7:30
8 patterns to solve 80% Leetcode problems
Sahil & Sarra
Overview
This video introduces eight common algorithmic patterns that can help solve a majority of LeetCode problems. Instead of memorizing solutions, the focus is on recognizing recurring problem structures. The patterns discussed include Sliding Window, Subset, Modified Binary Search, Top K Elements, Binary Tree DFS, Topological Sort, Binary Tree BFS, and Two Pointers. Understanding these patterns and their underlying data structures and algorithms is crucial for efficient problem-solving in coding interviews.
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Chapters
- Used for processing linear data structures (arrays, strings) by examining a sub-part (window) at a time.
- The window slides one element at a time, useful for finding subsets that meet specific conditions.
- Ideal for problems asking for the longest or shortest substring/subarray satisfying a condition, like finding the longest substring with K unique characters.
This pattern efficiently processes sequential data by avoiding redundant computations, making it suitable for optimization problems on linear structures.
Finding the longest substring with K unique characters.
- Applies when needing to find all possible combinations or arrangements of elements from a given set.
- Repetitions of elements may or may not be allowed, depending on the problem.
- Can be solved iteratively by building subsets level by level, similar to Breadth-First Search (BFS).
This pattern is fundamental for problems involving permutations, combinations, and exploring all possible configurations of a dataset.
The permutations problem on LeetCode.
- Builds upon the core binary search idea of repeatedly dividing the search space by half.
- Requires adjusting the standard binary search logic to handle specific problem constraints.
- Understanding the behavior of pointers in edge cases (duplicates, target not found) is key.
- Implementing functions like `bisect_left` and `bisect_right` can improve visualization and understanding.
This pattern allows for efficient searching in sorted (even if rotated or modified) data structures by leveraging the divide-and-conquer principle.
Searching in a rotated sorted array.
- Used to find the 'k' most important or relevant elements from a larger dataset based on a condition.
- Commonly applied to problems asking for top-ranking elements.
- Often solved efficiently using a Heap data structure to maintain the 'k' elements seen so far.
- A min-heap can store the k largest elements, allowing quick updates when a new, larger element is encountered.
This pattern provides an efficient way to extract specific ranked elements from large datasets, crucial for performance-sensitive applications.
Finding the k-th largest number in an array.
- Binary Tree DFS (Depth-First Search) explores one branch completely before backtracking and exploring others, typically using recursion.
- Binary Tree BFS (Breadth-First Search) explores nodes level by level, using a queue to process all nodes at the current depth before moving to the next.
- DFS is good for problems requiring deep exploration of a single path, while BFS is suitable for level-based processing.
These patterns are fundamental for navigating and processing tree structures, enabling solutions for problems related to tree depth, levels, and node relationships.
DFS for maximum depth of a binary tree; BFS for level order traversal.
- Arranges elements in a specific order when they have dependencies on each other.
- Applicable to Directed Acyclic Graphs (DAGs) where connections are one-way and no cycles exist.
- Useful for scheduling tasks or ordering items where prerequisites must be met first.
- Creates a sequence ensuring each item is processed only after all its dependencies are completed.
This pattern is essential for managing ordered processes and dependencies, ensuring tasks are executed in a valid sequence.
Determining the order of courses to take given prerequisites (Course Schedule problem).
- Used for problems involving sorted arrays where two pointers iterate through the data.
- Typically, one pointer starts at the beginning and the other at the end.
- Pointers move inwards based on comparisons, allowing efficient single-pass solutions.
- Effective for finding pairs or triplets that sum to a target value.
This pattern optimizes array traversal by intelligently moving pointers, often reducing time complexity to linear.
The two-sum problem on a sorted array, or finding triplets that sum to zero.
Key takeaways
- Focusing on recurring algorithmic patterns is more effective than memorizing individual problem solutions.
- Understanding the underlying data structures (like heaps and queues) is crucial for implementing these patterns efficiently.
- Binary search, even in modified forms, relies on repeatedly halving the search space.
- Tree traversals (DFS and BFS) offer different but complementary ways to explore tree structures.
- Topological sort is vital for problems involving ordered dependencies and directed acyclic graphs.
- The two-pointer technique is a powerful optimization for problems on sorted arrays.
- A strong foundation in data structures and algorithms is a prerequisite for mastering these patterns.
Key terms
Sliding WindowSubset PatternModified Binary SearchTop K ElementsHeapBinary Tree DFSBinary Tree BFSQueueTopological SortDirected Acyclic Graph (DAG)Two Pointers
Test your understanding
- How does the sliding window pattern differ from a simple linear scan, and when is it most applicable?
- What is the core idea behind the subset pattern, and how does it relate to graph traversal algorithms?
- Why is understanding pointer movement crucial for modified binary search problems, especially with duplicates?
- How does a heap data structure facilitate the efficient solution of 'Top K Elements' problems?
- What are the fundamental differences in approach between Binary Tree DFS and BFS, and what types of problems does each excel at?
- When would you choose to use topological sort, and what kind of graph structure does it apply to?
- How does the two-pointer pattern leverage the sorted nature of an array to achieve efficiency?