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 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 Dzenle 1078000000 700650060 800006400 060000000 050000021 006000000 004000000 060020000 000010000 output1 - Not Defteri Dosya Dzenle Grn p 14873265 input2 - Not Defteri Dosya Dzenle Grnm 0210000200344010000000300000040005604005000000600 output2 - Not Defteri Dosya Dzenle Grnm