Algorithms
Master essential algorithms with interactive visualizations. Learn sorting, searching, dynamic programming, and graph algorithms used by Google, Meta, and Amazon in technical interviews. [Image of sorting algorithm visualization]
All Algorithms
Interactive tutorials covering fundamental sorting, searching, dynamic programming, and graph algorithms
Bubble Sort
EasyLearn O(n²) sorting with visual step-by-step swaps, best for small datasets and educational purposes
Selection Sort
EasyMaster O(n²) selection algorithm with minimum element finding in each pass
Insertion Sort
EasyUnderstand O(n²) but efficient for nearly sorted data, used in Timsort hybrid
Merge Sort
MediumMaster O(n log n) divide-and-conquer stable sorting used in Java Arrays.sort()
Quick Sort
MediumLearn O(n log n) average, O(n²) worst case partitioning used in C++ std::sort
Linear Search
EasyBasic O(n) sequential search for unsorted arrays, simple but exhaustive
Binary Search
MediumMaster O(log n) divide-and-conquer search on sorted arrays, essential interview topic
Breadth-First Search (BFS)
MediumLearn O(V+E) level-order graph traversal using queue, for shortest path in unweighted graphs
Depth-First Search (DFS)
MediumMaster O(V+E) recursive/stack-based traversal for cycle detection and topological sort
Free Interactive Algorithm Visualizer: Learn Sorting, Searching, Dynamic Programming & Graph Algorithms Online
Master computer science algorithms with step-by-step visualizations for sorting (merge sort, quick sort, heap sort), searching (binary search), dynamic programming (knapsack, LCS), and graph algorithms (Dijkstra, BFS, DFS). Perfect for technical interviews at Google, Meta, Amazon, and algorithm competitions.
What Are Algorithms (And Why Master Them)?
Algorithms are step-by-step procedures for solving computational problems efficiently. From O(n log n) merge sort powering Python's sorted() to Dijkstra's algorithm routing billions of Google Maps queries daily, algorithms are the foundation of modern software. According to Wikipedia, understanding time complexity (Big O notation) and algorithm design patterns is essential for 95% of technical interviews at FAANG companies.
Why Algorithms Matter for Developers:
Technical Interview Success
- ⢠FAANG interviews: 80% algorithm/data structure problems
- ⢠LeetCode patterns: Two pointers, sliding window, dynamic programming
- ⢠System design: Load balancing, caching algorithms, rate limiting
- ⢠Optimization: Time/space complexity trade-offs
Production Performance
- ⢠Database indexing: B-tree algorithms for O(log n) queries
- ⢠Route optimization: Dijkstra, A* for logistics, GPS
- ⢠Recommendation systems: Collaborative filtering algorithms
- ⢠Search engines: PageRank, TF-IDF algorithms
5 Essential Algorithm Categories for Interviews
1. Sorting Algorithms (O(n log n) is the goal)
Merge Sort: O(n log n) stable, divide-and-conquer, used in Java Arrays.sort() for objects. Quick Sort: O(n log n) average, in-place, used in C++ std::sort. Heap Sort: O(n log n) worst-case, in-place using binary heap. Master these for interviewsâexplain trade-offs (stability, space, practical performance). GeeksforGeeks sorting guide.
2. Searching Algorithms (Binary Search is your friend)
Binary Search: O(log n) on sorted arraysâmost important algorithm to master. Variations: lower/upper bound, rotated arrays, search in 2D matrix. Used in database indexes, dictionaries, auto-complete. Interview tip: Always consider binary search for "find in sorted" problems. Practice: LeetCode #704, #35, #33, #34, #74. Works on monotonic functions, not just arrays.
3. Dynamic Programming (Memoization + Tabulation)
Key pattern: Break problem into overlapping subproblems, store results to avoid recomputation. Fibonacci: O(2âż) â O(n) with DP. 0/1 Knapsack: O(2âż) â O(nW) with 2D table. LCS: String similarity O(mn). Used in diff tools, spell checkers, bioinformatics. Top interview topics: subset sum, coin change, edit distance, matrix chain multiplication. Start with LeetCode DP problems.
4. Graph Algorithms (BFS, DFS, Dijkstra)
BFS: O(V+E) shortest path in unweighted graphs, level-order traversal, used in social networks (friend recommendations). DFS: O(V+E) cycle detection, topological sort, maze solving. Dijkstra: O((V+E) log V) shortest path with positive weightsâGPS, network routing. Bellman-Ford: O(VE) handles negative weights. Master these for system design questions (load balancing, routing, dependency resolution).
5. Greedy Algorithms (Locally optimal choices)
Strategy: Make locally optimal choice at each step, hoping for global optimum. Works when greedy choice property holds. Examples: Activity selection, Huffman coding, fractional knapsack, Prim's MST, Kruskal's MST. Interview tip: Prove greedy works (exchange argument) or show counterexample. Contrast with DP (optimal substructure + overlapping subproblems). Try: heap-based priority queues for greedy algorithms.
10 Real-World Algorithm Applications
1. Google Search (PageRank Algorithm)
PageRank uses graph algorithms to rank web pages by importanceâtreating links as votes. O(n) per iteration with power iteration method. Combined with TF-IDF for relevance scoring. Processes 8.5 billion searches/day. Modern Google uses 200+ ranking factors but PageRank remains foundational.
2. Netflix Recommendations (Collaborative Filtering)
Matrix factorization algorithms (SVD, ALS) predict user preferences from viewing history. O(k Ă iterations Ă (users + items)) where k = latent factors. Processes 250M+ users. Alternative: deep learning (neural collaborative filtering). Try our complexity calculator.
3. Uber/Lyft Routing (Dijkstra + A*)
Dijkstra's algorithm finds shortest paths in road networks. A* adds heuristic (haversine distance) for faster convergence. Pre-computed contraction hierarchies reduce O((V+E) log V) to O(log V) for repeated queries. Handles 23M+ rides/day (Uber).
4. Git Version Control (Diff Algorithm)
Longest Common Subsequence (LCS) DP algorithm finds differences between file versions. O(mn) where m, n = file lengths. Git uses Myers' algorithm (O(n+d²) where d = edit distance)âfaster for similar files. git diff shows minimal changeset.
5. Database Query Optimization (Join Algorithms)
Hash Join: O(n+m) using hash tables for equi-joins. Sort-Merge Join: O(n log n + m log m) for sorted inputs. Nested Loop Join: O(nm) fallback. PostgreSQL query planner chooses algorithm based on statistics. Indexes use B-tree algorithms (O(log n) search).
6. Spotify Shuffle (Fisher-Yates Algorithm)
Fisher-Yates shuffle generates random permutations in O(n) time. Unbiasedâeach permutation equally likely. Old Spotify bug: random() sorting O(n log n) was biased. Modern shuffle uses proper algorithm. Used in card games, A/B testing, data sampling.
7. Autocomplete (Trie + Prefix Search)
Trie data structure stores dictionary for O(k) prefix search (k = query length). Google autocomplete processes 6B queries/day. Combined with popularity ranking, spell correction (edit distance), and caching. Alternative: ternary search trees (less space).
8. Image Compression (Huffman Coding)
Huffman coding builds optimal prefix-free codes using greedy algorithm with min-heap. O(n log n) where n = unique symbols. Used in ZIP, JPEG, MP3. Assigns shorter codes to frequent symbolsâlossless compression. Alternative: arithmetic coding (better but patented).
9. Social Network Friend Suggestions (BFS)
BFS from user's friends finds friends-of-friends (2 hops away) in O(V+E). LinkedIn "People You May Know" uses this plus shared connections, common employers, etc. Facebook processes 3B+ usersâuses distributed graph algorithms (Pregel model). See our graph visualizer.
10. Cache Replacement (LRU Algorithm)
Least Recently Used (LRU) evicts oldest accessed item when cache full. O(1) get/put using hash map + doubly linked list. Used in CPU caches, CDNs (Cloudflare, Akamai), Redis, Memcached. Alternative: LFU (least frequently used), ARC (adaptive replacement cache). Classic interview problem (LeetCode #146).
Master Data Structures & Algorithms Together
Algorithms and data structures go hand-in-hand. Explore our complete learning path:
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