Explore introductory algorithms in computer science, covering searching, sorting, recursion, and graph theory, with visualizations, quizzes, and coding challenges in Java, Python, C++, or Javascript.

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Learn introductory computer science algorithms, including searching, sorting, recursion, and graph theory through a combination of articles, visualizations, quizzes, and coding challenges. Implement Challenges in Java, Python, C++ or Javascript.

A Visual Introduction to Algorithms

32 teams qualified for the 2014 World Cup. If the names of the teams were arranged in sorted order (an array), how many items in the array would binary search have to examine to find the location of a particular team in the array, in the worst case?

32 teams qualified for the 2014 World Cup. If the names of the teams were arranged in sorted order (an array), how many items in the array would binary search have to examine to find the location of a particular team in the array, in the worst case?

What is the base-2 logarithm of $32 (\log_2 (32))$?

What is the base-2 logarithm of <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>32</mn><mo stretchy="false">(</mo><msub><mrow><mi>log</mi><mo>⁡</mo></mrow><mn>2</mn></msub><mo stretchy="false">(</mo><mn>32</mn><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">32 (\log_2 (32))</annotation></semantics></math>32(log2​(32))?

You have an array containing the prime numbers from $2$ to $311$ in sorted order: $[2, 3, 5, 7, 11, 13, ..., 307, 311]$. There are 64 items in the array. About how many items of the array would binary search have to examine before concluding that $52$ is not in the array, and therefore not prime?

You have an array containing the prime numbers from <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn></mrow><annotation encoding="application/x-tex">2</annotation></semantics></math>2 to <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>311</mn></mrow><annotation encoding="application/x-tex">311</annotation></semantics></math>311 in sorted order: <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mn>2</mn><mo separator="true">,</mo><mn>3</mn><mo separator="true">,</mo><mn>5</mn><mo separator="true">,</mo><mn>7</mn><mo separator="true">,</mo><mn>11</mn><mo separator="true">,</mo><mn>13</mn><mo separator="true">,</mo><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mo separator="true">,</mo><mn>307</mn><mo separator="true">,</mo><mn>311</mn><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[2, 3, 5, 7, 11, 13, ..., 307, 311]</annotation></semantics></math>[2,3,5,7,11,13,...,307,311]. There are 64 items in the array. About how many items of the array would binary search have to examine before concluding that <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>52</mn></mrow><annotation encoding="application/x-tex">52</annotation></semantics></math>52 is not in the array, and therefore not prime?

In 2013, there were 193 member states in the United Nations. If the names of these states were sorted alphabetically in an array, about how many names would binary search examine to locate a particular name in the array, in the worst case?

In 2013, there were 193 member states in the United Nations. If the names of these states were sorted alphabetically in an array, about how many names would binary search examine to locate a particular name in the array, in the worst case?

The 2014 "Catalogue of Life" contains about 1580000 names of species. If these names were sorted in an array, in the worst case, how long would it take to use binary search to find the name of a particular species in the array?

The 2014 “Catalogue of Life” contains about 1580000 names of species. If these names were sorted in an array, in the worst case, how long would it take to use binary search to find the name of a particular species in the array?

Intro to Algorithms

Binary Search

Asymptotic Analysis

Selection Sort

Insertion Sort

Recursion Algorithms

Towers of Hanoi

Merge Sort

Quick Sort

Graphs

Breadth-first Search

License

Non-comparison based sorting algorithms

Quiz: Running time of binary search