C++ Program to Implement Fibonacci Heap

This C++ Program demonstrates the implementation of Fibonacci Heap.

Here is source code of the C++ Program to demonstrate Fibonacci Heap. The C++ program is successfully compiled and run on a Linux system. The program output is also shown below.

```
/*
```

 * C++ Program to Implement Fibonacci Heap

```
 */
```
```
#include <iostream>
```
```
#include <cmath>
```
```
#include <cstdlib>
```
```
using namespace std;
```
```
/*
```
```
 * Node Declaration
```
```
 */
```
```
struct node
```
```
{
```
```
    int n;
```
```
    int degree;
```
```
    node* parent;
```
```
    node* child;
```
```
    node* left;
```
```
    node* right;
```
```
    char mark;
```
```
    char C;
```
```
};
```
```
/*
```
```
 * Class Declaration
```
```
 */
```
```
class FibonacciHeap
```
```
{
```
```
    private:
```
```
        int nH;
```
```
        node *H;
```
```
    public:
```
```
        node* InitializeHeap();
```

        int Fibonnaci_link(node*, node*, node*);

```
        node *Create_node(int);
```
```
        node *Insert(node *, node *);
```
```
        node *Union(node *, node *);
```
```
        node *Extract_Min(node *);
```
```
        int Consolidate(node *);
```
```
        int Display(node *);
```
```
        node *Find(node *, int);
```

        int Decrease_key(node *, int, int);

```
        int Delete_key(node *,int);
```

        int Cut(node *, node *, node *);

        int Cascase_cut(node *, node *);

```
        FibonacciHeap()
```
```
        {
```
```
            H = InitializeHeap();
```
```
        }
```
```
};
```
```
/*
```
```
 * Initialize Heap
```
```
 */
```
```
node* FibonacciHeap::InitializeHeap()
```
```
{
```
```
    node* np;
```
```
    np = NULL;
```
```
    return np;
```
```
}
```
```
/*
```
```
 * Create Node
```
```
 */
```

node* FibonacciHeap::Create_node(int value)

```
{
```
```
    node* x = new node;
```
```
    x->n = value;
```
```
    return x;
```
```
}
```
```
/*
```
```
 * Insert Node
```
```
 */
```

node* FibonacciHeap::Insert(node* H, node* x)

```
{
```
```
    x->degree = 0;
```
```
    x->parent = NULL;
```
```
    x->child = NULL;
```
```
    x->left = x;
```
```
    x->right = x;
```
```
    x->mark = 'F';
```
```
    x->C = 'N';
```
```
    if (H != NULL)
```
```
    {
```
```
        (H->left)->right = x;
```
```
        x->right = H;
```
```
        x->left = H->left;
```
```
        H->left = x;
```
```
        if (x->n < H->n)
```
```
            H = x;
```
```
    }
```
```
    else
```
```
    {
```
```
        H = x;
```
```
    }
```
```
    nH = nH + 1;
```
```
    return H;
```
```
}
```
```
/*
```
```
 * Link Nodes in Fibonnaci Heap
```
```
 */
```

int FibonacciHeap::Fibonnaci_link(node* H1, node* y, node* z)

```
{
```
```
    (y->left)->right = y->right;
```
```
    (y->right)->left = y->left;
```
```
    if (z->right == z)
```
```
        H1 = z;
```
```
    y->left = y;
```
```
    y->right = y;
```
```
    y->parent = z;
```
```
    if (z->child == NULL)
```
```
        z->child = y;
```
```
    y->right = z->child;
```
```
    y->left = (z->child)->left;
```
```
    ((z->child)->left)->right = y;
```
```
    (z->child)->left = y;
```
```
    if (y->n < (z->child)->n)
```
```
        z->child = y;
```
```
    z->degree++;
```
```
}
```
```
/*
```
```
 * Union Nodes in Fibonnaci Heap
```
```
 */
```

node* FibonacciHeap::Union(node* H1, node* H2)

```
{
```
```
    node* np;
```
```
    node* H = InitializeHeap();
```
```
    H = H1;
```
```
    (H->left)->right = H2;
```
```
    (H2->left)->right = H;
```
```
    np = H->left;
```
```
    H->left = H2->left;
```
```
    H2->left = np;
```
```
    return H;
```
```
}
```
```
/*
```
```
 * Display Fibonnaci Heap
```
```
 */
```
```
int FibonacciHeap::Display(node* H)
```
```
{
```
```
    node* p = H;
```
```
    if (p == NULL)
```
```
    {
```

        cout<<"The Heap is Empty"<<endl;

```
        return 0;
```
```
    }
```

    cout<<"The root nodes of Heap are: "<<endl;

```
    do
```
```
    {
```
```
        cout<<p->n;
```
```
        p = p->right;
```
```
        if (p != H)
```
```
        {
```
```
            cout<<"-->";
```
```
        }
```
```
    }
```
```
    while (p != H && p->right != NULL);
```
```
    cout<<endl;
```
```
}
```
```
/*
```
```
 * Extract Min Node in Fibonnaci Heap
```
```
 */
```

node* FibonacciHeap::Extract_Min(node* H1)

```
{
```
```
    node* p;
```
```
    node* ptr;
```
```
    node* z = H1;
```
```
    p = z;
```
```
    ptr = z;
```
```
    if (z == NULL)
```
```
        return z;
```
```
    node* x;
```
```
    node* np;
```
```
    x = NULL;
```
```
    if (z->child != NULL)
```
```
        x = z->child;
```
```
    if (x != NULL)
```
```
    {
```
```
        ptr = x;
```
```
        do
```
```
        {
```
```
            np = x->right;
```
```
            (H1->left)->right = x;
```
```
            x->right = H1;
```
```
            x->left = H1->left;
```
```
            H1->left = x;
```
```
            if (x->n < H1->n)
```
```
                H1 = x;
```
```
            x->parent = NULL;
```
```
            x = np;
```
```
        }
```
```
        while (np != ptr);
```
```
    }
```
```
    (z->left)->right = z->right;
```
```
    (z->right)->left = z->left;
```
```
    H1 = z->right;
```

    if (z == z->right && z->child == NULL)

```
        H = NULL;
```
```
    else
```
```
    {
```
```
        H1 = z->right;
```
```
        Consolidate(H1);
```
```
    }
```
```
    nH = nH - 1;
```
```
    return p;
```
```
}
```
```
/*
```
```
 * Consolidate Node in Fibonnaci Heap
```
```
 */
```

int FibonacciHeap::Consolidate(node* H1)

```
{
```
```
    int d, i;
```
```
    float f = (log(nH)) / (log(2));
```
```
    int D = f;
```
```
    node* A[D];
```
```
    for (i = 0; i <= D; i++)
```
```
        A[i] = NULL;
```
```
    node* x = H1;
```
```
    node* y;
```
```
    node* np;
```
```
    node* pt = x;
```
```
    do
```
```
    {
```
```
        pt = pt->right;
```
```
        d = x->degree;
```
```
        while (A[d] != NULL)
```
```
        {
```
```
            y = A[d];
```
```
            if (x->n > y->n)
```
```
            {
```
```
                np = x;
```
```
                x = y;
```
```
                y = np;
```
```
            }
```
```
            if (y == H1)
```
```
                H1 = x;
```
```
            Fibonnaci_link(H1, y, x);
```
```
            if (x->right == x)
```
```
                H1 = x;
```
```
                A[d] = NULL;
```
```
            d = d + 1;
```
```
        }
```
```
        A[d] = x;
```
```
        x = x->right;
```
```
    }
```
```
    while (x != H1);
```
```
    H = NULL;
```
```
    for (int j = 0; j <= D; j++)
```
```
    {
```
```
        if (A[j] != NULL)
```
```
        {
```
```
            A[j]->left = A[j];
```
```
            A[j]->right =A[j];
```
```
            if (H != NULL)
```
```
            {
```

                (H->left)->right = A[j];

```
                A[j]->right = H;
```
```
                A[j]->left = H->left;
```
```
                H->left = A[j];
```
```
                if (A[j]->n < H->n)
```
```
                H = A[j];
```
```
            }
```
```
            else
```
```
            {
```
```
                H = A[j];
```
```
            }
```
```
            if(H == NULL)
```
```
                H = A[j];
```
```
            else if (A[j]->n < H->n)
```
```
                H = A[j];
```
```
        }
```
```
    }
```
```
}
```
```
 
```
```
/*
```

 * Decrease key of Nodes in Fibonnaci Heap

```
 */
```

int FibonacciHeap::Decrease_key(node*H1, int x, int k)

```
{
```
```
    node* y;
```
```
    if (H1 == NULL)
```
```
    {
```

        cout<<"The Heap is Empty"<<endl;

```
        return 0;
```
```
    }
```
```
    node* ptr = Find(H1, x);
```
```
    if (ptr == NULL)
```
```
    {
```

        cout<<"Node not found in the Heap"<<endl;

```
        return 1;
```
```
    }
```
```
    if (ptr->n < k)
```
```
    {
```

        cout<<"Entered key greater than current key"<<endl;

```
        return 0;
```
```
    }
```
```
    ptr->n = k;
```
```
    y = ptr->parent;
```
```
    if (y != NULL && ptr->n < y->n)
```
```
    {
```
```
        Cut(H1, ptr, y);
```
```
        Cascase_cut(H1, y);
```
```
    }
```
```
    if (ptr->n < H->n)
```
```
        H = ptr;
```
```
    return 0;
```
```
}
```
```
/*
```
```
 * Cut Nodes in Fibonnaci Heap
```
```
 */
```

int FibonacciHeap::Cut(node* H1, node* x, node* y)

```
{
```
```
    if (x == x->right)
```
```
        y->child = NULL;
```
```
    (x->left)->right = x->right;
```
```
    (x->right)->left = x->left;
```
```
    if (x == y->child)
```
```
        y->child = x->right;
```
```
    y->degree = y->degree - 1;
```
```
    x->right = x;
```
```
    x->left = x;
```
```
    (H1->left)->right = x;
```
```
    x->right = H1;
```
```
    x->left = H1->left;
```
```
    H1->left = x;
```
```
    x->parent = NULL;
```
```
    x->mark = 'F';
```
```
}
```
```
 
```
```
/*
```
```
 * Cascade Cutting in Fibonnaci Heap
```
```
 */
```

int FibonacciHeap::Cascase_cut(node* H1, node* y)

```
{
```
```
    node* z = y->parent;
```
```
    if (z != NULL)
```
```
    {
```
```
        if (y->mark == 'F')
```
```
        {
```
```
            y->mark = 'T';
```
```
	}
```
```
        else
```
```
        {
```
```
            Cut(H1, y, z);
```
```
            Cascase_cut(H1, z);
```
```
        }
```
```
    }
```
```
}
```
```
 
```
```
/*
```
```
 * Find Nodes in Fibonnaci Heap
```
```
 */
```

node* FibonacciHeap::Find(node* H, int k)

```
{
```
```
    node* x = H;
```
```
    x->C = 'Y';
```
```
    node* p = NULL;
```
```
    if (x->n == k)
```
```
    {
```
```
        p = x;
```
```
        x->C = 'N';
```
```
        return p;
```
```
    }
```
```
    if (p == NULL)
```
```
    {
```
```
        if (x->child != NULL )
```
```
            p = Find(x->child, k);
```
```
        if ((x->right)->C != 'Y' )
```
```
            p = Find(x->right, k);
```
```
    }
```
```
    x->C = 'N';
```
```
    return p;
```
```
}
```
```
/*
```
```
 * Delete Nodes in Fibonnaci Heap
```
```
 */
```

int FibonacciHeap::Delete_key(node* H1, int k)

```
{
```
```
    node* np = NULL;
```
```
    int t;
```
```
    t = Decrease_key(H1, k, -5000);
```
```
    if (!t)
```
```
        np = Extract_Min(H);
```
```
    if (np != NULL)
```
```
        cout<<"Key Deleted"<<endl;
```
```
    else
```
```
        cout<<"Key not Deleted"<<endl;
```
```
    return 0;
```
```
}
```
```
/*
```
```
 * Main Contains Menu
```
```
 */
```
```
int main()
```
```
{
```
```
    int n, m, l;
```
```
    FibonacciHeap fh;
```
```
    node* p;
```
```
    node* H;
```
```
    H = fh.InitializeHeap();
```
```
    while (1)
```
```
    {
```

        cout<<"----------------------------"<<endl;

        cout<<"Operations on Binomial heap"<<endl;

        cout<<"----------------------------"<<endl;

        cout<<"1)Insert Element in the heap"<<endl;

        cout<<"2)Extract Minimum key node"<<endl;

        cout<<"3)Decrease key of a node"<<endl;

```
        cout<<"4)Delete a node"<<endl;
```
```
        cout<<"5)Display Heap"<<endl;
```
```
        cout<<"6)Exit"<<endl;
```
```
        cout<<"Enter Your Choice: ";
```
```
        cin>>l;
```
```
        switch(l)
```
```
        {
```
```
        case 1:
```

            cout<<"Enter the element to be inserted: ";

```
            cin>>m;
```
```
            p = fh.Create_node(m);
```
```
            H = fh.Insert(H, p);
```
```
            break;
```
```
        case 2:
```
```
            p = fh.Extract_Min(H);
```
```
            if (p != NULL)
```

                cout<<"The node with minimum key: "<<p->n<<endl;

```
            else
```

                cout<<"Heap is empty"<<endl;

```
            break;
```
```
        case 3:
```

            cout<<"Enter the key to be decreased: ";

```
            cin>>m;
```

            cout<<"Enter new key value: ";

```
            cin>>l;
```
```
            fh.Decrease_key(H, m, l);
```
```
            break;
```
```
        case 4:
```

            cout<<"Enter the key to be deleted: ";

```
            cin>>m;
```
```
            fh.Delete_key(H, m);
```
```
            break;
```
```
        case 5:
```

            cout<<"The Heap is: "<<endl;

```
            fh.Display(H);
```
```
            break;
```
```
        case 6:
```
```
            exit(1);
```
```
        default:
```
```
            cout<<"Wrong Choice"<<endl;
```
```
        }
```
```
    }
```
```
    return 0;
```
```
}
```

$ g++ fibonnaciheap.cpp
$ a.out
----------------------------
Operations on Binomial heap
----------------------------
1)Insert Element in the heap
2)Extract Minimum key node
3)Decrease key of a node
4)Delete a node
5)Display Heap
6)Exit
Enter Your Choice: 1
Enter the element to be inserted: 9
----------------------------
Operations on Binomial heap
----------------------------
1)Insert Element in the heap
2)Extract Minimum key node
3)Decrease key of a node
4)Delete a node
5)Display Heap
6)Exit
Enter Your Choice: 1
Enter the element to be inserted: 8
----------------------------
Operations on Binomial heap
----------------------------
1)Insert Element in the heap
2)Extract Minimum key node
3)Decrease key of a node
4)Delete a node
5)Display Heap
6)Exit
Enter Your Choice: 1
Enter the element to be inserted: 7
----------------------------
Operations on Binomial heap
----------------------------
1)Insert Element in the heap
2)Extract Minimum key node
3)Decrease key of a node
4)Delete a node
5)Display Heap
6)Exit
Enter Your Choice: 1
Enter the element to be inserted: 6
----------------------------
Operations on Binomial heap
----------------------------
1)Insert Element in the heap
2)Extract Minimum key node
3)Decrease key of a node
4)Delete a node
5)Display Heap
6)Exit
Enter Your Choice: 1
Enter the element to be inserted: 5
----------------------------
Operations on Binomial heap
----------------------------
1)Insert Element in the heap
2)Extract Minimum key node
3)Decrease key of a node
4)Delete a node
5)Display Heap
6)Exit
Enter Your Choice: 5
The Heap is: 
The root nodes of Heap are: 
5-->6-->7-->8-->9
----------------------------
Operations on Binomial heap
----------------------------
1)Insert Element in the heap
2)Extract Minimum key node
3)Decrease key of a node
4)Delete a node
5)Display Heap
6)Exit
Enter Your Choice: 2
The node with minimum key: 5
----------------------------
Operations on Binomial heap
----------------------------
1)Insert Element in the heap
2)Extract Minimum key node
3)Decrease key of a node
4)Delete a node
5)Display Heap
6)Exit
Enter Your Choice: 3
Enter the key to be decreased: 3
Enter new key value: 1
Node not found in the Heap
----------------------------
Operations on Binomial heap
----------------------------
1)Insert Element in the heap
2)Extract Minimum key node
3)Decrease key of a node
4)Delete a node
5)Display Heap
6)Exit
Enter Your Choice: 3
Enter the key to be decreased: 5
Enter new key value: 2
----------------------------
Operations on Binomial heap
----------------------------
1)Insert Element in the heap
2)Extract Minimum key node
3)Decrease key of a node
4)Delete a node
5)Display Heap
6)Exit
Enter Your Choice: 2
The node with minimum key: 2
----------------------------
Operations on Binomial heap
----------------------------
1)Insert Element in the heap
2)Extract Minimum key node
3)Decrease key of a node
4)Delete a node
5)Display Heap
6)Exit
Enter Your Choice: 6
 
 
------------------
(program exited with code: 1)
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