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SRT Algorithm Exponential search Steps 1, 2, 4, 8, … until you overshoot, then binary search: when the bound is unknown or the answer is near. 2⌊log₂ i⌋ + 1 questions to position i 1 problem STR Algorithm The Burrows–Wheeler transform A permutation that compresses a text and serves as an index to it: backward search, LF, and read alignment. O(m) to count a pattern, O(m + k·s) for k positions 2 problems STR Algorithm Edit distance The fewest insertions, deletions and substitutions between two strings: an m × n table and the alignment read from it. O(m · n) 2 problems SYS Data structure Inverted index and BM25 A dictionary “word → documents that contain it”: a query reads a few short lists instead of all the texts. O(total length of the query words' lists); AND by galloping O(m·log(n/m)) 2 problems

Problems

A compressed list of positions The best paragraphs A dictionary of typos In the same sentence

Often together

compression 3 interviews 3 searching 2 binary search 2 classic 2 bioinformatics 2 in production 2 suffix structures 1 string matching 1 similarity 1 dynamic programming 1 matrix 1

Written by Viacheslav Legostin. Everything is free; readers’ code is not stored.

Computer Science The algorithms catalogue Problems Base course Mathematics legost.in

The algorithms catalogue

Problems

SRT Searching and sorting

  1. Binary search
  2. Binary search on the answer
  3. Exponential search
  4. Interpolation search
  5. External sorting
  6. Heapsort
  7. Counting sort and radix sort

DS Data structures

  1. Dynamic array
  2. Hash table
  3. Cuckoo hashing
  4. Bloom filter
  5. Binary heap
  6. Binary search tree
  7. AVL tree
  8. B-tree
  9. Disjoint set union
  10. Fenwick tree

GRA Graphs

  1. Storing a graph
  2. Breadth-first search
  3. Depth-first search
  4. Bridges and articulation points
  5. Dijkstra's algorithm
  6. A*
  7. Bidirectional search
  8. The Bellman–Ford algorithm
  9. Floyd–Warshall algorithm
  10. Johnson's algorithm
  11. Contraction hierarchies
  12. Dinic's algorithm
  13. Graph colouring
  14. Bipartite matching
  15. Hungarian algorithm
  16. Eulerian path
  17. Heavy paths
  18. Centroid decomposition

STR Strings and text

  1. The Aho–Corasick algorithm
  2. Boyer–Moore
  3. The Burrows–Wheeler transform
  4. Edit distance
  5. BK-tree
  6. Huffman code

DP Dynamic programming

  1. Dynamic programming
  2. Interval DP
  3. Bitmask DP
  4. Digit DP
  5. Convex hull trick
  6. Knuth and divide-and-conquer optimisations

PAR Paradigms

  1. Greedy algorithms
  2. Backtracking
  3. Branch and bound
  4. Divide and conquer
  5. Closest pair of points

NUM Numbers and algebra

  1. Euclid's algorithm
  2. Fast exponentiation
  3. Chinese remainder theorem
  4. Big integers
  5. Fast Fourier transform
  6. Gaussian elimination

GEO Geometry

  1. Vectors and orientation
  2. Convex hull
  3. Delaunay triangulation and Voronoi diagram

NUM~ Numerical methods

  1. Bisection and Newton's method
  2. Gradient descent

SYS Systems and big data

  1. Consistent hashing
  2. Count-Min Sketch
  3. HyperLogLog
  4. Inverted index and BM25
  5. Retry with jitter
  6. CRDT

ML Data and machine learning

  1. k-means
  2. DBSCAN
  3. Decision tree
  4. Perceptron and backpropagation

RND Randomness

  1. Genetic algorithm

TEC Techniques

  1. Big O
  2. Fast input and output
  3. How to benchmark honestly
  4. Cache-friendly data
  5. Complexity from measurements
  6. Amortized analysis
  7. Choosing a data structure
  8. Coordinate compression
  9. Bit tricks