Unit 9 Session 2 (Click for link to problem statements)
Understand what the interviewer is asking for by using test cases and questions about the problem.
- Established a set (2-3) of test cases to verify their own solution later.
- Established a set (1-2) of edge cases to verify their solution handles complexities.
- Have fully understood the problem and have no clarifying questions.
- Have you verified any Time/Space Constraints for this problem?
Can the tree be empty?
What should be returned if the tree has only one node?
HAPPY CASE
1 (root)
/ \
2 3
Input: root
Output: 1
Explanation:
- Node 1: left sum = 2, right sum = 3, tilt = |2 - 3| = 1
- Node 2: left sum = 0, right sum = 0, tilt = |0 - 0| = 0
- Node 3: left sum = 0, right sum = 0, tilt = |0 - 0| = 0
- Total tilt = 1 + 0 + 0 = 1EDGE CASE
1 (root)
Input: root
Output: 0
Explanation: The tree has only one node, so the tilt is 0.Match what this problem looks like to known categories of problems, e.g., Linked List or Dynamic Programming, and strategies or patterns in those categories.
For Tree problems, we want to consider the following approaches:
Plan the solution with appropriate visualizations and pseudocode.
General Idea: Use a DFS approach to traverse the tree. For each node, calculate the sum of the left and right subtrees and their tilt. Keep a running total of the tilts and return it at the end.
1) Define a helper function `dfs(node, total_tilt)` to calculate the tilt and subtree sums.
a) If the current node is None, return 0.
b) Recursively calculate the sum of the left subtree.
c) Recursively calculate the sum of the right subtree.
d) Calculate the tilt of the current node as the absolute difference between left and right subtree sums.
e) Add the current node's tilt to the total tilt.
f) Return the sum of values of the subtree rooted at the current node.
2) In the main function `find_tilt(root)`, initialize total_tilt to 0.
3) Call the helper function to start the DFS from the root.
4) Return the total tilt.⚠️ Common Mistakes
Implement the code to solve the algorithm.
class TreeNode:
def __init__(self, val=0, left=None, right=None):
self.val = val
self.left = left
self.right = right
def dfs(node, total_tilt):
if not node:
return 0
# Recursive call to calculate the sum of left and right subtrees
left_sum = dfs(node.left, total_tilt)
right_sum = dfs(node.right, total_tilt)
# Tilt of the current node
tilt = abs(left_sum - right_sum)
# Add the current node's tilt to the total tilt
total_tilt[0] += tilt
# Return the sum of values of the subtree rooted at the current node
return node.val + left_sum + right_sum
def find_tilt(root):
total_tilt = [0] # Use a list to allow modification within dfs function
dfs(root, total_tilt)
return total_tilt[0]Review the code by running specific example(s) and recording values (watchlist) of your code's variables along the way.
Evaluate the performance of your algorithm and state any strong/weak or future potential work.
