Algorithms Theory

Sorting Algorithms

Comparison-Based Sorting

• Bubble sort
• Selection sort
• Insertion sort
• Merge sort
• Quick sort
• Heap sort
• Time and space complexity analysis
• Stability of sorting algorithms

Non-Comparison Sorting

• Counting sort
• Radix sort
• Bucket sort
• When to use non-comparison sorts

Searching Algorithms

Linear Search

• Sequential search
• Time complexity: O(n)
• When to use

Binary Search

• Binary search algorithm
• Requirements (sorted array)
• Time complexity: O(log n)
• Variations (finding first/last occurrence)
• Binary search on answer

Graph Algorithms

Shortest Path Algorithms

• Dijkstra's algorithm
• Bellman-Ford algorithm
• Floyd-Warshall algorithm
• A* algorithm

Minimum Spanning Tree

• Kruskal's algorithm
• Prim's algorithm
• Applications

Other Graph Algorithms

• Topological sort
• Strongly connected components
• Network flow algorithms

Dynamic Programming Intro

Concepts

• Overlapping subproblems
• Optimal substructure
• Memoization vs tabulation
• Top-down vs bottom-up approaches

Common Patterns

• 1D DP problems
• 2D DP problems
• State machine DP
• DP on trees
• DP on strings

Classic Problems

• Fibonacci sequence
• Longest common subsequence
• Knapsack problem
• Coin change problem
• Edit distance

Practice Questions

Test your understanding with the questions in the interactive quiz below (when available).

Resources

• "Algorithm Design Manual" by Steven Skiena
• "Algorithms" by Sedgewick and Wayne
• Algorithm Visualization: https://algorithm-visualizer.org/
• LeetCode Dynamic Programming: https://leetcode.com/tag/dynamic-programming/