Mathematics
Mathematical Algorithms for Coding Interviews
Mathematical algorithms are the quiet prerequisite in a lot of interview questions. A problem is rarely stated as "compute a GCD" — it asks you to simplify a fraction, or to find when two cycles align, and the mathematics is the step you are expected to recognise on your own.
Each lesson here visualises the mechanism rather than the identity. You watch the Euclidean algorithm shrink a pair of numbers, see the Sieve of Eratosthenes strike out composites in passes, and step through fast exponentiation halving an exponent. Bit manipulation is included because interviewers reach for it constantly and it is the topic most often learned as a set of tricks rather than as a model.
Interactive lessons
Free to open
Languages (JS, TS, Python, Java, C, C++)
Mathematics lessons
Mathematics time and space complexity compared
Best, average and worst-case running time and extra space for every mathematics lesson, as each lesson derives them.
| Lesson | Best | Average | Worst | Space |
|---|---|---|---|---|
| GCD / LCM | O(1) | O(log(min(A, B))) | O(log(min(A, B))) | O(1) |
| Prime Numbers | O(1) | O(√N) | O(√N) | O(1) |
| Sieve of Eratosthenes | O(N log log N) | O(N log log N) | O(N log log N) | O(N) |
| Modular Arithmetic | O(1) | O(1) | O(1) | O(1) |
| Fast Exponentiation | O(log B) | O(log B) | O(log B) | O(1) |
| Bit Manipulation | O(1) | O(1) | O(1) | O(1) |
Continue the DSA curriculum
Mathematics is one of 12 topics in the interactive DSA visualizer curriculum. Once this topic is comfortable, the coding interview pattern library reorganises the same material around the patterns interview questions are built on.
Every other DSA visualizer
Data Structures · 28 lessons
- StackFree
- QueueFree
- Deque
- Circular Queue
- Priority Queue (ADT)
- Tree Traversal
- Binary Tree
- Binary Search Tree
- AVL Tree
- Trie (Prefix Tree)
- Segment Tree
- Fenwick Tree
- Red-Black Tree
- Singly Linked List
- Doubly Linked List
- Circular Linked List
- Graph RepresentationFree
- Breadth First SearchFree
- Depth First Search
- Topological Sort
- Cycle Detection
- Connected Components
- Bipartite Graph
- Dijkstra's Algorithm
- Bellman-Ford Algorithm
- Minimum Spanning Tree
- Floyd-Warshall Algorithm
- Bridges & Articulation Points