Problems with Implementing Fibonacci Heap for Prim's Algorithm in Python - Incorrect Minimum Edge Selection
I've looked through the documentation and I'm still confused about I'm currently implementing Prim's algorithm using a Fibonacci heap in Python, but I'm running into issues with the minimum edge selection part of the algorithm. My Fibonacci heap implementation seems to be returning incorrect minimum values after several insertions and deletions. Here’s a simplified version of my Fibonacci heap class: ```python class FibonacciHeap: def __init__(self): self.trees = [] self.min_node = None def insert(self, value): new_node = Node(value) self.trees.append(new_node) if self.min_node is None or new_node.value < self.min_node.value: self.min_node = new_node def extract_min(self): if self.min_node is None: return None min_node = self.min_node # Perform necessary tree consolidation... self.trees.remove(min_node) return min_node.value class Node: def __init__(self, value): self.value = value self.children = [] ``` In Prim's algorithm, I call `extract_min()` to get the next edge to add to my MST. However, after several insertions, the minimum node I get seems to be larger than expected. I've tried debugging by printing the contents of `self.trees` before and after calling `extract_min()`, but it doesn't seem to reflect my insert order correctly, especially when multiple nodes have the same value. Here’s how I’m using the heap in my Prim's implementation: ```python def prim(graph, start_vertex): fib_heap = FibonacciHeap() for vertex in graph: fib_heap.insert(vertex.weight) mst_edges = [] while fib_heap: min_edge = fib_heap.extract_min() mst_edges.append(min_edge) return mst_edges ``` The question occurs particularly when I have multiple edges with the same weight in the graph. I suspect that my heap doesn’t handle the equal weights properly during consolidation. I would appreciate any insights into what might be going wrong or how to properly manage minimum node selection in a Fibonacci heap. Additionally, I’m using Python 3.10 and the `heapq` library for heap operations, but I want to implement this from scratch for learning purposes. My development environment is Windows. Is there a better approach?