PYTHON PROGRAMMING: Improving the MST ImplementationRead the problem below.Given the sample inputs and outputs.The code to be modified: https://pastebin.com/LxkCwpPj • Modify the given code implementation for the MinHeap such that:Instead of having separate lists for keys and values (i.e., keys and values), you will instead havea single list called heap. This heap variable should contain Node class objects. Each Node objectshould contain a key and a value as its attribute.OriginalExpected modificationclass MinHeap:class MinHeap:def _init_(self)- None:_init__(self) - None:self.size = 0self.size = 0self.keys = [None]self.heap = [None]%3D%3Dself.values = [None]• Modify all the necessary methods and lines of code given that you will only have a list of Nodeobjects• You can also choose to add/remove methods as you see fit• Hint: make sure to define the __repr__ method for Node class to make it easier to debug• Modify the implementation of Prim's and Kruskal's algorithms such that:• Both classes (PrimMST and KruskalMST) would each have an mst attribute (i.e., a variable mst)that stores a list of sets, where each set represents an edge of the Minimum Spanning Tree.• Optional but highly recommended: Change the condition for Kruskal's algorithm to be when thenumber of edges in the mst is equal to the (number of nodes - 1) instead of when the PQ is emptyInput Format• The first line contains the number N which is the number of vertices. Graph will then havenodes/vertices from 0 to N-1The second line contains the number E which is the number of edgesEach of the next E lines contains 3 numbers separated by commas: v,w,weight.This means thereis an undirected edge connecting v and w with weight= weightConstraintsv and w are not equal• N, E 0• weight 0v and w are guaranteed to be valid nodes/verticesOutput Format• First line of the output should be the edges of the MST from Prim's algorithm• Second line of the output should be the edges of the MST from Kruskal's algorithmBoth outputs should be a list of sets, where each set is an edge of the MST. For example, the MSTcontains edges 1-2 and 2-3. The output should then be [{1,2}, {2,3}].Note that the checker is order agnostic (i.e., it doesn't matter what order you output the edges; it willcheck the presence/absence of edges) Sample Input 0120,1,20,2,11,2,51,4,31,3,114,2,14,5,44,6,32,5,153,4,26,3,16,5,1Sample Output 0[{0, 2}, {2, 4}, {0, 1}, {3, 4}, {3, 6}, {5, 6}][{4, 2}, {2, 0}, {3, 6}, {5, 6}, {0, 1}, {3, 4}]Sample Input 17110,1,70,3,51,3,91,2,81,4,72,4,53,4,153,5,64,5,84,6,95,6,11Sample Output 1[{0, 3}, {3, 5}, {0, 1}, {1, 4}, {2, 4}, {4, 6}][{0, 3}, {2, 4}, {3, 5}, {0, 1}, {1, 4}, {4, 6}]

Question

PYTHON PROGRAMMING: Improving the MST ImplementationRead the problem below.Given the sample inputs and outputs.The code to be modified: https://pastebin.com/LxkCwpPj • Modify the given code implementation for the MinHeap such that:Instead of having separate lists for keys and values (i.e., keys and values), you will instead havea single list called heap. This heap variable should contain Node class objects. Each Node objectshould contain a key and a value as its attribute.OriginalExpected modificationclass MinHeap:class MinHeap:def _init_(self)-> None:_init__(self) -> None:self.size = 0self.size = 0self.keys = [None]self.heap = [None]%3D%3Dself.values = [None]• Modify all the necessary methods and lines of code given that you will only have a list of Nodeobjects• You can also choose to add/remove methods as you see fit• Hint: make sure to define the __repr__ method for Node class to make it easier to debug• Modify the implementation of Prim's and Kruskal's algorithms such that:• Both classes (PrimMST and KruskalMST) would each have an mst attribute (i.e., a variable mst)that stores a list of sets, where each set represents an edge of the Minimum Spanning Tree.• Optional but highly recommended: Change the condition for Kruskal's algorithm to be when thenumber of edges in the mst is equal to the (number of nodes - 1) instead of when the PQ is emptyInput Format• The first line contains the number N which is the number of vertices. Graph will then havenodes/vertices from 0 to N-1The second line contains the number E which is the number of edgesEach of the next E lines contains 3 numbers separated by commas: v,w,weight.This means thereis an undirected edge connecting v and w with weight= weightConstraintsv and w are not equal• N, E > 0• weight >0v and w are guaranteed to be valid nodes/verticesOutput Format• First line of the output should be the edges of the MST from Prim's algorithm• Second line of the output should be the edges of the MST from Kruskal's algorithmBoth outputs should be a list of sets, where each set is an edge of the MST. For example, the MSTcontains edges 1-2 and 2-3. The output should then be [{1,2}, {2,3}].Note that the checker is order agnostic (i.e., it doesn't matter what order you output the edges; it willcheck the presence/absence of edges) Sample Input 0120,1,20,2,11,2,51,4,31,3,114,2,14,5,44,6,32,5,153,4,26,3,16,5,1Sample Output 0[{0, 2}, {2, 4}, {0, 1}, {3, 4}, {3, 6}, {5, 6}][{4, 2}, {2, 0}, {3, 6}, {5, 6}, {0, 1}, {3, 4}]Sample Input 17110,1,70,3,51,3,91,2,81,4,72,4,53,4,153,5,64,5,84,6,95,6,11Sample Output 1[{0, 3}, {3, 5}, {0, 1}, {1, 4}, {2, 4}, {4, 6}][{0, 3}, {2, 4}, {3, 5}, {0, 1}, {1, 4}, {4, 6}]

Accepted Answer

Improving the MST Implementation in Python: