Fibonacci Heap

# Fibonacci Heap in python

import math

# Creating fibonacci tree
class FibonacciTree:
    def __init__(self, value):
        self.value = value
        self.child = []
        self.order = 0

    # Adding tree at the end of the tree
    def add_at_end(self, t):
        self.child.append(t)
        self.order = self.order + 1


# Creating Fibonacci heap
class FibonacciHeap:
    def __init__(self):
        self.trees = []
        self.least = None
        self.count = 0

    # Insert a node
    def insert_node(self, value):
        new_tree = FibonacciTree(value)
        self.trees.append(new_tree)
        if (self.least is None or value < self.least.value):
            self.least = new_tree
        self.count = self.count + 1

    # Get minimum value
    def get_min(self):
        if self.least is None:
            return None
        return self.least.value

    # Extract the minimum value
    def extract_min(self):
        smallest = self.least
        if smallest is not None:
            for child in smallest.child:
                self.trees.append(child)
            self.trees.remove(smallest)
            if self.trees == []:
                self.least = None
            else:
                self.least = self.trees[0]
                self.consolidate()
            self.count = self.count - 1
            return smallest.value

    # Consolidate the tree
    def consolidate(self):
        aux = (floor_log(self.count) + 1) * [None]

        while self.trees != []:
            x = self.trees[0]
            order = x.order
            self.trees.remove(x)
            while aux[order] is not None:
                y = aux[order]
                if x.value > y.value:
                    x, y = y, x
                x.add_at_end(y)
                aux[order] = None
                order = order + 1
            aux[order] = x

        self.least = None
        for k in aux:
            if k is not None:
                self.trees.append(k)
                if (self.least is None
                        or k.value < self.least.value):
                    self.least = k


def floor_log(x):
    return math.frexp(x)[1] - 1


fibonacci_heap = FibonacciHeap()

fibonacci_heap.insert_node(7)
fibonacci_heap.insert_node(3)
fibonacci_heap.insert_node(17)
fibonacci_heap.insert_node(24)

print('the minimum value of the fibonacci heap: {}'.format(fibonacci_heap.get_min()))

print('the minimum value removed: {}'.format(fibonacci_heap.extract_min()))

// Operations on Fibonacci Heap in Java

// Node creation
class node {
  node parent;
  node left;
  node right;
  node child;
  int degree;
  boolean mark;
  int key;

  public node() {
    this.degree = 0;
    this.mark = false;
    this.parent = null;
    this.left = this;
    this.right = this;
    this.child = null;
    this.key = Integer.MAX_VALUE;
  }

  node(int x) {
    this();
    this.key = x;
  }

  void set_parent(node x) {
    this.parent = x;
  }

  node get_parent() {
    return this.parent;
  }

  void set_left(node x) {
    this.left = x;
  }

  node get_left() {
    return this.left;
  }

  void set_right(node x) {
    this.right = x;
  }

  node get_right() {
    return this.right;
  }

  void set_child(node x) {
    this.child = x;
  }

  node get_child() {
    return this.child;
  }

  void set_degree(int x) {
    this.degree = x;
  }

  int get_degree() {
    return this.degree;
  }

  void set_mark(boolean m) {
    this.mark = m;
  }

  boolean get_mark() {
    return this.mark;
  }

  void set_key(int x) {
    this.key = x;
  }

  int get_key() {
    return this.key;
  }
}

public class fibHeap {
  node min;
  int n;
  boolean trace;
  node found;

  public boolean get_trace() {
    return trace;
  }

  public void set_trace(boolean t) {
    this.trace = t;
  }

  public static fibHeap create_heap() {
    return new fibHeap();
  }

  fibHeap() {
    min = null;
    n = 0;
    trace = false;
  }

  private void insert(node x) {
    if (min == null) {
      min = x;
      x.set_left(min);
      x.set_right(min);
    } else {
      x.set_right(min);
      x.set_left(min.get_left());
      min.get_left().set_right(x);
      min.set_left(x);
      if (x.get_key() < min.get_key())
        min = x;
    }
    n += 1;
  }

  public void insert(int key) {
    insert(new node(key));
  }

  public void display() {
    display(min);
    System.out.println();
  }

  private void display(node c) {
    System.out.print("(");
    if (c == null) {
      System.out.print(")");
      return;
    } else {
      node temp = c;
      do {
        System.out.print(temp.get_key());
        node k = temp.get_child();
        display(k);
        System.out.print("->");
        temp = temp.get_right();
      } while (temp != c);
      System.out.print(")");
    }
  }

  public static void merge_heap(fibHeap H1, fibHeap H2, fibHeap H3) {
    H3.min = H1.min;

    if (H1.min != null && H2.min != null) {
      node t1 = H1.min.get_left();
      node t2 = H2.min.get_left();
      H1.min.set_left(t2);
      t1.set_right(H2.min);
      H2.min.set_left(t1);
      t2.set_right(H1.min);
    }
    if (H1.min == null || (H2.min != null && H2.min.get_key() < H1.min.get_key()))
      H3.min = H2.min;
    H3.n = H1.n + H2.n;
  }

  public int find_min() {
    return this.min.get_key();
  }

  private void display_node(node z) {
    System.out.println("right: " + ((z.get_right() == null) ? "-1" : z.get_right().get_key()));
    System.out.println("left: " + ((z.get_left() == null) ? "-1" : z.get_left().get_key()));
    System.out.println("child: " + ((z.get_child() == null) ? "-1" : z.get_child().get_key()));
    System.out.println("degree " + z.get_degree());
  }

  public int extract_min() {
    node z = this.min;
    if (z != null) {
      node c = z.get_child();
      node k = c, p;
      if (c != null) {
        do {
          p = c.get_right();
          insert(c);
          c.set_parent(null);
          c = p;
        } while (c != null && c != k);
      }
      z.get_left().set_right(z.get_right());
      z.get_right().set_left(z.get_left());
      z.set_child(null);
      if (z == z.get_right())
        this.min = null;
      else {
        this.min = z.get_right();
        this.consolidate();
      }
      this.n -= 1;
      return z.get_key();
    }
    return Integer.MAX_VALUE;
  }

  public void consolidate() {
    double phi = (1 + Math.sqrt(5)) / 2;
    int Dofn = (int) (Math.log(this.n) / Math.log(phi));
    node[] A = new node[Dofn + 1];
    for (int i = 0; i <= Dofn; ++i)
      A[i] = null;
    node w = min;
    if (w != null) {
      node check = min;
      do {
        node x = w;
        int d = x.get_degree();
        while (A[d] != null) {
          node y = A[d];
          if (x.get_key() > y.get_key()) {
            node temp = x;
            x = y;
            y = temp;
            w = x;
          }
          fib_heap_link(y, x);
          check = x;
          A[d] = null;
          d += 1;
        }
        A[d] = x;
        w = w.get_right();
      } while (w != null && w != check);
      this.min = null;
      for (int i = 0; i <= Dofn; ++i) {
        if (A[i] != null) {
          insert(A[i]);
        }
      }
    }
  }

  // Linking operation
  private void fib_heap_link(node y, node x) {
    y.get_left().set_right(y.get_right());
    y.get_right().set_left(y.get_left());

    node p = x.get_child();
    if (p == null) {
      y.set_right(y);
      y.set_left(y);
    } else {
      y.set_right(p);
      y.set_left(p.get_left());
      p.get_left().set_right(y);
      p.set_left(y);
    }
    y.set_parent(x);
    x.set_child(y);
    x.set_degree(x.get_degree() + 1);
    y.set_mark(false);
  }

  // Search operation
  private void find(int key, node c) {
    if (found != null || c == null)
      return;
    else {
      node temp = c;
      do {
        if (key == temp.get_key())
          found = temp;
        else {
          node k = temp.get_child();
          find(key, k);
          temp = temp.get_right();
        }
      } while (temp != c && found == null);
    }
  }

  public node find(int k) {
    found = null;
    find(k, this.min);
    return found;
  }

  public void decrease_key(int key, int nval) {
    node x = find(key);
    decrease_key(x, nval);
  }

  // Decrease key operation
  private void decrease_key(node x, int k) {
    if (k > x.get_key())
      return;
    x.set_key(k);
    node y = x.get_parent();
    if (y != null && x.get_key() < y.get_key()) {
      cut(x, y);
      cascading_cut(y);
    }
    if (x.get_key() < min.get_key())
      min = x;
  }

  // Cut operation
  private void cut(node x, node y) {
    x.get_right().set_left(x.get_left());
    x.get_left().set_right(x.get_right());

    y.set_degree(y.get_degree() - 1);

    x.set_right(null);
    x.set_left(null);
    insert(x);
    x.set_parent(null);
    x.set_mark(false);
  }

  private void cascading_cut(node y) {
    node z = y.get_parent();
    if (z != null) {
      if (y.get_mark() == false)
        y.set_mark(true);
      else {
        cut(y, z);
        cascading_cut(z);
      }
    }
  }

  // Delete operations
  public void delete(node x) {
    decrease_key(x, Integer.MIN_VALUE);
    int p = extract_min();
  }

  public static void main(String[] args) {
    fibHeap obj = create_heap();
    obj.insert(7);
    obj.insert(26);
    obj.insert(30);
    obj.insert(39);
    obj.insert(10);
    obj.display();

    System.out.println(obj.extract_min());
    obj.display();
    System.out.println(obj.extract_min());
    obj.display();
    System.out.println(obj.extract_min());
    obj.display();
    System.out.println(obj.extract_min());
    obj.display();
    System.out.println(obj.extract_min());
    obj.display();
  }
}

// Operations on a Fibonacci heap in C

#include <math.h>
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>

typedef struct _NODE {
  int key;
  int degree;
  struct _NODE *left_sibling;
  struct _NODE *right_sibling;
  struct _NODE *parent;
  struct _NODE *child;
  bool mark;
  bool visited;
} NODE;

typedef struct fibanocci_heap {
  int n;
  NODE *min;
  int phi;
  int degree;
} FIB_HEAP;

FIB_HEAP *make_fib_heap();
void insertion(FIB_HEAP *H, NODE *new, int val);
NODE *extract_min(FIB_HEAP *H);
void consolidate(FIB_HEAP *H);
void fib_heap_link(FIB_HEAP *H, NODE *y, NODE *x);
NODE *find_min_node(FIB_HEAP *H);
void decrease_key(FIB_HEAP *H, NODE *node, int key);
void cut(FIB_HEAP *H, NODE *node_to_be_decrease, NODE *parent_node);
void cascading_cut(FIB_HEAP *H, NODE *parent_node);
void Delete_Node(FIB_HEAP *H, int dec_key);

FIB_HEAP *make_fib_heap() {
  FIB_HEAP *H;
  H = (FIB_HEAP *)malloc(sizeof(FIB_HEAP));
  H->n = 0;
  H->min = NULL;
  H->phi = 0;
  H->degree = 0;
  return H;
}

// Printing the heap
void print_heap(NODE *n) {
  NODE *x;
  for (x = n;; x = x->right_sibling) {
    if (x->child == NULL) {
      printf("node with no child (%d) \n", x->key);
    } else {
      printf("NODE(%d) with child (%d)\n", x->key, x->child->key);
      print_heap(x->child);
    }
    if (x->right_sibling == n) {
      break;
    }
  }
}

// Inserting nodes
void insertion(FIB_HEAP *H, NODE *new, int val) {
  new = (NODE *)malloc(sizeof(NODE));
  new->key = val;
  new->degree = 0;
  new->mark = false;
  new->parent = NULL;
  new->child = NULL;
  new->visited = false;
  new->left_sibling = new;
  new->right_sibling = new;
  if (H->min == NULL) {
    H->min = new;
  } else {
    H->min->left_sibling->right_sibling = new;
    new->right_sibling = H->min;
    new->left_sibling = H->min->left_sibling;
    H->min->left_sibling = new;
    if (new->key < H->min->key) {
      H->min = new;
    }
  }
  (H->n)++;
}

// Find min node
NODE *find_min_node(FIB_HEAP *H) {
  if (H == NULL) {
    printf(" \n Fibonacci heap not yet created \n");
    return NULL;
  } else
    return H->min;
}

// Union operation
FIB_HEAP *unionHeap(FIB_HEAP *H1, FIB_HEAP *H2) {
  FIB_HEAP *Hnew;
  Hnew = make_fib_heap();
  Hnew->min = H1->min;

  NODE *temp1, *temp2;
  temp1 = Hnew->min->right_sibling;
  temp2 = H2->min->left_sibling;

  Hnew->min->right_sibling->left_sibling = H2->min->left_sibling;
  Hnew->min->right_sibling = H2->min;
  H2->min->left_sibling = Hnew->min;
  temp2->right_sibling = temp1;

  if ((H1->min == NULL) || (H2->min != NULL && H2->min->key < H1->min->key))
    Hnew->min = H2->min;
  Hnew->n = H1->n + H2->n;
  return Hnew;
}

// Calculate the degree
int cal_degree(int n) {
  int count = 0;
  while (n > 0) {
    n = n / 2;
    count++;
  }
  return count;
}

// Consolidate function
void consolidate(FIB_HEAP *H) {
  int degree, i, d;
  degree = cal_degree(H->n);
  NODE *A[degree], *x, *y, *z;
  for (i = 0; i <= degree; i++) {
    A[i] = NULL;
  }
  x = H->min;
  do {
    d = x->degree;
    while (A[d] != NULL) {
      y = A[d];
      if (x->key > y->key) {
        NODE *exchange_help;
        exchange_help = x;
        x = y;
        y = exchange_help;
      }
      if (y == H->min)
        H->min = x;
      fib_heap_link(H, y, x);
      if (y->right_sibling == x)
        H->min = x;
      A[d] = NULL;
      d++;
    }
    A[d] = x;
    x = x->right_sibling;
  } while (x != H->min);

  H->min = NULL;
  for (i = 0; i < degree; i++) {
    if (A[i] != NULL) {
      A[i]->left_sibling = A[i];
      A[i]->right_sibling = A[i];
      if (H->min == NULL) {
        H->min = A[i];
      } else {
        H->min->left_sibling->right_sibling = A[i];
        A[i]->right_sibling = H->min;
        A[i]->left_sibling = H->min->left_sibling;
        H->min->left_sibling = A[i];
        if (A[i]->key < H->min->key) {
          H->min = A[i];
        }
      }
      if (H->min == NULL) {
        H->min = A[i];
      } else if (A[i]->key < H->min->key) {
        H->min = A[i];
      }
    }
  }
}

// Linking
void fib_heap_link(FIB_HEAP *H, NODE *y, NODE *x) {
  y->right_sibling->left_sibling = y->left_sibling;
  y->left_sibling->right_sibling = y->right_sibling;

  if (x->right_sibling == x)
    H->min = x;

  y->left_sibling = y;
  y->right_sibling = y;
  y->parent = x;

  if (x->child == NULL) {
    x->child = y;
  }
  y->right_sibling = x->child;
  y->left_sibling = x->child->left_sibling;
  x->child->left_sibling->right_sibling = y;
  x->child->left_sibling = y;
  if ((y->key) < (x->child->key))
    x->child = y;

  (x->degree)++;
}

// Extract min
NODE *extract_min(FIB_HEAP *H) {
  if (H->min == NULL)
    printf("\n The heap is empty");
  else {
    NODE *temp = H->min;
    NODE *pntr;
    pntr = temp;
    NODE *x = NULL;
    if (temp->child != NULL) {
      x = temp->child;
      do {
        pntr = x->right_sibling;
        (H->min->left_sibling)->right_sibling = x;
        x->right_sibling = H->min;
        x->left_sibling = H->min->left_sibling;
        H->min->left_sibling = x;
        if (x->key < H->min->key)
          H->min = x;
        x->parent = NULL;
        x = pntr;
      } while (pntr != temp->child);
    }

    (temp->left_sibling)->right_sibling = temp->right_sibling;
    (temp->right_sibling)->left_sibling = temp->left_sibling;
    H->min = temp->right_sibling;

    if (temp == temp->right_sibling && temp->child == NULL)
      H->min = NULL;
    else {
      H->min = temp->right_sibling;
      consolidate(H);
    }
    H->n = H->n - 1;
    return temp;
  }
  return H->min;
}

void cut(FIB_HEAP *H, NODE *node_to_be_decrease, NODE *parent_node) {
  NODE *temp_parent_check;

  if (node_to_be_decrease == node_to_be_decrease->right_sibling)
    parent_node->child = NULL;

  node_to_be_decrease->left_sibling->right_sibling = node_to_be_decrease->right_sibling;
  node_to_be_decrease->right_sibling->left_sibling = node_to_be_decrease->left_sibling;
  if (node_to_be_decrease == parent_node->child)
    parent_node->child = node_to_be_decrease->right_sibling;
  (parent_node->degree)--;

  node_to_be_decrease->left_sibling = node_to_be_decrease;
  node_to_be_decrease->right_sibling = node_to_be_decrease;
  H->min->left_sibling->right_sibling = node_to_be_decrease;
  node_to_be_decrease->right_sibling = H->min;
  node_to_be_decrease->left_sibling = H->min->left_sibling;
  H->min->left_sibling = node_to_be_decrease;

  node_to_be_decrease->parent = NULL;
  node_to_be_decrease->mark = false;
}

void cascading_cut(FIB_HEAP *H, NODE *parent_node) {
  NODE *aux;
  aux = parent_node->parent;
  if (aux != NULL) {
    if (parent_node->mark == false) {
      parent_node->mark = true;
    } else {
      cut(H, parent_node, aux);
      cascading_cut(H, aux);
    }
  }
}

void decrease_key(FIB_HEAP *H, NODE *node_to_be_decrease, int new_key) {
  NODE *parent_node;
  if (H == NULL) {
    printf("\n FIbonacci heap not created ");
    return;
  }
  if (node_to_be_decrease == NULL) {
    printf("Node is not in the heap");
  }

  else {
    if (node_to_be_decrease->key < new_key) {
      printf("\n Invalid new key for decrease key operation \n ");
    } else {
      node_to_be_decrease->key = new_key;
      parent_node = node_to_be_decrease->parent;
      if ((parent_node != NULL) && (node_to_be_decrease->key < parent_node->key)) {
        printf("\n cut called");
        cut(H, node_to_be_decrease, parent_node);
        printf("\n cascading cut called");
        cascading_cut(H, parent_node);
      }
      if (node_to_be_decrease->key < H->min->key) {
        H->min = node_to_be_decrease;
      }
    }
  }
}

void *find_node(FIB_HEAP *H, NODE *n, int key, int new_key) {
  NODE *find_use = n;
  NODE *f = NULL;
  find_use->visited = true;
  if (find_use->key == key) {
    find_use->visited = false;
    f = find_use;
    decrease_key(H, f, new_key);
  }
  if (find_use->child != NULL) {
    find_node(H, find_use->child, key, new_key);
  }
  if ((find_use->right_sibling->visited != true)) {
    find_node(H, find_use->right_sibling, key, new_key);
  }

  find_use->visited = false;
}

FIB_HEAP *insertion_procedure() {
  FIB_HEAP *temp;
  int no_of_nodes, ele, i;
  NODE *new_node;
  temp = (FIB_HEAP *)malloc(sizeof(FIB_HEAP));
  temp = NULL;
  if (temp == NULL) {
    temp = make_fib_heap();
  }
  printf(" \n enter number of nodes to be insert = ");
  scanf("%d", &no_of_nodes);
  for (i = 1; i <= no_of_nodes; i++) {
    printf("\n node %d and its key value = ", i);
    scanf("%d", &ele);
    insertion(temp, new_node, ele);
  }
  return temp;
}
void Delete_Node(FIB_HEAP *H, int dec_key) {
  NODE *p = NULL;
  find_node(H, H->min, dec_key, -5000);
  p = extract_min(H);
  if (p != NULL)
    printf("\n Node deleted");
  else
    printf("\n Node not deleted:some error");
}

int main(int argc, char **argv) {
  NODE *new_node, *min_node, *extracted_min, *node_to_be_decrease, *find_use;
  FIB_HEAP *heap, *h1, *h2;
  int operation_no, new_key, dec_key, ele, i, no_of_nodes;
  heap = (FIB_HEAP *)malloc(sizeof(FIB_HEAP));
  heap = NULL;
  while (1) {
    printf(" \n Operations \n 1. Create Fibonacci heap \n 2. Insert nodes into fibonacci heap \n 3. Find min \n 4. Union \n 5. Extract min \n 6. Decrease key \n 7.Delete node \n 8. print heap \n 9. exit \n enter operation_no = ");
    scanf("%d", &operation_no);

    switch (operation_no) {
      case 1:
        heap = make_fib_heap();
        break;

      case 2:
        if (heap == NULL) {
          heap = make_fib_heap();
        }
        printf(" enter number of nodes to be insert = ");
        scanf("%d", &no_of_nodes);
        for (i = 1; i <= no_of_nodes; i++) {
          printf("\n node %d and its key value = ", i);
          scanf("%d", &ele);
          insertion(heap, new_node, ele);
        }
        break;

      case 3:
        min_node = find_min_node(heap);
        if (min_node == NULL)
          printf("No minimum value");
        else
          printf("\n min value = %d", min_node->key);
        break;

      case 4:
        if (heap == NULL) {
          printf("\n no FIbonacci heap created \n ");
          break;
        }
        h1 = insertion_procedure();
        heap = unionHeap(heap, h1);
        printf("Unified Heap:\n");
        print_heap(heap->min);
        break;

      case 5:
        if (heap == NULL)
          printf("Empty Fibonacci heap");
        else {
          extracted_min = extract_min(heap);
          printf("\n min value = %d", extracted_min->key);
          printf("\n Updated heap: \n");
          print_heap(heap->min);
        }
        break;

      case 6:
        if (heap == NULL)
          printf("Fibonacci heap is empty");
        else {
          printf(" \n node to be decreased = ");
          scanf("%d", &dec_key);
          printf(" \n enter the new key = ");
          scanf("%d", &new_key);
          find_use = heap->min;
          find_node(heap, find_use, dec_key, new_key);
          printf("\n Key decreased- Corresponding heap:\n");
          print_heap(heap->min);
        }
        break;
      case 7:
        if (heap == NULL)
          printf("Fibonacci heap is empty");
        else {
          printf(" \n Enter node key to be deleted = ");
          scanf("%d", &dec_key);
          Delete_Node(heap, dec_key);
          printf("\n Node Deleted- Corresponding heap:\n");
          print_heap(heap->min);
          break;
        }
      case 8:
        print_heap(heap->min);
        break;

      case 9:
        free(new_node);
        free(heap);
        exit(0);

      default:
        printf("Invalid choice ");
    }
  }
}

// Operations on a Fibonacci heap in C++

#include <cmath>
#include <cstdlib>
#include <iostream>

using namespace std;

// Node creation
struct node {
  int n;
  int degree;
  node *parent;
  node *child;
  node *left;
  node *right;
  char mark;

  char C;
};

// Implementation of Fibonacci heap
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;
}

// Create linking
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 Operation
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 the heap
int FibonacciHeap::Display(node *H) {
  node *p = H;
  if (p == NULL) {
    cout << "Empty Heap" << endl;
    return 0;
  }
  cout << "Root Nodes: " << endl;

  do {
    cout << p->n;
    p = p->right;
    if (p != H) {
      cout << "-->";
    }
  } while (p != H && p->right != NULL);
  cout << endl;
}

// Extract min
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;
}

// Consolidation Function
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 Operation
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;
}

// Cutting Function
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 cut
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);
    }
  }
}

// Search function
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;
}

// Deleting key
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;
}

int main() {
  int n, m, l;
  FibonacciHeap fh;
  node *p;
  node *H;
  H = fh.InitializeHeap();

  p = fh.Create_node(7);
  H = fh.Insert(H, p);
  p = fh.Create_node(3);
  H = fh.Insert(H, p);
  p = fh.Create_node(17);
  H = fh.Insert(H, p);
  p = fh.Create_node(24);
  H = fh.Insert(H, p);

  fh.Display(H);

  p = fh.Extract_Min(H);
  if (p != NULL)
    cout << "The node with minimum key: " << p->n << endl;
  else
    cout << "Heap is empty" << endl;

  m = 26;
  l = 16;
  fh.Decrease_key(H, m, l);

  m = 16;
  fh.Delete_key(H, m);
}