Advanced Trees, Intervals, and Data Structure Challenges: Week 4 Breakdown

In this article, we’ll dive into 10 critical problems from Week 4 of the 75 Blind Leetcode Questions, focusing on trees, intervals, data streams, and advanced graph search techniques. These problems often appear in technical interviews, pushing the boundaries of efficient recursion, dynamic programming, and data structure mastery. Below, you’ll find the solution steps, time and space complexities, and conclusions for each of the problems.

1. Subtree of Another Tree

The task is to check if one tree is a subtree of another tree.

• Solution Steps:
• Time Complexity: O(m * n), where m is the number of nodes in the main tree and n is the number of nodes in the subtree.
• Space Complexity: O(h), where h is the height of the main tree for the recursion stack.
• Conclusion: This problem tests recursive tree traversal, a key concept in binary tree problems. The solution involves checking every node of the main tree to see if the structure of the subtree matches.

2. Lowest Common Ancestor of a Binary Search Tree (BST)

The goal is to find the lowest common ancestor (LCA) of two nodes in a binary search tree.

• Solution Steps:
• Time Complexity: O(h), where h is the height of the tree.
• Space Complexity: O(h), due to the recursion stack or O(1) in the iterative version.
• Conclusion: This problem efficiently leverages the properties of BSTs, demonstrating how understanding tree structure can reduce complexity to O(h), where h is the height of the tree.

3. Implement Trie (Prefix Tree)

This problem requires constructing a Trie (prefix tree) to efficiently store and search strings.

• Solution Steps:
• Time Complexity: O(m), where m is the length of the word being inserted or searched.
• Space Complexity: O(m * n), where n is the number of words and m is the average length of each word.
• Conclusion: Tries offer fast lookups and insertions, making them ideal for word storage and prefix searching. This problem is essential for understanding how to optimize search operations in large datasets.

4. Add and Search Word

This is an extension of the Trie problem with the added complexity of supporting wildcards ('.' matches any character).

• Solution Steps:
• Time Complexity: O(m) for normal searches, and O(26^m) in the worst case when all characters are wildcards.
• Space Complexity: O(m * n).
• Conclusion: This problem extends the Trie data structure with recursive DFS, adding complexity but offering a flexible and powerful search mechanism. This is a common pattern in problems that require adaptability in search.

5. Kth Smallest Element in a BST

The task is to find the k-th smallest element in a binary search tree (BST).

• Solution Steps:
• Time Complexity: O(k), as we only traverse k nodes.
• Space Complexity: O(h), where h is the height of the tree for recursion.
• Conclusion: This problem is an excellent example of how in-order traversal leverages the sorted property of BSTs. It’s often used to find the smallest or largest elements efficiently.

6. Merge K Sorted Lists

The task is to merge k sorted linked lists into one sorted list.

• Solution Steps:
• Time Complexity: O(n log k), where n is the total number of nodes and k is the number of lists.
• Space Complexity: O(k) for storing nodes in the heap.
• Conclusion: This problem demonstrates the power of heaps for merging multiple sorted structures. It’s frequently asked in interviews due to its application in data merging scenarios.

7. Find Median from Data Stream

This problem requires maintaining a dynamic data stream and finding the median in constant time.

• Solution Steps:
• Time Complexity: O(log n) for insertion, O(1) for finding the median.
• Space Complexity: O(n).
• Conclusion: This problem is a classic example of heap usage to dynamically manage data streams. Understanding how to balance heaps is crucial in solving real-time data processing problems efficiently.

8. Insert Interval

The goal is to insert a new interval into a list of non-overlapping intervals, merging intervals if necessary.

• Solution Steps:
• Time Complexity: O(n)
• Space Complexity: O(n)
• Conclusion: This problem tests your ability to work with intervals and edge cases involving merging and sorting. It’s a common interval manipulation problem in interviews.

9. Longest Consecutive Sequence

The task is to find the length of the longest consecutive sequence in an unsorted array.

• Solution Steps:
• Time Complexity: O(n)
• Space Complexity: O(n)
• Conclusion: Using a set enables efficient lookups and sequence counting, reducing the problem's time complexity from O(n log n) to O(n). This problem is a great example of optimizing search operations in large datasets.

10. Word Search II

Given a 2D board of letters, find all words from a list that can be formed by tracing adjacent cells on the board.

• Solution Steps:
• Time Complexity: O(m n l), where m is the number of rows, n is the number of columns, and l is the length of the longest word.
• Space Complexity: O(l), where l is the total length of all words in the Trie.
• Conclusion: This problem combines graph traversal with advanced Trie usage. It’s a challenging problem that tests your ability to manage both grid search and dynamic word searching efficiently.

Overall Conclusion:

In Week 4 of the 75 Blind Leetcode Questions, the problems become more advanced, requiring the use of heaps, tries, and efficient tree and graph traversal techniques. Mastering these problems is crucial for building a deep understanding of data structures, recursion, and dynamic programming. These skills are essential for tackling the most complex coding interview questions efficiently and optimally.