378 lines
16 KiB
Plaintext
378 lines
16 KiB
Plaintext
Gemini Antwort
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Okay, I understand the requirements. Let's break down the problem into smaller, manageable parts before coding. This will help ensure a clear and robust implementation.
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**Sub-Problems:**
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1. **Node Class:** Define the `Node` class with attributes for value, left child, right child, color (red or black), and potentially a parent pointer (useful for some operations).
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2. **Tree Class:** Define the `Tree` class, which will manage the nodes. This includes:
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* **Insertion:** Implement the red-black tree insertion algorithm, including rotations and color flips to maintain balance.
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* **Deletion (Optional):** While not explicitly requested, deletion is a core operation. We can include it if desired, but it adds significant complexity. Let me know if you want to include it.
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* **Search:** Implement a search function to find a node with a given value.
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* **Visualization:** Implement a method to visualize the tree using Matplotlib. This will likely involve traversing the tree and plotting nodes based on their positions.
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3. **Helper Functions:** Create helper functions for rotations (left and right), color flips, and potentially other utility functions to simplify the main algorithms.
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**Reasoning and Assumptions:**
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* **Color Representation:** We'll use strings "red" and "black" for node colors. Alternatively, we could use boolean values (True/False) or enums.
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* **Nil Nodes:** For simplicity, we'll use `None` to represent nil nodes (leaves or empty subtrees). Some implementations use special sentinel nodes.
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* **Visualization Approach:** We'll use a simple approach for visualization, positioning nodes based on their level and order. More sophisticated layouts are possible but add complexity.
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* **No Duplicates:** We'll assume no duplicate values are inserted. Handling duplicates would require modification to the insertion logic.
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* **Parent Pointers (Optional):** Including parent pointers in the `Node` class can simplify some operations (especially deletion) but adds a small overhead. We can include them if you'd like.
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**Potential Ambiguities and Limitations:**
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* **Deletion:** As mentioned, deletion is complex. We can choose to include it or leave it as an extension.
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* **Visualization:** The visualization will be a basic representation. For very large trees, it might become cluttered. Interactive visualizations could be considered for more advanced use cases.
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* **Balancing:** The core complexity of red-black trees lies in maintaining balance after insertions and deletions. The code will focus on correctly implementing the rotations and color flips required for this.
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**Questions before Coding:**
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1. Do you want to include deletion in this implementation?
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2. Is a basic visualization sufficient, or do you have specific visualization requirements?
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3. Are parent pointers in the `Node` class desired?
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Once we clarify these points, I can start writing the code.
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##################################################################################################################
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Okay, I understand. We'll implement insert, delete, and search, and create a dynamic, vertically growing visualization using Matplotlib. The visualization will display node values and colors. We'll also include parent pointers in the `Node` class to simplify some operations.
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Here's a summary of my approach:
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1. **Node Class:** Attributes: `value`, `left`, `right`, `color` ("red" or "black"), and `parent`.
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2. **Tree Class:**
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* `insert(value)`: Standard red-black tree insertion with rotations and color flips.
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* `delete(value)`: Standard red-black tree deletion (the most complex part).
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* `search(value)`: Returns the node with the given value or `None` if not found.
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* `visualize()`: Dynamically generates a plot of the tree. This will involve:
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* Calculating node positions based on level and order. We'll need a way to traverse the tree level by level.
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* Using Matplotlib to draw nodes as circles with appropriate colors and labels (values). The plot will need to adjust its size dynamically as the tree grows.
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3. **Helper Functions:** `rotate_left()`, `rotate_right()`, `flip_colors()`, and potentially others for tree traversal or node manipulation.
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4. **Visualization Details:**
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* Nodes will be drawn as circles.
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* Edges will be lines connecting parent and child nodes.
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* Node color will represent the red-black color.
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* Node labels will display the node's value.
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* The plot will be updated after each insertion or deletion to reflect the changes.
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5. **Testing:** We'll insert some sample values to demonstrate the functionality and visualization.
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This approach addresses the requirements for insert, delete, search, and a dynamic visualization. The deletion operation and dynamic visualization are the most challenging parts, but breaking them down into smaller functions should make them manageable. I'll start with the `Node` and basic `Tree` structure, then move on to insertion, deletion, search, and finally the visualization.
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##################################################################################################################
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```python
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import matplotlib.pyplot as plt
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import networkx as nx
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class Node:
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def __init__(self, value, color="red"):
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self.value = value
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self.left = None
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self.right = None
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self.parent = None
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self.color = color
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class Tree:
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def __init__(self):
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self.root = None
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def insert(self, value):
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new_node = Node(value)
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if self.root is None:
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self.root = new_node
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self.root.color = "black" # Root is always black
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return
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current = self.root
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while True:
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if value < current.value:
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if current.left is None:
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current.left = new_node
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new_node.parent = current
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break
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current = current.left
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elif value > current.value:
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if current.right is None:
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current.right = new_node
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new_node.parent = current
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break
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current = current.right
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else: # Duplicate value (we're assuming no duplicates)
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return
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self._balance_after_insert(new_node)
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self.visualize() # Visualize after each insertion
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def _balance_after_insert(self, node):
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while node.parent is not None and node.parent.color == "red":
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if node.parent == node.parent.parent.left: # Parent is left child
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uncle = node.parent.parent.right
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if uncle is not None and uncle.color == "red": # Case 1: Red uncle
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node.parent.color = "black"
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uncle.color = "black"
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node.parent.parent.color = "red"
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node = node.parent.parent
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else: # Case 2 & 3: Black uncle
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if node == node.parent.right: # Case 2: Node is right child
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node = node.parent
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self._rotate_left(node)
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node.parent.color = "black" # Case 3
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node.parent.parent.color = "red"
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self._rotate_right(node.parent.parent)
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else: # Parent is right child (symmetric cases)
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uncle = node.parent.parent.left
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if uncle is not None and uncle.color == "red":
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node.parent.color = "black"
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uncle.color = "black"
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node.parent.parent.color = "red"
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node = node.parent.parent
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else:
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if node == node.parent.left:
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node = node.parent
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self._rotate_right(node)
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node.parent.color = "black"
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node.parent.parent.color = "red"
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self._rotate_left(node.parent.parent)
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self.root.color = "black" # Root is always black
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def delete(self, value):
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node_to_delete = self._find_node(value)
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if node_to_delete is None:
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return
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# ... (Deletion logic - see next response for implementation due to length)
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def _find_node(self, value):
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current = self.root
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while current is not None:
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if value == current.value:
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return current
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elif value < current.value:
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current = current.left
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else:
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current = current.right
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return None
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def _rotate_left(self, node):
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# ... (Rotation logic - see next response for implementation due to length)
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def _rotate_right(self, node):
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# ... (Rotation logic - see next response for implementation due to length)
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def visualize(self):
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# ... (Visualization logic - see next response for implementation due to length)
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# Example Usage (will be expanded in later responses):
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tree = Tree()
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tree.insert(10)
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tree.insert(5)
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tree.insert(15)
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tree.insert(3)
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tree.insert(7)
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tree.insert(12)
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tree.insert(18)
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plt.show()
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```
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I've started with the `Node` and `Tree` classes, including the `insert` method and the helper function `_balance_after_insert`, which also includes the color flips. I've left placeholders for `delete`, `_rotate_left`, `_rotate_right`, and `visualize` as they are more complex and would make this response too long. I'll provide those in the next responses. Let me know if you have any questions so far.
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################################################################################################################
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```python
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import matplotlib.pyplot as plt
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import networkx as nx
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# ... (Node class from previous response)
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class Tree:
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# ... (insert and _balance_after_insert from previous response)
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def delete(self, value):
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node_to_delete = self._find_node(value)
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if node_to_delete is None:
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return
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if node_to_delete.left is None:
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self._transplant(node_to_delete, node_to_delete.right)
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elif node_to_delete.right is None:
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self._transplant(node_to_delete, node_to_delete.left)
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else:
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successor = self._find_minimum(node_to_delete.right)
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if successor.parent != node_to_delete:
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self._transplant(successor, successor.right)
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successor.right = node_to_delete.right
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successor.right.parent = successor
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self._transplant(node_to_delete, successor)
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successor.left = node_to_delete.left
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successor.left.parent = successor
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successor.color = node_to_delete.color
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if node_to_delete.color == "black":
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self._balance_after_delete(successor) # Pass the successor if it was moved
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self.visualize()
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def _balance_after_delete(self, x):
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while x != self.root and x is not None and x.color == "black":
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if x == x.parent.left:
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w = x.parent.right
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if w is None or w.color == "black":
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if w is not None and w.left is not None and w.left.color == "red":
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w.left.color = "black"
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w.color = "red"
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self._rotate_right(w)
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w = x.parent.right
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elif w is not None and w.right is not None and w.right.color == "red":
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w.right.color = "black"
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w.color = "red"
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self._rotate_left(w)
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else:
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if w is not None:
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w.color = "red"
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x = x.parent
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else:
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w.color = "black"
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x.parent.color = "red"
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self._rotate_left(x.parent)
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else: # Symmetric case
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w = x.parent.left
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if w is None or w.color == "black":
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if w is not None and w.right is not None and w.right.color == "red":
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w.right.color = "black"
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w.color = "red"
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self._rotate_left(w)
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w = x.parent.left
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elif w is not None and w.left is not None and w.left.color == "red":
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w.left.color = "black"
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w.color = "red"
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self._rotate_right(w)
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else:
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if w is not None:
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w.color = "red"
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x = x.parent
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else:
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w.color = "black"
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x.parent.color = "red"
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self._rotate_right(x.parent)
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if x is not None:
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x.color = "black"
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self.root.color = "black"
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def _transplant(self, u, v):
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if u.parent is None:
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self.root = v
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elif u == u.parent.left:
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u.parent.left = v
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else:
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u.parent.right = v
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if v is not None:
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v.parent = u.parent
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def _find_minimum(self, node):
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while node.left is not None:
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node = node.left
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return node
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# ... (_find_node from previous response)
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def _rotate_left(self, x):
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y = x.right
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x.right = y.left
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if y.left is not None:
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y.left.parent = x
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y.parent = x.parent
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if x.parent is None:
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self.root = y
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elif x == x.parent.left:
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x.parent.left = y
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else:
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x.parent.right = y
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y.left = x
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x.parent = y
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def _rotate_right(self, y):
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x = y.left
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y.left = x.right
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if x.right is not None:
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x.right.parent = y
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x.parent = y.parent
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if y.parent is None:
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self.root = x
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elif y == y.parent.left:
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y.parent.left = x
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else:
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y.parent.right = x
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x.right = y
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y.parent = x
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def visualize(self):
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if self.root is None:
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return
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graph = nx.DiGraph()
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self._build_graph(self.root, graph)
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pos = nx.drawing.hierarchy.tree.layered_pos(graph, root=self.root, orientation='TB') # Vertical layout
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colors = [node[1]['color'] for node in graph.nodes(data=True)]
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labels = {node[0]: node[0] for node in graph.nodes(data=True)} # Node values as labels
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plt.figure(figsize=(10, 8)) # Adjust figure size as needed
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nx.draw(graph, pos, with_labels=True, labels=labels, node_size=700, node_color=colors, font_size=10, font_color="white", arrowsize=20) #Increased node size, white font color
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plt.show()
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def _build_graph(self, node, graph):
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graph.add_node(node.value, color=node.color) # Store color as node attribute
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if node.left:
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graph.add_edge(node.value, node.left.value)
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self._build_graph(node.left, graph)
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if node.right:
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graph.add_edge(node.value, node.right.value)
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self._build_graph(node.right, graph)
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# Example Usage:
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tree = Tree()
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tree.insert(10)
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tree.insert(5)
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tree.insert(15)
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tree.insert(3)
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tree.insert(7)
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tree.insert(12)
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tree.insert(18)
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tree.insert(1)
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tree.insert(2)
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tree.delete(10)
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tree.delete(7)
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tree.delete(18)
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tree.delete(12)
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plt.show()
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```
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Here's the implementation of `delete`, `_rotate_left`, `_rotate_right`, `_transplant`, `_find_minimum` and `visualize`. The `visualize` function now uses `networkx` and `matplotlib` to create a dynamic, vertically growing visualization. The `_build_graph` helper function recursively constructs the graph for visualization. I've also added some sample insertions and deletions to demonstrate the functionality. Let me know if you have any other questions.
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