diff --git a/data_structures/heap/fibonacci_heap.py b/data_structures/heap/fibonacci_heap.py
index 79ed58ec5..68ad764be 100644
--- a/data_structures/heap/fibonacci_heap.py
+++ b/data_structures/heap/fibonacci_heap.py
@@ -1,357 +1,178 @@
-"""
-Fibonacci Heap
-A more efficient priority queue implementation that provides amortized time bounds
-that are better than those of the binary and binomial heaps.
-reference: https://en.wikipedia.org/wiki/Fibonacci_heap
+import math
 
-Operations supported:
-- Insert: O(1) amortized
-- Find minimum: O(1)
-- Delete minimum: O(log n) amortized
-- Decrease key: O(1) amortized
-- Merge: O(1)
-"""
 
-class Node:
-    """
-    A node in a Fibonacci heap.
-
-    Args:
-        val: The value stored in the node.
-
-    Attributes:
-        val: The value stored in the node.
-        parent: Reference to parent node.
-        child: Reference to one child node.
-        left: Reference to left sibling.
-        right: Reference to right sibling.
-        degree: Number of children.
-        mark: Boolean indicating if node has lost a child.
-    """
-    def __init__(self, val):
-        self.val = val
+class FibonacciHeapNode:
+    def __init__(self, key, value=None):
+        self.key = key
+        self.value = value
+        self.degree = 0
         self.parent = None
         self.child = None
-        self.left = self
-        self.right = self
-        self.degree = 0
         self.mark = False
-
-    def add_sibling(self, node):
-        """
-        Adds a node as a sibling to the current node.
-
-        Args:
-            node: The node to add as a sibling.
-        """
-        node.left = self
-        node.right = self.right
-        self.right.left = node
-        self.right = node
+        self.next = self
+        self.prev = self
 
     def add_child(self, node):
-        """
-        Adds a node as a child of the current node.
-
-        Args:
-            node: The node to add as a child.
-        """
-        node.parent = self
         if not self.child:
             self.child = node
         else:
-            self.child.add_sibling(node)
+            node.prev = self.child
+            node.next = self.child.next
+            self.child.next.prev = node
+            self.child.next = node
+        node.parent = self
         self.degree += 1
 
-    def remove(self):
-        """Removes this node from its sibling list."""
-        self.left.right = self.right
-        self.right.left = self.left
+    def remove_child(self, node):
+        if node.next == node:  # Single child
+            self.child = None
+        elif self.child == node:
+            self.child = node.next
+        node.prev.next = node.next
+        node.next.prev = node.prev
+        node.parent = None
+        self.degree -= 1
 
 
 class FibonacciHeap:
-    """
-    A Fibonacci heap implementation providing
-    amortized efficient priority queue operations.
-
-    This implementation provides the following time complexities:
-        - Insert: O(1) amortized
-        - Find minimum: O(1)
-        - Delete minimum: O(log n) amortized
-        - Decrease key: O(1) amortized
-        - Merge: O(1)
-
-    Example:
-    >>> heap = FibonacciHeap()
-    >>> node1 = heap.insert(3)
-    >>> node2 = heap.insert(2)
-    >>> node3 = heap.insert(15)
-    >>> heap.peek()
-    2
-    >>> heap.delete_min()
-    2
-    >>> heap.peek()
-    3
-    >>> other_heap = FibonacciHeap()
-    >>> node4 = other_heap.insert(1)
-    >>> heap.merge_heaps(other_heap)
-    >>> heap.peek()
-    1
-    """
-
     def __init__(self):
-        """Initializes an empty Fibonacci heap."""
         self.min_node = None
-        self.size = 0
+        self.total_nodes = 0
 
     def is_empty(self):
-        """
-        Checks if the heap is empty.
-
-        Returns:
-            bool: True if heap is empty, False otherwise.
-        """
         return self.min_node is None
 
-    def insert(self, val):
-        """
-        Inserts a new value into the heap.
-
-        Args:
-            val: Value to insert.
-
-        Returns:
-            Node: The newly created node.
-        """
-        node = Node(val)
-        if not self.min_node:
+    def insert(self, key, value=None):
+        node = FibonacciHeapNode(key, value)
+        self._merge_with_root_list(node)
+        if not self.min_node or node.key < self.min_node.key:
             self.min_node = node
-        else:
-            self.min_node.add_sibling(node)
-            if node.val < self.min_node.val:
-                self.min_node = node
-        self.size += 1
+        self.total_nodes += 1
         return node
 
-    def peek(self):
-        """
-        Returns the minimum value without removing it.
+    def find_min(self):
+        return self.min_node
 
-        Returns:
-            The minimum value in the heap.
-
-        Raises:
-            IndexError: If the heap is empty.
-        """
+    def union(self, other_heap):
+        if not other_heap.min_node:
+            return self
         if not self.min_node:
-            raise IndexError("Heap is empty")
-        return self.min_node.val
-
-    def merge_heaps(self, other):
-        """
-        Merges another Fibonacci heap into this one.
-
-        Args:
-            other: Another FibonacciHeap instance to merge with this one.
-        """
-        if not other.min_node:
-            return
-        if not self.min_node:
-            self.min_node = other.min_node
+            self.min_node = other_heap.min_node
         else:
-            # Merge root lists
-            self.min_node.right.left = other.min_node.left
-            other.min_node.left.right = self.min_node.right
-            self.min_node.right = other.min_node
-            other.min_node.left = self.min_node
+            self._merge_with_root_list(other_heap.min_node)
+            if other_heap.min_node.key < self.min_node.key:
+                self.min_node = other_heap.min_node
+        self.total_nodes += other_heap.total_nodes
 
-            if other.min_node.val < self.min_node.val:
-                self.min_node = other.min_node
+    def extract_min(self):
+        z = self.min_node
+        if z:
+            if z.child:
+                children = list(self._iterate(z.child))
+                for child in children:
+                    self._merge_with_root_list(child)
+                    child.parent = None
+            self._remove_from_root_list(z)
+            if z == z.next:
+                self.min_node = None
+            else:
+                self.min_node = z.next
+                self._consolidate()
+            self.total_nodes -= 1
+        return z
 
-        self.size += other.size
+    def decrease_key(self, x, new_key):
+        if new_key > x.key:
+            raise ValueError("New key is greater than current key")
+        x.key = new_key
+        y = x.parent
+        if y and x.key < y.key:
+            self._cut(x, y)
+            self._cascading_cut(y)
+        if x.key < self.min_node.key:
+            self.min_node = x
 
-    def __link_trees(self, node1, node2):
-        """
-        Links two trees of same degree.
+    def delete(self, x):
+        self.decrease_key(x, -math.inf)
+        self.extract_min()
 
-        Args:
-            node1: First tree's root node.
-            node2: Second tree's root node.
-        """
-        node1.remove()
-        if node2.child:
-            node2.child.add_sibling(node1)
-        else:
-            node2.child = node1
-        node1.parent = node2
-        node2.degree += 1
-        node1.mark = False
+    def _cut(self, x, y):
+        y.remove_child(x)
+        self._merge_with_root_list(x)
+        x.mark = False
 
-    def delete_min(self):
-        """
-        Removes and returns the minimum value from the heap.
+    def _cascading_cut(self, y):
+        if z := y.parent:
+            if not y.mark:
+                y.mark = True
+            else:
+                self._cut(y, z)
+                self._cascading_cut(z)
 
-        Returns:
-            The minimum value that was removed.
-
-        Raises:
-            IndexError: If the heap is empty.
-        """
+    def _merge_with_root_list(self, node):
         if not self.min_node:
-            raise IndexError("Heap is empty")
+            self.min_node = node
+        else:
+            node.prev = self.min_node
+            node.next = self.min_node.next
+            self.min_node.next.prev = node
+            self.min_node.next = node
 
-        min_val = self.min_node.val
-
-        # Add all children to root list
-        if self.min_node.child:
-            curr = self.min_node.child
-            while True:
-                next_node = curr.right
-                curr.parent = None
-                curr.mark = False
-                self.min_node.add_sibling(curr)
-                if curr.right == self.min_node.child:
-                    break
-                curr = next_node
-
-        # Remove minimum node
-        if self.min_node.right == self.min_node:
+    def _remove_from_root_list(self, node):
+        if node.next == node:
             self.min_node = None
         else:
-            self.min_node.remove()
-            self.min_node = self.min_node.right
-            self.__consolidate()
+            node.prev.next = node.next
+            node.next.prev = node.prev
 
-        self.size -= 1
-        return min_val
+    def _consolidate(self):
+        array_size = int(math.log(self.total_nodes) * 2) + 1
+        array = [None] * array_size
+        nodes = list(self._iterate(self.min_node))
+        for w in nodes:
+            x = w
+            d = x.degree
+            while array[d]:
+                y = array[d]
+                if x.key > y.key:
+                    x, y = y, x
+                self._link(y, x)
+                array[d] = None
+                d += 1
+            array[d] = x
+        self.min_node = None
+        for i in range(array_size):
+            if array[i]:
+                if not self.min_node:
+                    self.min_node = array[i]
+                else:
+                    self._merge_with_root_list(array[i])
+                    if array[i].key < self.min_node.key:
+                        self.min_node = array[i]
 
-    def __consolidate(self):
-        """
-        Consolidates the trees in the heap after a delete_min operation.
+    def _link(self, y, x):
+        self._remove_from_root_list(y)
+        x.add_child(y)
+        y.mark = False
 
-        This is an internal method that maintains the heap's structure.
-        """
-        max_degree = int(self.size ** 0.5) + 1
-        degree_table = [None] * max_degree
-
-        # Collect all roots
-        roots = []
-        curr = self.min_node
+    def _iterate(self, start):
+        node = start
         while True:
-            roots.append(curr)
-            curr = curr.right
-            if curr == self.min_node:
+            yield node
+            node = node.next
+            if node == start:
                 break
 
-        # Consolidate trees
-        for root in roots:
-            degree = root.degree
-            while degree_table[degree]:
-                other = degree_table[degree]
-                if root.val > other.val:
-                    root, other = other, root
-                self.__link_trees(other, root)
-                degree_table[degree] = None
-                degree += 1
-            degree_table[degree] = root
-
-        # Find new minimum
-        self.min_node = None
-        for degree in range(max_degree):
-            if degree_table[degree]:
-                if not self.min_node:
-                    self.min_node = degree_table[degree]
-                    self.min_node.left = self.min_node
-                    self.min_node.right = self.min_node
-                else:
-                    self.min_node.add_sibling(degree_table[degree])
-                    if degree_table[degree].val < self.min_node.val:
-                        self.min_node = degree_table[degree]
-
-    def decrease_key(self, node, new_val):
-        """
-        Decreases the value of a node.
-
-        Args:
-            node: The node whose value should be decreased.
-            new_val: The new value for the node.
-
-        Raises:
-            ValueError: If new value is greater than current value.
-        """
-        if new_val > node.val:
-            raise ValueError("New value is greater than current value")
-
-        node.val = new_val
-        parent = node.parent
-
-        if parent and node.val < parent.val:
-            self.__cut(node, parent)
-            self.__cascading_cut(parent)
-
-        if node.val < self.min_node.val:
-            self.min_node = node
-
-    def __cut(self, node, parent):
-        """
-        Cuts a node from its parent
-
-        Args:
-            node: Node to be cut.
-            parent: Parent of the node to be cut.
-        """
-
-        parent.degree -= 1
-        if parent.child == node:
-            parent.child = node.right if node.right != node else None
-        node.remove()
-        node.left = node
-        node.right = node
-        node.parent = None
-        node.mark = False
-        self.min_node.add_sibling(node)
-
-    def __cascading_cut(self, node):
-        """
-        Performs cascading cut operation.
-
-        Args:
-            node: Starting node for cascading cut.
-        """
-
-        parent = node.parent
-        if parent:
-            if not node.mark:
-                node.mark = True
-            else:
-                self.__cut(node, parent)
-                self.__cascading_cut(parent)
-
-    def __str__(self):
-        """
-        Returns a string representation of the heap.
-
-        Returns:
-            str: A string showing the heap structure.
-        """
-        if not self.min_node:
-            return "Empty heap"
-
-        def print_tree(node, level=0):
-            result = []
-            curr = node
-            while True:
-                result.append("-" * level + str(curr.val))
-                if curr.child:
-                    result.extend(print_tree(curr.child, level + 1))
-                curr = curr.right
-                if curr == node:
-                    break
-            return result
-
-        return "\n".join(print_tree(self.min_node))
-
 
+# Example usage
 if __name__ == "__main__":
-    import doctest
-    doctest.testmod()
+    fh = FibonacciHeap()
+    n1 = fh.insert(10, "value1")
+    n2 = fh.insert(2, "value2")
+    n3 = fh.insert(15, "value3")
+
+    print("Min:", fh.find_min().key)  # Output: 2
+    fh.decrease_key(n3, 1)
+    print("Min after decrease key:", fh.find_min().key)  # Output: 1
+    fh.extract_min()
+    print("Min after extract:", fh.find_min().key)  # Output: 2