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'.
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.
1 2 1
2 3 2
3 1 3
1 2 2
2 3 2
3 4 2
4 1 2
The question ： Ask if the minimum spanning tree is unique .
analysis ： I want to make a small tree , Infer whether the second smallest spanning tree and the smallest spanning tree are equal .
The steps of finding the next smallest spanning tree ：
(1) First use Prime Find the minimum spanning tree MST, stay Prime Using a matrix at the same time mmax[ ][ ] Recorded in the MST Connect two random points in u,v Right in the only path of
The weight of the side with the largest value . practice ：Prime Is to add one node at a time t. Use this point to add MST The edge of is joined with its previous one MST Point of mmax Compare the values of .
(2) Enumerate edges other than the minimum spanning tree , And delete the edge with the largest weight on the ring where the edge is located .
(3) The tree with the smallest weight of all spanning trees obtained is the tree to be calculated .
The time complexity of the algorithm is O(n^2).
using namespace std;
#define maxn 111
#define inf 0x3f3f3f3f int map[maxn][maxn],mmax[maxn][maxn];//map Adjacency matrix is a graph ,mmax In the minimum spanning tree i To j The maximum edge weight of
bool used[maxn][maxn];// Determine whether the edge is added to the minimum spanning tree
int pre[maxn],dis[maxn];//pre be used for mmax The construction of , Put one in before loading MST The node of ,dis Used to build MST void init(int n)
for (int i=;i<=n;i++)// Graph initialization
for (int j=;j<=n;j++)
} void read(int m)
for (int i=;i<m;i++)// Read in the picture
int prime(int n)// structure MST
for (int i=;i<=n;i++)
pre[i]=;//1 Point for the first to put in MST The point of , Let's set it as the leading node of all points
for (int i=;i<=n;i++)
for (int j=;j<=n;j++)
if (min_dis==inf)// If there is no minimum spanning tree
used[k][pre[k]]=used[pre[k]][k]=true;// Mark as put in MST The point of
for (int j=;j<=n;j++)
mmax[j][k]=mmax[k][j]=max(mmax[j][pre[k]],dis[k]);// The largest edge of the smallest spanning tree ring
return ans;// The sum of the weights of the minimum spanning tree
int smst(int n,int min_ans)//min_ans Is the sum of the weights of the minimum spanning tree
for (int i=;i<=n;i++)// Enumerate the edges outside the minimum spanning tree
for (int j=i+;j<=n;j++)
ans=min(ans,min_ans+map[i][j]-mmax[i][j]);// This side is the second smallest MST A weight of MST Add the edge and subtract the maximum of the ring where the edge is located MST edge
void solve(int n)
if (smst(n,ans)==ans)// Minor MST The weight is equal to MST explain MST Is not the only
int t,n,m; scanf("%d",&t);
} return ;
- POJ_1679_The Unique MST( Sub small spanning tree template )
The Unique MST Time Limit: 1000MS Memory Limit: 10000K Total Submissions: 23942 Accepted: 8492 D ...
- POJ1679 The Unique MST[ Secondary spanning tree ]
The Unique MST Time Limit: 1000MS Memory Limit: 10000K Total Submissions: 28673 Accepted: 10239 ...
- POJ 1679 The Unique MST ( Secondary spanning tree Determine whether the minimum spanning tree is unique )
Topic link Description Given a connected undirected graph, tell if its minimum spanning tree is unique. De ...
- POJ1679 The Unique MST —— Secondary spanning tree
Topic link :http://poj.org/problem?id=1679 The Unique MST Time Limit: 1000MS Memory Limit: 10000K Total S ...
- POJ-1679 The Unique MST, Sub small spanning tree template problem
The Unique MST Time Limit: 1000MS Memory Limit: 10000K Description Given a connected undirec ...
- POJ 1679 The Unique MST ( Secondary spanning tree )
Topic link :http://poj.org/problem?id=1679 Yes t Group data , Here you are. n A little bit ,m side , Find out whether there is a minimum spanning tree with the same weight ( The weight of the second smallest spanning tree is equal to the smallest spanning tree ). First, find out the size of the minimum spanning tree , ...
- poj1679The Unique MST( Sub small spanning tree template )
Sub small spanning tree template , Don't forget to judge that there is no minimum spanning tree #include <iostream> #include <cstdio> #include <cstring> ...
- POJ 1679 The Unique MST ( Secondary spanning tree kruskal Algorithm ）
The Unique MST The time limit : 10 Sec Memory limit : 128 MB Submit : 25 solve : 10[ Submit ][ state ][ Discussion board ] Title Description Given a connected undirect ...
- poj 1679 The Unique MST ( Secondary spanning tree (sec_mst)【kruskal】)
The Unique MST Time Limit: 1000MS Memory Limit: 10000K Total Submissions: 35999 Accepted: 13145 ...
- PHP Process control structure of
1.break Use break Statement can exit the statement deeply embedded in the nested loop to a specified number of layers or directly exit to the outermost layer ,break It takes an optional numeric parameter to decide how many statements to jump out of .break You can jump out a few sentences .break You can jump a few times ...
- Spring MVC 3.0 In depth and detailed explanation of annotations
The core principle 1. User sends request to server .url:user.do 2. The server receives the request . Find out Dispatchservlet Can handle . So call DispatchServlet. 3. ...
- Python Study ( Two ) function Python, compile Python
No matter what windos still Linux Once installed python, Configured environment variables , Enter... On the command line python This command will go into interactive mode . In this mode, you can do some simple python Code writing . Exit can be used exi ...
- docker And docker-compose Quick installation and easy use of
This article will use DaoCloud Source in Ubuntu It's easy and fast to install docker And docker-compose And added through Dockerfile And docker-compose.yml Use n ...
- [JSON] First time to know JSON
1: What is? json json yes , It's the syntax for storing and exchanging text information , Be similar to xml, But compared to xml smaller , faster , Easier to parse . 2:JSON Grammatical rules JSON in : The data is in key/velue Alignment , The data is separated by a check mark , Huakuo ...
- Python Common library Pilow
Basic usage Static methods PIL.Image.open(fp, mode=’r’) Incoming file path (str), Return to one image object PIL.Image.alpha_composite(im1, im2) mixed ...
- maven Study diary （ 3、 ... and ）------- Development environment construction （springmvc+hibernate4） Various maven Error summary
1.maven code gbk Unmapped characters of The way to solve this problem : stay maven Declare the correct character set encoding in the compiler plug-in for —— The character set code used in compilation is the same as that used in code file !! After installing the system , General Chinese system ...
- dapper.net Reprint
Dapper.NET—— Light weight ORM Dapper.NET Use Contents of this article Dapper.NET Use 1. Why choose Dapper 2. With Dapper(4.0) For example . 2.1 Create several tables in the database . 2 ...
- CentOS Deploy Kubernetes1.13 colony -1（ Use kubeadm install K8S）
Reference resources :https://www.kubernetes.org.cn/4956.html 1. Get ready explain : The preparatory work needs to be performed on all the hosts in the cluster 1.1 The system configuration Before installation , We need to do the following preparations first . Three stations CentOS ...
- eclipse Download and install and test
Download address :www.ecplise.org After downloading, double-click install After installation , First run eclipse Will pop up Workspace Launcher Dialog box , Requires setting up a workspace to store project documents . ...