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, say…

The Unique MST Time Limit: 1000MS   Memory Limit: 10000K Total Submissions: 20421   Accepted: 7183 Description Given a connected undirected graph, tell if its minimum spanning tree is unique.  Definition 1 (Spanning Tree): Consider a connected, undir…

题意: 判断最小生成树是否唯一. 思路: 首先求出最小生成树,记录现在这个最小生成树上所有的边,然后通过取消其中一条边,找到这两点上其他的边形成一棵新的生成树,求其权值,通过枚举所有可能,通过这些权值看与原最小生成树的权值比较看其是否唯一.其实也可以理解成次小生成树加上最大边权的边后是否唯一. 代码: krusual: #include <iostream> #include <cstdio> #include <cstdlib> #include <cmath&…

Time Limit: 1000MS   Memory Limit: 10000K Total Submissions: 22335   Accepted: 7922 Description Given a connected undirected graph, tell if its minimum spanning tree is unique. Definition 1 (Spanning Tree): Consider a connected, undirected graph G =…

The Unique MST Time Limit: 1000MS   Memory Limit: 10000K Total Submissions: 25203   Accepted: 8995 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 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…

The Unique MST Time Limit: 1000MS   Memory Limit: 10000K Total Submissions: 19941   Accepted: 6999 Description Given a connected undirected graph, tell if its minimum spanning tree is unique.  Definition 1 (Spanning Tree): Consider a connected, undir…

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>…

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] =…

可以依次枚举MST上的各条边并删去再求最小生成树,如果结果和第一次求的一样,那就是最小生成树不唯一. 用prim算法,时间复杂度O(n^3). #include<cstdio> #include<cstring> using namespace std; #define MAXN 111 #define INF (1<<30) struct Edge{ int u,v; }edge[MAXN]; int NE; int n,G[MAXN][MAXN]; int lowc…

题目链接 参考博客 希望注释足够清楚..欢迎指出不足~ #include<cstdio> #include<cstring> #include<algorithm> using namespace std; ; const int INF=0x3f3f3f3f; int n,m; int mp[maxn][maxn]; int maxlen[maxn][maxn]; //maxlen[i][j]表示 //生成树上,从 点i到点j的所有边中的最大边长 int dis[ma…

找出最小生成树,同时用Max[i][j]记录i到j的唯一路径上最大边权.然后用不在最小生成树里的边i-j来替换,看看是否差值为0. #include <algorithm> #include <cstdio> #include <cstring> using namespace std; const int N=101; const int INF=0x3f3f3f3f; int n,m,ans,s; int lowc[N],vis[N],g[N][N]; int Ma…

The Unique MST Time Limit: 1000MS   Memory Limit: 10000K Total Submissions: 24201   Accepted: 8596 Description Given a connected undirected graph, tell if its minimum spanning tree is unique. Definition 1 (Spanning Tree): Consider a connected, undire…

次小生成树求法:例如求最小生成树用到了 1.2.4这三条边,总共5条边,那循环3次的时候,每次分别不用1.2.4求得最小生成树的MST,最小的MST即为次小生成树 如下代码maxx即求最小生成树时求得的最大边 #include<map> #include<set> #include<cmath> #include<queue> #include<stack> #include<vector> #include<cstdio>…

prim方法:先求过一遍prim,同时标记使用过得边.然后同时记录任意2点间的最大值. 每次加入一条新的边,会产生环,删去环中的最大值即可. #include<stdio.h> #include<string.h> #define INF 99999999 ; int map[maxn][maxn],vis[maxn],dis[maxn],n,pre[maxn],m,used[maxn][maxn]; int maxd[maxn][maxn]; int max(int x,int…

题目大意: 给一张无向图,可以将图中权值为v的边修改为k-v,求修改后的最小生成树边权和. 题目分析: 最小生成树的环切定理:任何非树边一定比对应树链上的所有边权值要大.否则我们可以将链上最大的树边删去而连接这一条边. 运用这个性质,先求出原图的最小生成树,然后再来枚举边,如果枚举到一条边: 它是最小生成树中的边,如果更优, 那么更新答案. 它不是最小生成树中的边,找到它连接的两点在最小生成树中的链上边权的最大值,如果山出发这条边,加入枚举的这条更优,就更新答案 code #include<bi…

The Unique MST Time Limit: 1000MS   Memory Limit: 10000K Total Submissions: 36692   Accepted: 13368 Description Given a connected undirected graph, tell if its minimum spanning tree is unique. Definition 1 (Spanning Tree): Consider a connected, undir…

[题目大意] 共T组数据,对于每组数据,给你一个n个点,m条边的图,设图的最小生成树为MST,次小生成树为ans,若MST=ans,输出Not Unique!,否则输出MST [题解] 很明确,先求MST再求ans. 关于求次小生成树,我打算写一个总结,先留个坑. #include<iostream> #include<cstdio> #include<cstdlib> #include<cstring> #include<cmath> #inc…

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…

思路: Prim: 这道题目中有重边 Prim可以先加一个sec数组来保存重边的次小边,这样不会影响到最小生成树,在算次小生成树时要同时判断次小边(不需判断是否在MST中) Kruskal: Kruskal对重边就很友好了,不用考虑 原理是这样的:我们先找最小生成树并用used标记好哪些边是MST的边,然后我们暴力遍历每一条MST边被删去的情况,如果还能生成MST就找出这些MST最小的,这棵MST就是次小生成树 Prim代码: #include<cmath> #include<stack…

The Unique MST Time Limit: 1000MS   Memory Limit: 10000K Total Submissions: 28673   Accepted: 10239 Description Given a connected undirected graph, tell if its minimum spanning tree is unique. Definition 1 (Spanning Tree): Consider a connected, undir…

题目链接:http://poj.org/problem?id=1679 The Unique MST Time Limit: 1000MS   Memory Limit: 10000K Total Submissions: 31378   Accepted: 11306 Description Given a connected undirected graph, tell if its minimum spanning tree is unique. Definition 1 (Spannin…

The Unique MST Time Limit: 1000MS   Memory Limit: 10000K       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 t…

The Unique MST Time Limit: 1000MS   Memory Limit: 10000K Total Submissions: 23180   Accepted: 8235 Description Given a connected undirected graph, tell if its minimum spanning tree is unique.  Definition 1 (Spanning Tree): Consider a connected, undir…

The Unique MST Time Limit: 1000MS   Memory Limit: 10000K Total Submissions: 39561   Accepted: 14444 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 (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…