prims-algorithm | 易学教程

Prim and Kruskal's algorithms complexity

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问题 Given an undirected connected graph with weights. w:E->{1,2,3,4,5,6,7} - meaning there is only 7 weights possible. I need to find a spanning tree using Prim's algorithm in O(n+m) and Kruskal's algorithm in O( m*a(m,n)). I have no idea how to do this and really need some guidance about how the weights can help me in here. 回答1: You can sort edges weights faster. In Kruskal algorithm you don't need O(M lg M) sort, you just can use count sort (or any other O(M) algorithm). So the final complexity

Prim's Algorithm: How to get index of key on which DECREASE_KEY operation is to be performed?

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问题 So I am following this algorithm for Prim's MST input: graph G(V,E) in the form of adjacency list Create a min heap for vertices using build heap time complexity: O(V) Repeat following steps until no more elements in heap. Call extract-min on heap to get vertex with minimum cost O(log V) For vertex extracted find the adjacent vertices in adjacency list. Perform decrease key operation on adjacent vertices in the heap. O(logn V) The time complexity analysis for the algorithm given in my class

Prim's Algorithm: How to get index of key on which DECREASE_KEY operation is to be performed?

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Difference between Prim's and Dijkstra's algorithms?

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问题 What is the exact difference between Dijkstra's and Prim's algorithms? I know Prim's will give a MST but the tree generated by Dijkstra will also be a MST. Then what is the exact difference? 回答1: Prim's algorithm constructs a minimum spanning tree for the graph, which is a tree that connects all nodes in the graph and has the least total cost among all trees that connect all the nodes. However, the length of a path between any two nodes in the MST might not be the shortest path between those

select and change color of a line in html5 canvas?

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问题 I wrote this code to draw random graphs. I have been trying in vain to find how I can select a line in the graph so that I can apply the prim's algorithm as one selects lines and see if they have found the minimum tree. function draw(n,rep){ var cvs=document.getElementsByTagName('canvas')[0]; /** * @type CanvasRenderingContext2D **/ var ctx=cvs.getContext('2d'); ctx.beginPath(); var randomX=[]; var randomY=[]; ctx.lineWidth=2; ctx.font = '3'+' Arial'; var weights=[]; var lastRandomx=Math

Time Complexity of Prims Algorithm?

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问题 I found the time complexity of Prims algorithm everywhere as O((V + E) log V) = E log V . But as we can see the algorithm: It seems like the time complexity is O(V(log V + E log V)) . But if its time complexity is O((V + E) log V) . Then the nesting must have to be like this: But the above nesting is seems to be wrong. 回答1: MST-PRIM(G, w, r) 1 for each u ∈ G.V 2 u.key ← ∞ 3 u.π ← NIL 4 r.key ← 0 5 Q ← G.V 6 while Q ≠ Ø 7 u ← EXTRACT-MIN(Q) 8 for each v ∈ G.Adjacent[u] 9 if v ∈ Q and w(u, v) <

Running time of Prim's algorithm

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问题 Suppose that all edge weights in a graph are integers in the range from 1 to |V|. How fast can you make Prim's algorithm run? What if the edge weights are integers in the range from 1 to W for some constant W? MST-PRIM(G,w,r) 1. for each u∈ G.V 2. u.key=inf 3. u.π=NIL 4. r.key=0 5. Q=G.V 6. while Q != Ø 7. u=EXTRACT-MIN(Q) 8. for each v ∈ G.Adj[u] 9. if v∈ Q and w(u,v)<v.key 10. v. π=u 11. v.key=w(u,v) According to my textbook: The running time of Prim's algorithm depends on how we implement

Maze generation prim algorithm not all cells are traversed

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问题 I'm trying to implement Prim maze generation algorithm: Start with a grid full of walls. Pick a cell, mark it as part of the maze. Add the walls of the cell to the wall list. While there are walls in the list: Pick a random wall from the list. If the cell on the opposite side isn't in the maze yet: Make the wall a passage and mark the cell on the opposite side as part of the maze. Add the neighboring walls of the cell to the wall list. If the cell on the opposite side already was in the maze,

How to update element priorities in a heap for Prim's Algorithm?

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问题 I am studying Prim's Algorithm. There is a part within the code the next vertex across the cut will be coming to the set of the vertices belonging to the MST . While doing that, we also have to 'update all vertices in the other set which are adjacent to the departing vertex'. This is a snapshot from CLRS : The interesting part lies in line no. 11. But since we are using a heap here, we have access to only the minimum element, right ( heap[0] )? So how do we search and update vertices from the

How to update element priorities in a heap for Prim's Algorithm?

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I am studying Prim's Algorithm. There is a part within the code the next vertex across the cut will be coming to the set of the vertices belonging to the MST . While doing that, we also have to 'update all vertices in the other set which are adjacent to the departing vertex'. This is a snapshot from CLRS : The interesting part lies in line no. 11. But since we are using a heap here, we have access to only the minimum element, right ( heap[0] )? So how do we search and update vertices from the heap even though they are not the minimum one and thus we have knowing where they are except by linear