# Content ## 1. Introduction to Algorithms * [Introduction](https://grokking.realtemirov.uz/1.-introduction-to-algorithms/1.-introduction) * [What you'll learn about performance](https://grokking.realtemirov.uz/1.-introduction-to-algorithms/1.-introduction#what-youll-learn-about-performance) * [What you'll learn about solving problems](https://github.com/realtemirov/grokking-algorithms/blob/main/1.%20Introduction%20to%20Algorithms/01%20Introduction.md#what-youll-learn-about-solving-problems) * [Binary search](https://grokking.realtemirov.uz/1.-introduction-to-algorithms/2.-binary-search) * [A better way to search](https://grokking.realtemirov.uz/1.-introduction-to-algorithms/2.-binary-search#a-better-way-to-search) * [Running time](https://grokking.realtemirov.uz/1.-introduction-to-algorithms/2.-binary-search#running-time) * [Big O notation](https://grokking.realtemirov.uz/1.-introduction-to-algorithms/3.-big-o-notation) * [Algorithm running times grow at different rates](https://grokking.realtemirov.uz/1.-introduction-to-algorithms/3.-big-o-notation#algorithm-running-times-grow-at-different-rates) * [Visualizing different Big O run times](https://grokking.realtemirov.uz/1.-introduction-to-algorithms/3.-big-o-notation#visualizing-different-big-o-run-times) * [Big O establishes a worst-case run time](https://grokking.realtemirov.uz/1.-introduction-to-algorithms/3.-big-o-notation#big-o-establishes-a-worst-case-run-time) * [Some common Big O run times](https://grokking.realtemirov.uz/1.-introduction-to-algorithms/3.-big-o-notation#some-common-big-o-run-times) * [The traveling salesperson](https://grokking.realtemirov.uz/1.-introduction-to-algorithms/3.-big-o-notation#the-traveling-salesperson) * [Recap](https://grokking.realtemirov.uz/1.-introduction-to-algorithms/4.-recap) ## 2. Selection sort * [How memory works](https://grokking.realtemirov.uz/2.-selection-sort/1.-how-memory-works) * [Arrays and linked lists](https://grokking.realtemirov.uz/2.-selection-sort/2.-arrays-and-linked-lists) * [Linked lists](https://grokking.realtemirov.uz/2.-selection-sort/2.-arrays-and-linked-lists#linked-lists) * [Arrays](https://grokking.realtemirov.uz/2.-selection-sort/2.-arrays-and-linked-lists#arrays) * [Terminology](https://grokking.realtemirov.uz/2.-selection-sort/2.-arrays-and-linked-lists#terminology) * [Inserting into the middle of a list](https://grokking.realtemirov.uz/2.-selection-sort/2.-arrays-and-linked-lists#inserting-into-the-middle-of-a-list) * [Deletions](https://grokking.realtemirov.uz/2.-selection-sort/2.-arrays-and-linked-lists#deletions) * [Selection sort](https://grokking.realtemirov.uz/2.-selection-sort/3.-selection-sort) * [Recap](https://grokking.realtemirov.uz/2.-selection-sort/4.-recap) ## 3. Recursion * [Recursion](https://grokking.realtemirov.uz/3.-recursion/1.-recursion) * [Base case and recursive case](https://grokking.realtemirov.uz/3.-recursion/2.-base-case-and-recursive-case) * [The stack](https://grokking.realtemirov.uz/3.-recursion/3.-the-stack) * [The call stack](https://grokking.realtemirov.uz/3.-recursion/3.-the-stack#the-call-stack) * [The call stack with recursion](https://grokking.realtemirov.uz/3.-recursion/3.-the-stack#the-call-stack-with-recursion) * [Recap](https://grokking.realtemirov.uz/3.-recursion/4.-recap) ## 4. Quicksort * [Divide & conquer](https://grokking.realtemirov.uz/4.-quicksort/1.-divide-and-conquer) * [Quicksort](https://grokking.realtemirov.uz/4.-quicksort/2.-quicksort) * [Big O notation revisited](https://grokking.realtemirov.uz/4.-quicksort/3.-big-o-notation-revisited) * [Merge sort vs. quicksort](https://grokking.realtemirov.uz/4.-quicksort/3.-big-o-notation-revisited#merge-sort-vs.-quicksort) * [Average case vs. worst case](https://grokking.realtemirov.uz/4.-quicksort/3.-big-o-notation-revisited#average-case-vs.-worst-case) * [Recap](https://grokking.realtemirov.uz/4.-quicksort/4.-recap) ## 5. Hash tables * [Hash functions](https://grokking.realtemirov.uz/5.-hash-tables/1.-hash-functions) * [Use cases](https://grokking.realtemirov.uz/5.-hash-tables/2.-use-cases) * [Using hash tables for lookups](https://grokking.realtemirov.uz/5.-hash-tables/2.-use-cases#using-hash-tables-for-lookups) * [Preventing duplicate entries](https://grokking.realtemirov.uz/5.-hash-tables/2.-use-cases#preventing-duplicate-entries) * [Using hash tables as a cache](https://grokking.realtemirov.uz/5.-hash-tables/2.-use-cases#using-hash-tables-as-a-cache) * [Recap](https://grokking.realtemirov.uz/5.-hash-tables/2.-use-cases#recap) * [Collisions](https://grokking.realtemirov.uz/5.-hash-tables/3.-collisions) * [Performance](https://grokking.realtemirov.uz/5.-hash-tables/4.-performance) * [Load factor](https://grokking.realtemirov.uz/5.-hash-tables/4.-performance#load-factor) * [A good hash function](https://grokking.realtemirov.uz/5.-hash-tables/4.-performance#a-good-hash-function) * [Recap](https://grokking.realtemirov.uz/5.-hash-tables/5.-recap) ## 6. Breadth-first search * [Introduction to graph](https://grokking.realtemirov.uz/6.-breadth-first-search/1.-introduction-to-graph) * [What is a graph](https://grokking.realtemirov.uz/6.-breadth-first-search/2.-what-is-a-graph) * [Breadth-first search](https://grokking.realtemirov.uz/6.-breadth-first-search/3.-breadth-first-search) * [Finding the shortes path](https://grokking.realtemirov.uz/6.-breadth-first-search/3.-breadth-first-search#finding-the-shortes-path) * [Queues](https://grokking.realtemirov.uz/6.-breadth-first-search/3.-breadth-first-search#queues) * [Implementing the graph](https://grokking.realtemirov.uz/6.-breadth-first-search/4.-implementing-the-graph) * [Implementing the algorithm](https://grokking.realtemirov.uz/6.-breadth-first-search/5.-implementing-the-algorithm) * [Running time](https://grokking.realtemirov.uz/6.-breadth-first-search/5.-implementing-the-algorithm#running-time) * [Recap](https://grokking.realtemirov.uz/6.-breadth-first-search/6.-recap) ## 7. Dijkstra's algorithm * [Working with Dijkstra's algorithm](https://grokking.realtemirov.uz/7.-dijkstras-algorithm/1.-working-with-dijkstras-algorithm) * [Terminology](https://grokking.realtemirov.uz/7.-dijkstras-algorithm/2.-terminology) * [Trading for a piano](https://grokking.realtemirov.uz/7.-dijkstras-algorithm/3.-trading-for-a-piano) * [Negative-weight edges](https://grokking.realtemirov.uz/7.-dijkstras-algorithm/4.-negative-weight-edges) * [Implementation](https://grokking.realtemirov.uz/7.-dijkstras-algorithm/5.-implementation) * [Recap](https://grokking.realtemirov.uz/7.-dijkstras-algorithm/6.-recap) ## 8. Greedy Algorithms * [The classroom scheduling problem](https://grokking.realtemirov.uz/8.-greedy-algorithms/1.-the-classroom-scheduling-problem) * [The knapsack problem](https://grokking.realtemirov.uz/8.-greedy-algorithms/2.-the-knapsack-problem) * [The set-covering problem](https://grokking.realtemirov.uz/8.-greedy-algorithms/3.-the-set-covering-problem) * [Approximation algorithms](https://grokking.realtemirov.uz/8.-greedy-algorithms/3.-the-set-covering-problem#approximation-algorithms) * [NP-complete problems](https://grokking.realtemirov.uz/8.-greedy-algorithms/4.-np-complete-problems) * [Traveling salesperson, step by step](https://grokking.realtemirov.uz/8.-greedy-algorithms/5.-traveling-salesperson-step-by-step) * [How do you tell if a problem is NP-complete?](https://grokking.realtemirov.uz/8.-greedy-algorithms/5.-traveling-salesperson-step-by-step#how-do-you-tell-if-a-problem-is-np-complete) * [Recap](https://grokking.realtemirov.uz/8.-greedy-algorithms/6.-recap) ## 9. Dynamic programming * [The knapsack problem](https://grokking.realtemirov.uz/9.-dynamic-programming/1.-the-knapsack-problem) * [The simple solution](https://grokking.realtemirov.uz/9.-dynamic-programming/1.-the-knapsack-problem#the-simple-solution) * [Dynamic programming](https://grokking.realtemirov.uz/9.-dynamic-programming/1.-the-knapsack-problem#dynamic-programming) * [Knapsack problem FAQ](https://grokking.realtemirov.uz/9.-dynamic-programming/2.-knapsack-problem-faq) * [What happens if you add an item?](https://grokking.realtemirov.uz/9.-dynamic-programming/2.-knapsack-problem-faq#what-happens-if-you-add-an-item) * [What happens if you change the order of the rows?](https://grokking.realtemirov.uz/9.-dynamic-programming/2.-knapsack-problem-faq#what-happens-if-you-change-the-order-of-the-rows) * [Can you fill in the grid column-wise instead of row-wise?](https://grokking.realtemirov.uz/9.-dynamic-programming/2.-knapsack-problem-faq#can-you-fill-in-the-grid-column-wise-instead-of-row-wise) * [What happens if you add a smaller item?](https://grokking.realtemirov.uz/9.-dynamic-programming/2.-knapsack-problem-faq#what-happens-if-you-add-a-smaller-item) * [Can you steal fractions of an item?](https://grokking.realtemirov.uz/9.-dynamic-programming/2.-knapsack-problem-faq#can-you-steal-fractions-of-an-item) * [Optimizing your travel itinerary](https://grokking.realtemirov.uz/9.-dynamic-programming/2.-knapsack-problem-faq#optimizing-your-travel-itinerary) * [Handling items that depend on each other](https://grokking.realtemirov.uz/9.-dynamic-programming/2.-knapsack-problem-faq#handling-items-that-depend-on-each-other) * [Is it possible that the solution will require more than two sub-knapsacks?](https://grokking.realtemirov.uz/9.-dynamic-programming/2.-knapsack-problem-faq#is-it-possible-that-the-solution-will-require-more-than-two-sub-knapsacks) * [Is it possible that the best solution doesn't fill the knapsack completely?](https://grokking.realtemirov.uz/9.-dynamic-programming/2.-knapsack-problem-faq#is-it-possible-that-the-best-solution-doesnt-fill-the-knapsack-completely) * [Longest common substring](https://grokking.realtemirov.uz/9.-dynamic-programming/3.-longest-common-substring) * [Making the grid](https://grokking.realtemirov.uz/9.-dynamic-programming/3.-longest-common-substring#making-the-grid) * [Filling in the grid](https://grokking.realtemirov.uz/9.-dynamic-programming/3.-longest-common-substring#filling-in-the-grid) * [The solution](https://grokking.realtemirov.uz/9.-dynamic-programming/3.-longest-common-substring#the-solution) * [Longest common subsequence](https://grokking.realtemirov.uz/9.-dynamic-programming/3.-longest-common-substring#longest-common-subsequence) * [Longest common subsequence—solution](https://grokking.realtemirov.uz/9.-dynamic-programming/3.-longest-common-substring#longest-common-subsequencesolution) * [Recap](https://grokking.realtemirov.uz/12.-answers-to-exercises/chapter-2) ## 10. K-nearest neighbors * [Classifying oranges vs. grapefruit](https://grokking.realtemirov.uz/10.-k-nearest-neighbors/1.-classifying-oranges-vs.-grapefruit) * [Building a recommendations system](https://grokking.realtemirov.uz/10.-k-nearest-neighbors/2.-building-a-recommendations-system) * [Feature extraction](https://grokking.realtemirov.uz/10.-k-nearest-neighbors/2.-building-a-recommendations-system#feature-extraction) * [Regression](https://grokking.realtemirov.uz/10.-k-nearest-neighbors/2.-building-a-recommendations-system#regression) * [Picking good features](https://grokking.realtemirov.uz/10.-k-nearest-neighbors/2.-building-a-recommendations-system#picking-good-features) * [Introduction to machine learning](https://grokking.realtemirov.uz/10.-k-nearest-neighbors/3.-introduction-to-machine-learning) * [OCR](https://grokking.realtemirov.uz/10.-k-nearest-neighbors/3.-introduction-to-machine-learning#ocr) * [Building a spam filter](https://grokking.realtemirov.uz/10.-k-nearest-neighbors/3.-introduction-to-machine-learning#building-a-spam-filter) * [Predicting the stock market](https://grokking.realtemirov.uz/10.-k-nearest-neighbors/3.-introduction-to-machine-learning#predicting-the-stock-market) * [Recap](https://grokking.realtemirov.uz/10.-k-nearest-neighbors/4.-recap) ## 11. Where to go next * [Trees](https://grokking.realtemirov.uz/11.-where-to-go-next/1.-trees) * [Inverted indexes](https://grokking.realtemirov.uz/11.-where-to-go-next/2.-inverted-indexes) * [The Fourier transform](https://grokking.realtemirov.uz/11.-where-to-go-next/3.-the-fourier-transform) * [Parallel algorithms](https://grokking.realtemirov.uz/11.-where-to-go-next/4.-parallel-algorithms) * [MapReduce](https://grokking.realtemirov.uz/11.-where-to-go-next/5.-mapreduce) * [Why are distributed algorithms useful?](https://grokking.realtemirov.uz/11.-where-to-go-next/5.-mapreduce#why-are-distributed-algorithms-useful) * [The map function](https://grokking.realtemirov.uz/11.-where-to-go-next/5.-mapreduce#the-map-function) * [The reduce function](https://grokking.realtemirov.uz/11.-where-to-go-next/5.-mapreduce#the-reduce-function) * [Bloom filters and HyperLogLog](https://grokking.realtemirov.uz/11.-where-to-go-next/6.-bloom-filters-and-hyperloglog) * [Bloom filters](https://grokking.realtemirov.uz/11.-where-to-go-next/6.-bloom-filters-and-hyperloglog#bloom-filters) * [HyperLogLog](https://grokking.realtemirov.uz/11.-where-to-go-next/6.-bloom-filters-and-hyperloglog#hyperloglog) * [The SHA algorithms](https://grokking.realtemirov.uz/11.-where-to-go-next/7.-the-sha-algorithms) * [Comparing files](https://grokking.realtemirov.uz/11.-where-to-go-next/7.-the-sha-algorithms#comparing-files) * [Checking passwords](https://grokking.realtemirov.uz/11.-where-to-go-next/7.-the-sha-algorithms#checking-passwords) * [Locality-sensitive hashing](https://grokking.realtemirov.uz/11.-where-to-go-next/8.-locality-sensitive-hashing) * [Diffie-Hellman key exchange](https://grokking.realtemirov.uz/11.-where-to-go-next/9.-diffie-hellman-key-exchange) * [Linear programming](https://grokking.realtemirov.uz/11.-where-to-go-next/10.-linear-programming) * [Epilogue](https://grokking.realtemirov.uz/11.-where-to-go-next/11.-epilogue) ## Answers to exercises * [Chapter 1](https://grokking.realtemirov.uz/12.-answers-to-exercises/chapter-1) * [Chapter 2](https://grokking.realtemirov.uz/12.-answers-to-exercises/chapter-5) * [Chapter 3](https://grokking.realtemirov.uz/12.-answers-to-exercises/chapter-6) * [Chapter 4](https://grokking.realtemirov.uz/12.-answers-to-exercises/chapter-7) * [Chapter 5](https://grokking.realtemirov.uz/12.-answers-to-exercises/chapter-8) * [Chapter 6](https://grokking.realtemirov.uz/12.-answers-to-exercises/chapter-9) * [Chapter 7](https://grokking.realtemirov.uz/12.-answers-to-exercises/chapter-10) * [Chapter 8](https://grokking.realtemirov.uz/broken-reference) * [Chapter 9](https://grokking.realtemirov.uz/broken-reference) * [Chapter 10](https://grokking.realtemirov.uz/broken-reference) --- # Agent Instructions: Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter: ``` GET https://grokking.realtemirov.uz/readme.md?ask= ``` The question should be specific, self-contained, and written in natural language. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.