Answer
See the explanation
Work Step by Step
To find and delete a given value from a tree stored in the fashion of Figure 8.20, you can follow these steps:
1. **Start at the root:** Begin at the root of the tree and traverse down until you find the node containing the value you want to delete.
2. **Locate the node:** If the value is present, locate the node containing that value.
3. **Identify the case:**
- If the node is a leaf (has no children), simply remove the node.
- If the node has one child, replace the node with its child.
- If the node has two children, find the node's in-order successor (or predecessor), replace the node's value with the successor's value, and then recursively delete the successor.
4. **Update the tree:** After deletion, ensure that the tree maintains its properties, such as maintaining the binary search tree (BST) order.
Here's a Python-like pseudocode snippet to illustrate the procedure:
```python
def delete_node(root, value):
if root is None:
return root
# Locate the node to be deleted
if value < root.value:
root.left = delete_node(root.left, value)
elif value > root.value:
root.right = delete_node(root.right, value)
else:
# Node with only one child or no child
if root.left is None:
return root.right
elif root.right is None:
return root.left
# Node with two children - find the in-order successor
root.value = find_min_value(root.right)
# Delete the in-order successor
root.right = delete_node(root.right, root.value)
return root
def find_min_value(node):
current = node
while current.left is not None:
current = current.left
return current.value
```
Make sure to implement the necessary tree structure based on your requirements and adapt the code accordingly.
