Count the Food Chain

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Unit 8 Session 1 Advanced (Click for link to problem statements)

Problem Highlights

• 💡 Difficulty: Easy
• ⏰ Time to complete: 10 mins
• 🛠️ Topics: Binary Tree, Tree Traversal, Recursion

1: U-nderstand

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?

• What does each node in the binary tree represent?
  • Each node represents a species in the marine food chain.
• What does the function need to return?
  • The function needs to return the total number of species (nodes) in the tree.
• How should the function behave if the tree is empty?
  • The function should return 0 if the tree is empty.

HAPPY CASE
Input: Binary tree with nodes ["Shark", "Grouper", "Snapper", "Conch", "Tang", "Zooplankton"]
Output: 6
Explanation: There are 6 species in the food chain.

EDGE CASE
Input: Binary tree with only one node ["Shark"]
Output: 1
Explanation: The tree has only the root, so the count is 1.

2: M-atch

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 Counting problems, we want to consider the following approaches:

• Binary Tree Traversal: Traverse the tree to count the total number of nodes.
• Recursion: Use recursion to count the nodes in each subtree and sum them up.

3: P-lan

Plan the solution with appropriate visualizations and pseudocode.

General Idea: Traverse the tree recursively, counting each node.

1) If the current node is None, return 0.
2) Recursively count the nodes in the left subtree.
3) Recursively count the nodes in the right subtree.
4) Add 1 (for the current node) to the counts from the left and right subtrees.
5) Return the total count.

⚠️ Common Mistakes

• Not correctly handling the base case where the tree is empty.
• Forgetting to include the current node in the total count.

4: I-mplement

Implement the code to solve the algorithm.

class TreeNode:
    def __init__(self, value, left=None, right=None):
        self.val = value
        self.left = left
        self.right = right

def count_species(node):
    if node is None:
        return 0
    
    # Recursively count the nodes in the left and right subtrees
    left_count = count_species(node.left)
    right_count = count_species(node.right)
    
    # Add 1 for the current node
    return 1 + left_count + right_count

5: R-eview

Review the code by running specific example(s) and recording values (watchlist) of your code's variables along the way.

• Test with the examples given:

  - Input 1: Binary tree with nodes ["Shark", "Grouper", "Snapper", "Conch", "Tang", "Zooplankton"]
  - Expected Output: 6

  - Input 2: Binary tree with only one node ["Shark"]
  - Expected Output: 1

6: E-valuate

Evaluate the performance of your algorithm and state any strong/weak or future potential work.

Assume N represents the number of nodes in the binary tree.

• Time Complexity: O(N) because the algorithm needs to visit each node in the tree.
• Space Complexity: O(H) where H is the height of the tree, due to the recursive call stack.