prims-algorithm

问题 I was looking at the Wikipedia entry for Prim's algorithm and I noticed that its time complexity with an adjacency matrix is O(V^2) and its time complexity with a heap and adjacency list is O(E lg(V)) where E is the number of edges and V is the number of vertices in the graph. Since Prim's algorithm is used in denser graphs, E can approach V^2, but when it does, the time complexity with a heap becomes O(V^2 lg(V)) which is greater than O(V^2). Obviously, a heap will improve performance over

问题 I was looking at the Wikipedia entry for Prim's algorithm and I noticed that its time complexity with an adjacency matrix is O(V^2) and its time complexity with a heap and adjacency list is O(E lg(V)) where E is the number of edges and V is the number of vertices in the graph. Since Prim's algorithm is used in denser graphs, E can approach V^2, but when it does, the time complexity with a heap becomes O(V^2 lg(V)) which is greater than O(V^2). Obviously, a heap will improve performance over

问题 I define an unordered_map like this: std::unordered_map<std::string, Edge> edges; Is there a efficient way to choose a random Edge from the unordered_map edges ? 回答1: Pre-C++11 solution: std::tr1::unordered_map<std::string, Edge> edges; std::tr1::unordered_map<std::string, Edge>::iterator random_it = edges.begin(); std::advance(random_it, rand_between(0, edges.size())); C++11 onward solution: std::unordered_map<std::string, Edge> edges; auto random_it = std::next(std::begin(edges), rand

问题 I have coded an algorithm to carry out the dijkstra's algorithm. This is for a maths revision game I am making as part of my A level coursework. I have this data: Vertices: {'M', 'Y', 'X', 'C', 'F', 'Q'} Edges: defaultdict(<class 'list'>, {'X': ['Y'], 'C': ['M'], 'M': ['C', 'F', 'Y'], 'Q': ['F'], 'Y': ['X', 'M'], 'F': ['M', 'Q']}) Weights: {('M', 'C'): 44, ('Q', 'F'): 27, ('Y', 'X'): 42, ('X', 'Y'): 42, ('Y', 'M'): 6, ('M', 'F'): 9, ('M', 'Y'): 6, ('F', 'Q'): 27, ('F', 'M'): 9, ('C', 'M'): 44

问题 Here is a Graph where I need to find the minimum spanning tree of G using Prim's and Kruskal's algorithms. I found the minimum spanning tree using Prim's algorithm. Here is my attempt. I am having difficulty in finding the minimum spanning tree using Kruskal's algorithm. I have seen many videos related to Kruskal's graph algorithm but I ended up getting the same graph as Prim's algorithm. Can anyone please show me how to find the minimum spanning tree of the graph using Kruskal's algorithm?

问题 I can write both Prim's and Kruskal's algorithms to find a minimum spanning tree in C++ or Java, but I want to know how to implement them in Haskell with O(mlogm) or O(mlogn) (pure functional programs is better). Thanks a lot. 回答1: As svenningsson suggests, priority search queue is well suited for both Kruskal's and Prim's (atleast the author proclaims it in his paper.) The problem with Kruskal is that it requires that you have an O(log n) union-find algorithm. A union-find datastructure with

问题 Tim Roughgarden in Algorithms 2 course teaches the following approach for updating the adjacent vertices in the min heap (after extracting min from the heap): When a vertice v is added to the MST: For each edge (v,w) in the unexplored tree: 1. Delete w from the min heap. 2. Recompute the key[w] (i.e. it's value from the unexplored tree to the explored one). 3. Add the value back to the heap. So, basically this involves deletion from the heap (and heapify which takes O(logn)) and then

问题 Prim’s Algorithm An algorithm for finding a minimum spanning tree. Begin by choosing any edge with smallest weight, putting it into the spanning tree. Successively add to the tree edges of minimum weight that are incident to a vertex already in the tree, never forming a simple circuit with those edges already in the tree. Stop when n − 1 edges have been added. I know that you must start at node A. Also by giving a list of the order in which nodes and/or edges are added. But im not sure on the

问题 I am working on a minimum spanning tree using Prim's Algorithm with PriorityQueue in Java. However, I am getting the totalWeight (the minimum weight of the tree) wrong. Did I misunderstand the concept behind total weight, or is there some problem with my code? public int getMinSpanningTree(Graph g) { int[][] matrix = g.getEdgeMatrix(); int totalVertices = g.getNumberOfVertices(); boolean[] visit = new boolean[totalVertices]; int visitNum = 1; int totalWeight = 0; PriorityQueue<PriorityVertex>

问题 #include <bits/stdc++.h> using namespace std; #define fast ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0); #define LL long long int #define pb push_back #define mp make_pair #define PI pair<int,int> #define PL pair<LL,LL> #define PIS pair< int,string> #define test int t;cin>>t;while(t--) #define ff first #define ss second #define INF 1000000000 #define input(a,n) for(i=1;i<=n;i++)cin>>a[i]; #define output(a,n) for(i=1;i<=n;i++)cout<<a[i]<<" "; vector< vector<LL> >v(3002, vector<LL>(3002,