Two Sum
The hash table trick that makes O(n²) become O(n) and why this pattern appears everywhere from feature stores to embedding lookups.
Data Structures & Algorithms
A comprehensive collection of data structures and algorithms problems, from fundamentals to advanced topics. Each problem explores multiple solutions, complexity analysis, and real-world applications.
Each problem includes:
- Multiple approaches (brute force → optimal)
- Time and space complexity analysis
- Production engineering considerations
- Connections to machine learning systems
- Code examples and edge cases
Browse by Topic
Arrays & Hash Tables:
Stacks:
Linked Lists:
Design:
Dynamic Programming:
- Best Time to Buy/Sell Stock
- Maximum Subarray
- Climbing Stairs
- Unique Paths
- Minimum Path Sum
- Decode Ways
- Word Break
- Regular Expression Matching
Trees & Graphs:
- Binary Tree Traversal
- Validate Binary Search Tree
- Validate Binary Search Tree (Day 25)
- Binary Tree Level Order Traversal
- Construct Binary Tree from Preorder and Inorder Traversal
- Kth Smallest Element in a BST
- Lowest Common Ancestor
- Number of Islands
- Course Schedule
- Word Ladder
- Clone Graph
- Evaluate Division
- Surrounded Regions
- Partition Equal Subset Sum
- Longest Increasing Subsequence
- Coin Change
- Binary Tree Maximum Path Sum
- Serialize and Deserialize Binary Tree
- Word Search II
- Course Schedule (Topological Sort)
- Alien Dictionary
Sorting & Searching:
Two Pointers & Greedy:
Backtracking:
String Manipulation & Hash Tables:
Intervals:
Matrix & In-place Algorithms:
Problem Index
Below you’ll find all DSA problems in chronological order:
Content created with the assistance of large language models and reviewed for technical accuracy.
Valid Parentheses
Why a simple stack solves bracket matching, expression parsing, and even neural network depth management in one elegant pattern.
Merge Two Sorted Lists
The pointer manipulation pattern that powers merge sort, data pipeline merging, and multi-source stream processing.
Best Time to Buy and Sell Stock
The single-pass pattern that powers streaming analytics, online algorithms, and real-time decision making in production systems.
Maximum Subarray (Kadane’s Algorithm)
Master the pattern behind online algorithms, streaming analytics, and dynamic programming, a single elegant idea powering countless production systems.
Climbing Stairs
The Fibonacci problem in disguise, teaching the fundamental transition from recursion to dynamic programming to space optimization.
Binary Tree Traversal
Master the fundamental patterns of tree traversal: the gateway to solving hundreds of tree problems in interviews.
Validate Binary Search Tree
Master BST validation to understand data integrity in tree structures, critical for indexing and search systems.
Binary Search
Master binary search to understand logarithmic algorithms and efficient searching, foundational for optimization and search systems.
Reverse Linked List
Master linked list manipulation through reversal - a fundamental pattern for understanding pointer logic and in-place algorithms.
LRU Cache
Master LRU cache design: O(1) get/put with hash map + doubly linked list. Critical for interviews and production caching systems.
Add Two Numbers
Master digit-by-digit addition with linked lists: Handle carry propagation elegantly. Classic problem teaching pointer manipulation and edge cases.
Container With Most Water
Master the two-pointer greedy technique that powers resource optimization in production ML systems.
Generate Parentheses
Master backtracking to generate all valid combinations—the foundation of ensemble model selection and multi-model systems.
Group Anagrams
Master hash-based grouping to solve anagrams—the foundation of clustering systems and speaker diarization in production ML.
Merge Intervals
Master interval processing to handle overlapping ranges—the foundation of event streams and temporal reasoning in production systems.
Add Two Numbers (Linked List)
Simulate arbitrary-precision addition on linked lists—the same sequential pattern used in large-scale distributed training and streaming pipelines.
Rotate Image
Master in-place matrix rotation—the same 2D transformation pattern that powers image and spectrogram augmentations in modern ML systems.
Spiral Matrix
Master systematic matrix traversal—the same pattern used for tracking experiments, processing logs, and managing state in ML systems.
Jump Game
Master greedy decision-making to determine reachability—the same adaptive strategy used in online learning and real-time speech systems.
Unique Paths
Master grid path counting with dynamic programming—the same optimization technique used in neural architecture search and speech model design.
Minimum Path Sum
The classic grid optimization problem that bridges the gap between simple recursion and 2D Dynamic Programming.
Decode Ways
A deceptive counting problem that teaches the fundamentals of state transitions and connects directly to Beam Search.
Word Break
The fundamental string segmentation problem that powers spell checkers, search engines, and tokenizers.
Validate Binary Search Tree
The gatekeeper of data integrity. How do we ensure our sorted structures are actually sorted?
Binary Tree Level Order Traversal
How do you print a corporate hierarchy level by level? CEO first, then VPs, then Managers…
Construct Binary Tree from Preorder and Inorder Traversal
Given two arrays, can you rebuild the original tree? It’s like solving a jigsaw puzzle where the pieces are numbers.
Kth Smallest Element in a BST
Finding the median or the 99th percentile is easy in a sorted array. Can we do it in a tree?
Lowest Common Ancestor of a Binary Tree
“Find the point where two paths in a tree first meet.”
Number of Islands
“Counting connected components in a 2D grid.”
Course Schedule (Topological Sort)
“Can you finish all courses given their prerequisites?”
Word Ladder (BFS)
“Transforming ‘cold’ to ‘warm’ one letter at a time.”
Clone Graph (DFS/BFS)
“Creating a deep copy of a graph structure.”
Evaluate Division (Graph/Union-Find)
“Modeling algebraic equations as graph path problems.”
Surrounded Regions (DFS/BFS)
“Capturing regions by identifying safe boundaries.”
Partition Equal Subset Sum
“Can you split the treasure evenly?”
Longest Increasing Subsequence (LIS)
“Finding the longest upward trend in chaos.”
Coin Change (Unbounded Knapsack)
“Making change with the fewest coins.”
Word Break
“Making sense of a stream of characters.”
Trapping Rain Water
“Calculating capacity in a fragmented landscape.”
Jump Game II
“Finding the optimal path through a sequence of choices.”
Merge K Sorted Lists
“Combining order from chaos, one element at a time.”
Median of Two Sorted Arrays
“Finding the middle ground between two ordered worlds.”
Largest Rectangle in Histogram
“Finding the maximum hidden in the valleys and peaks.”
Sliding Window Maximum
“Finding the king of every window.”
Binary Tree Maximum Path Sum
“Find the path to success—even if you have to start from the bottom, go up, and come back down.”
Serialize and Deserialize Binary Tree
“Data is only useful if it can survive the journey from RAM to Disk and back again.”
Word Search II
“Don’t look for one needle in a haystack. Magnetize the hay to find all needles at once.”
Course Schedule (Topological Sort)
“You can’t build the roof before you pour the foundation.”
Alien Dictionary
“Language is just a graph of symbols. If you know the order, you know the language.”
Median of Two Sorted Arrays
“Stop thinking ‘merge’. Think ‘partition’—the median is just the boundary between two halves.”
Trapping Rain Water
“Water doesn’t care about every bar—only the highest walls to the left and right.”
First Missing Positive
“The missing number is hiding in plain sight—use the array itself as the hash table.”
Wildcard Matching
“Wildcard matching is more than a string puzzle—it is the foundation of every file system glob, every firewall rule, and every log-routing engine you use tod...
N-Queens
“The N-Queens problem is the ‘Hello World’ of constraint satisfaction—it teaches us how to prune the search tree before it consumes our CPU.”
Minimum Window Substring
“Minimum Window Substring is the crown jewel of the sliding window pattern—it teaches us how to find the smallest container that satisfies a complex set of r...
Largest Rectangle in Histogram
“Largest Rectangle in Histogram is the masterclass of the Monotonic Stack. It requires maintaining a sorted state of indices to solve a local minimum problem...
Regular Expression Matching
“Regular Expression Matching is where string manipulation meets automata theory. It requires translating a sequence of patterns into a resilient state machin...
Sudoku Solver
“Sudoku Solver is the quintessential backtracking problem—it represents the transition from simple recursion to a multi-constraint search problem where every...
LFU Cache (Least Frequently Used)
“Designing an LFU Cache is the ultimate exercise in composite data structures—it forces you to synchronize multiple hash maps and linked lists to achieve O(1...