An algorithm is a step-by-step procedure or formula for solving a problem. In computer science, algorithms are essential for performing calculations, data processing, and automated reasoning tasks.
Follow this path from basic techniques to advanced algorithms. Each topic builds on concepts from the previous, so working through them in order gives you the strongest understanding.
A technique using two pointers to traverse data structures efficiently.
A technique using two pointers moving at different speeds to detect cycles.
A technique for processing contiguous subarrays or substrings efficiently.
An efficient algorithm for finding elements in sorted data by halving the search space.
A technique for preprocessing arrays to answer range sum queries in constant time.
A method where a function calls itself to solve smaller instances of the same problem.
Algorithms for visiting all nodes in a tree data structure systematically.
Algorithms for arranging elements in a specific order for efficient processing.
An algorithmic technique for solving problems by exploring all possibilities.
Dynamic programming applied to one-dimensional subproblem structures.
An approach that makes the locally optimal choice at each step.
Techniques for solving problems involving overlapping or merging intervals.
Techniques for manipulating individual bits in binary representations.
An algorithm for traversing graphs by exploring as far as possible along each branch.
An algorithm for traversing graphs level by level from the source.
Dynamic programming applied to two-dimensional subproblem structures.
A pattern using two heaps to efficiently track medians or extremes.
An algorithm for finding the shortest paths from a source vertex in weighted graphs.
A pathfinding algorithm that uses heuristics to find optimal paths efficiently.
An algorithm for finding shortest paths between all pairs of vertices.
An algorithm for finding shortest paths from a source, handling negative weights.
An algorithm for finding the minimum spanning tree of a weighted graph.
An algorithm for finding the minimum spanning tree using edge sorting.
An algorithm for ordering vertices in a directed acyclic graph linearly.
An algorithm for finding shortest paths in directed acyclic graphs efficiently.
Algorithms are important because they optimize the efficiency of programs, enabling tasks to be completed quickly and using fewer resources. They provide a clear, step-by-step method for solving problems, making complex tasks more manageable.
Efficient algorithms ensure reliable and consistent results, can be reused across different projects, and scale well to handle increasing amounts of data or users. As the foundation of all computer programs, algorithms are crucial for creating effective and reliable software.
Algorithms optimize the efficiency of programs, enabling tasks to be completed quickly and using fewer resources. The gap between O(n) and O(n²) is invisible at ten items, but at ten million it's the difference between a fast response and a request that never finishes.
Algorithm complexity is a measure of the amount of time and/or space required by an algorithm for an input of a given size (n). It is often expressed using Big-O notation, which describes the upper bound of an algorithm's running time or space requirements in the worst-case scenario.
These two costs usually trade off against each other. Faster algorithms tend to use more memory, and memory-efficient algorithms tend to take more time.
Selecting the right algorithm is important for solving a problem efficiently. Choosing the wrong algorithm can significantly impact the performance and scalability of your solution. Here are some key factors to consider when choosing an algorithm: