Fibonacci Heap Implementation for C++

References: Fibonacci Heaps and Their Uses in Improved Network Optimization Algorithms - Fredman, et al.

#Notes This was primarily implemented for use in Prim's Algorithm. Graph vertecies are stored in the heap, and ordered by an edge weight associated with each vertex. As such, each node in this implementation takes a vertex integer and weight integer and the heap uses the weight property for organization.

struct node
{
    int rank;
    char mark;
    
    int vertex;
    int weight;
    
    node* parent;
    node* child;
    node* left;
    node* right;
};

#Heap Operations This section will detail how to implement common heap operations using this library, and lists the amortized running time for each as described in Fredman, et al. ####Creating a Heap

FibonacciHeap F;

####Extract Min O(log(n))

node* h = F.Extract_Min();

####Insert O(1) Returns a pointer to that node so that you can directly reference it later for Decrease_Key() operations.

node* h = F.Insert(int weight,int vertex);

####Decrease Key O(1) Weight is set to new value for given node, and heap is reshuffled if the new weight violates the heap.

F.Decrease_Key(node* h, int weight); 

####Display Heap (Only use on small heaps, ~100 nodes) Publishes tree to fib.json, open fib.html to view this in D3.

F.Display_Heap();