> #include<iostream> #include<algorithm> #include<cmath> #include<cstring> #include<string> #define cl(a,b) memset(a,b,sizeof(a)) #define debug(x) cerr<<#x<…

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 followin…

The Unique MST Time Limit: 1000MS   Memory Limit: 10000K Total Submissions: 22668   Accepted: 8038 Description Given a connected undirected graph, tell if its minimum spanning tree is unique. Definition 1 (Spanning Tree): Consider a connected, undire…

The Unique MST 时间限制: 10 Sec  内存限制: 128 MB提交: 25  解决: 10[提交][状态][讨论版] 题目描述 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 tre…

The Unique MST Time Limit: 1000MS   Memory Limit: 10000K Total Submissions: 35999   Accepted: 13145 Description Given a connected undirected graph, tell if its minimum spanning tree is unique. Definition 1 (Spanning Tree): Consider a connected, undir…

http://poj.org/problem?id=1679 #include<iostream> #include<vector> #include<cstdio> #include<cstring> #include<algorithm> using namespace std; struct node{ int u,v,w; }e[]; ]; vector<int>vis; bool cmp(node p,node q){ re…

无向连通图(无重边),判断最小生成树是否唯一,若唯一求边权和. 分析生成树的生成过程,只有一个圈内出现权值相同的边才会出现权值和相等但“异构”的生成树.(并不一定是最小生成树) 分析贪心策略求最小生成树的过程(贪心地选最短的边来扩充已加入生成树的顶点集合U),发现只有当出现“U中两个不同的点到V-U中同一点的距离同时为当前最短边”时,才会出现“异构”的最小生成树. 上图为kruscal和prim生成过程中可能遇到的相等边的情况,红色和蓝色的为权值相等的边. 可以看到kruscal由于事先将所有边…

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 followi…

The Unique MST Time Limit: 1000MS   Memory Limit: 10000K Total Submissions: 22715   Accepted: 8055 Description Given a connected undirected graph, tell if its minimum spanning tree is unique.  Definition 1 (Spanning Tree): Consider a connected, undir…

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 followi…

借用的是Kruskal的并查集,算法中的一点添加和改动. 通过判定其中有多少条可选的边,然后跟最小生成树所需边做比较,可选的边多于所选边,那么肯定方案不唯一. 如果不知道这个最小生成树的算法,还是先去理解下这个算法的原理,再继续看. 多加的几行与cnt2很类似的cnt1统计,是统计当前未选边中相同长度的边还有哪些可以选,但不标记,只是为了把当前可选的边全部统计出来. 其他细节,自己要细心点- #include <stdio.h> #include <string.h> #inclu…

Description Given a connected undirected graph, tell if its minimum spanning tree is unique. Definition (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…

http://poj.org/problem?id=1679 题目大意: 给你一些点,判断MST(最小生成树)是否唯一. 思路: 以前做过这题,不过写的是O(n^3)的,今天学了一招O(n^2)的,哈哈~ 方法一: 首先先建立MST,然后把这个MST的边一个个尝试不使用,构建另外一颗MST,然后判断权值是否相等. 这样复杂度需要O(n^3).. 方法二: 还可以用次最小生成树的方法解决:如果最小生成树不唯一,那么次小生成树的权值和最小生成树相同. 我们可以枚举要加入哪一条新边.在最小生成树上加一…