Write a function cumulative_mul that mutates the Tree t so that each node's label becomes the product of its label and all labels in the subtrees rooted at the node. def cumulative_mul(t): II II || """Mutates t so that each node's label the corresponding subtree rooted at t. >>> t = Tree(1, [Tree(3, [Tree(5)]), Tr >>> cumulative_mul(t) >>> t Tree(105, [Tree(15, [Tree(5)]), Tree(7) IL |||| "*** YOUR CODE HERE ***"
Write a function cumulative_mul that mutates the Tree t so that each node's label becomes the product of its label and all labels in the subtrees rooted at the node. def cumulative_mul(t): II II || """Mutates t so that each node's label the corresponding subtree rooted at t. >>> t = Tree(1, [Tree(3, [Tree(5)]), Tr >>> cumulative_mul(t) >>> t Tree(105, [Tree(15, [Tree(5)]), Tree(7) IL |||| "*** YOUR CODE HERE ***"
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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![### Function Definition: `cumulative_mul`
This task involves implementing a function `cumulative_mul` to traverse and mutate a tree data structure. Each node's label must be updated to the product of its label and all labels in the subtrees rooted at that node.
#### Code Structure:
```python
def cumulative_mul(t):
"""Mutates t so that each node's label is the product of all labels in the corresponding subtree rooted at t."""
# Example of using the Tree class
>>> t = Tree(1, [Tree(3, [Tree(5)]), Tree(7)])
>>> cumulative_mul(t)
>>> t
Tree(105, [Tree(15, [Tree(5)]), Tree(7)])
""" YOUR CODE HERE """
```
#### Key Points:
- **Functionality**: The function should iterate over each node of the tree.
- **Mutation**: It mutates the tree in place, altering each node's label.
- **Example**:
- Input Tree: `Tree(1, [Tree(3, [Tree(5)]), Tree(7)])`
- After running `cumulative_mul`, the tree should be mutated to `Tree(105, [Tree(15, [Tree(5)]), Tree(7)])`.
#### Implementation Steps:
1. **Base Case**: If the tree has no children, the label remains the same.
2. **Recursive Case**: For trees with children:
- Recursively update each child.
- Multiply the node’s label by each child’s label to update the current node’s label.
These updates ensure that each node accumulates all product values from its subtree. The placeholder `"*** YOUR CODE HERE ***"` indicates where the function’s logic must be implemented.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fda4a7445-4cc9-4690-867b-b0862e018c2b%2F871a9310-85e4-4bba-bcb3-cd90a31dec7b%2F046qp7s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Function Definition: `cumulative_mul`
This task involves implementing a function `cumulative_mul` to traverse and mutate a tree data structure. Each node's label must be updated to the product of its label and all labels in the subtrees rooted at that node.
#### Code Structure:
```python
def cumulative_mul(t):
"""Mutates t so that each node's label is the product of all labels in the corresponding subtree rooted at t."""
# Example of using the Tree class
>>> t = Tree(1, [Tree(3, [Tree(5)]), Tree(7)])
>>> cumulative_mul(t)
>>> t
Tree(105, [Tree(15, [Tree(5)]), Tree(7)])
""" YOUR CODE HERE """
```
#### Key Points:
- **Functionality**: The function should iterate over each node of the tree.
- **Mutation**: It mutates the tree in place, altering each node's label.
- **Example**:
- Input Tree: `Tree(1, [Tree(3, [Tree(5)]), Tree(7)])`
- After running `cumulative_mul`, the tree should be mutated to `Tree(105, [Tree(15, [Tree(5)]), Tree(7)])`.
#### Implementation Steps:
1. **Base Case**: If the tree has no children, the label remains the same.
2. **Recursive Case**: For trees with children:
- Recursively update each child.
- Multiply the node’s label by each child’s label to update the current node’s label.
These updates ensure that each node accumulates all product values from its subtree. The placeholder `"*** YOUR CODE HERE ***"` indicates where the function’s logic must be implemented.
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