By : paurinaasg
Date : November 17 2020, 04:28 AM

I hope this helps . It is possible to solve this problem efficiently(in O(n log n) time), but it is not that easy. Just using the Prim's algorithm with a heap does not help(it actually makes it even slower), because its time complexity is O(E log V), which is O(n^2 * log n) in this case. However, you can use the Delaunay triangulation to reduce the number of edges in the graph. The Delaunay triangulation graph is planar, so it has linear number of edges. That's why running the Prim's algorithm with a heap on it gives O(n log n) time complexity(there are O(n) edges and n vertices). You can read more about it here(covering this algorithm in details and proving its correctness would make my answer way too long): http://en.wikipedia.org/wiki/Euclidean_minimum_spanning_tree. Note that even though the article is about the Euclidian mst, the approach for your case is essentially the same(it is possible to build the Delaunay triangulation for manhattan distance efficiently, too). code :
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Finding a Minimum Spanning Tree from an Adjacency List where the Adjacency List is in a string array using Prims Algorit
By : b r a n d o n
Date : March 29 2020, 07:55 AM
wish help you to fix your issue So I need some help coming up with a way to find a Minimum spanning tree. Suppose I have my graph in the form of an adjacency list: , Suppose I have my tree in the form of an adjacency list code :
A 2 B 12 I 25
B 3 C 10 H 40 I 8
A
12/_\25
B 8 I
A 2 B 12 I 25
B 3 C 10 H 40 I 8
C 2 D 18 G 55
D 1 E 44
E 2 F 60 G 38
F 0
G 1 H 35
H 1 I 35
E 2 F 60 G 38
F 0
A 2 B 12 I 25
B 4 A 12 C 10 H 40 I 8
C 3 B 10 D 18 G 55
D 2 C 18 E 44
E 3 D 44 F 60 G 38
F 1 E 60
G 3 C 55 E 38 H 35
H 3 B 40 G 35 I 35

What does π[v] ←u step mean in Prims algorithm for minimum spanning tree?
By : Simon
Date : March 29 2020, 07:55 AM
I think the issue was by ths following , π is just any old array variable. So this line of code isn’t really different from the other assignments. What it does in the algorithm however is save the predecessor node of the current node. π is sometimes also called the predecessor function because for any given node n, π[n] gives you the predecessor of that node (after the algorithm has completed).

Prims Algorithm for Minimum Spanning Tree Analysis
By : Mike Hanford
Date : March 29 2020, 07:55 AM

Preorder tree walk of a minimum spanning tree generated by Prim's algorithm
By : Liezel Lombard
Date : March 29 2020, 07:55 AM
With these it helps I suggest you to add a new list in your Node class named children for example. After your Prim's algorithm you can run through your obtained nodes and add them to their parent's children. The complexity is O(n), so not a big deal. After that the DFS traversal will be easy.

krukshal's algorithm or Prims Algorithm which one is better in finding minimum spanning tree?
By : y3gang
Date : March 29 2020, 07:55 AM
I hope this helps . I'll add one point in favour of Prim's algorithm I haven't seen mentioned. If you are given N points and a distance function d(x,y) for the distance between x and y, it is easy to implement Prim's algorithm using space O(N) (but time N^2). Start off with an arbitrary point A and create an array of size N1 giving you the distances from A to all other points. Pick the point, B, associated with the shortest distance, link A and B in the spanning tree and then update the distances in the array to be the minimum of the distance already noted down to that other point and the distance from B ot that other point, noting down where the shortest link is from B and where from A. Carry on.



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