(Solved): you need to write the solutions in python and provide a brief explanation of your codes and the effi ...

you need to write the solutions in python and provide a brief explanation of your codes and the efficiency analysis with comments.

 

 

3. Consider a loop tree which is an undirected wighted graph formed by taking a binary tree and adding an edge from exactly one of the leaves to another node in the tree as follows: Let \( \mathrm{n} \) be the number of vertices in a loop tree. How long does it take Prim's or Kruskal's algorithms to find the minimum spanning tree in terms of \( n \) ? Devise a more efficient algorithm that takes an nxn adjacency weighted matrix as input, and finds the minimum spanning tree of a loop tree. ? input1 - Not Defteri Dosya Düzenle 1078000000 700650060 800006400 060000000 050000021 006000000 004000000 060020000 000010000 output1 - Not Defteri Dosya Düzenle Görünü p 14873265 ? input2 - Not Defteri Dosya Düzenle Görünüm \( \begin{array}{lllllll}0 & 2 & 1 & 0 & 0 & 0 & 0 \\ 2 & 0 & 0 & 3 & 4 & 4 & 0 \\ 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 3 & 0 & 0 & 0 & 0 & 0 \\ 0 & 4 & 0 & 0 & 0 & 5 & 6 \\ 0 & 4 & 0 & 0 & 5 & 0 & 0 \\ 0 & 0 & 0 & 0 & 6 & 0 & 0\end{array} \) ? output2 - Not Defteri Dosya Düzenle Görünüm