## +23 ## Evolution of a Median Algorithm ## PETE ISENSEE ## 20 23 October 01 - 06 ## Output the median after the samples are collected ### cppreference.com ## Algorithms library The algorithms library been changed to return all potentially useful information computed during the execution of the algorithm. ## Execution policies Most algorithms have overloads that accept execution policies. The standard policy types and objects. Users may select an execution policy statically by invoking a parallel algorithm with an execution policy object of ## ChatGPT ## Brainstorm names for an orange cat we're

## CONSTRUCTING GENERIC ALGORITHMS ## algorithm noun al·go·rithm | \ 'al-gə-,ri-thəm ## Definition of algorithm : a procedure for solving a mathematical problem (as of finding the greatest common WE'LL COVER • Preliminaries: motivations etc • Case study: a nontrivial nonstandard algorithm • Principles for algorithm design • Some holes in the standard • Ponters to further work ## ALGORITHMS: THE ## THE PROBLEM Given an array of unique 61-bit integers in a random order, create a practical algorithm which returns an integer which is not in the array in linear time. From the board at CppCon 2019

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## Lecture 5: Gaussian Discriminant Analysis, Naive Bayes and EM Algorithm Feng Li Shandong University fli@sdu.edu.cn September 27, 2023 ## Outline  Expectation-Maximization (EM) Algorithm ## Probability Theory Review • Sample space, events and probability • Conditional probability bda_{i}\log(x_{i}) $$ $$ \log(E[X])\geq E[\log(X)] $$ ## The Expectation-Maximization (EM) Algorithm • A training set $ \{x^{(1)}, x^{(2)}, \cdots, x^{(m)}\} $ (without labels) • The log-likelihood

> __stl_threshold) { RandomAccessIterator cut = __unguarded_partition(first, last, T(__median(*first, *(first + (last - first)/2), *(last - 1), comp)), comp); if (cut - > __stl_threshold) { RandomAccessIterator cut = __unguarded_partition(first, last, T(__median(*first, *(*first + (last - first)/2), *(*last - 1), comp)), comp); if (cut - first >= > __stl_threshold) { RandomAccessIterator cut = __unguarded_partition(first, last, T(__median(*first, *(first + (last - first)/2), *(last - 1), comp)), comp); if (cut - first >= last

## Scalability # Computational Complexity Computational Complexity or simply Complexity of an algorithm is the amount of resources required to run it. - from Computational complexity in wikipedia ## n\to f(n) $$ n - is size of input $ f(n) $ - is the amount of resources required to run the algorithm Time - number of required elementary operations Often denoted by $T(n)$ or $t(n)$ Space - Amount unordered associative containers + requirements complexity of std::sort algorithm complexity of std::ranges::partition algorithm ## Then in CppReference (examples): complexity of std::vector::insert

ops with level parameter passed (GH545) • Ported skiplist data structure to C to speed up rolling_median by about 5-10x in most typical use cases (GH374) ###### 1.3 v.0.6.1 (December 13, 2011) #### 1.3 Out[236]: -0.28367872471747613 In [237]: s[:3] Out[237]: a -0.284 b -1.537 c 0.163 In [238]: s[s > s.median()] Out[238]: a -0.284 c 0.163 In [239]: s[[4, 3, 1]] Out[239]: e -1.703 d -0.648 b -1.537 In [240]: non-null observations| |sum|Sum of values| |mean|Mean of values| |mad|Mean absolute deviation| |median|Arithmetic median of values| |min|Minimum| |max|Maximum| |abs|Absolute Value| |prod|Product of values| |std|Unbiased

ops with level parameter passed (GH545) • Ported skiplist data structure to C to speed up rolling_median by about 5-10x in most typical use cases (GH374) ###### 1.5 v.0.6.1 (December 13, 2011) #### 1 Out[236]: -0.28367872471747613 In [237]: s[:3] Out[237]: a -0.284 b -1.537 c 0.163 In [238]: s[s > s.median()] Out[238]: a -0.284 c 0.163 In [239]: s[[4, 3, 1]] Out[239]: e -1.703 d -0.648 b -1.537 In [240]: non-null observations| |sum|Sum of values| |mean|Mean of values| |mad|Mean absolute deviation| |median|Arithmetic median of values| |min|Minimum| |max|Maximum| |abs|Absolute Value| |prod|Product of values| |std|Unbiased

ops with level parameter passed (GH545) • Ported skiplist data structure to C to speed up rolling_median by about 5-10x in most typical use cases (GH374) ###### 1.4 v.0.6.1 (December 13, 2011) #### 1 Out[236]: -0.28367872471747613 In [237]: s[:3] Out[237]: a -0.284 b -1.537 c 0.163 In [238]: s[s > s.median()] Out[238]: a -0.284 c 0.163 In [239]: s[[4, 3, 1]] Out[239]: e -1.703 d -0.648 b -1.537 In [240]: non-null observations| |sum|Sum of values| |mean|Mean of values| |mad|Mean absolute deviation| |median|Arithmetic median of values| |min|Minimum| |max|Maximum| |abs|Absolute Value| |prod|Product of values| |std|Unbiased

16 What is computer programming? ..... 17 What is a computer program? ..... 18 What is an algorithm? ..... 19 What is a programming language? ..... 20 Compilers and interpreters ..... 21 Types Integer to string conversion ..... 342 Minimum spanning tree ..... 352 The Prim algorithm ..... 353 Kruskal algorithm ..... 356 Disjoint-set data structure ..... 359 Kruskal with disjoint-set .. programming languages such as Algol, Fortran, C, Pascal, and Basic were created. ## What is an algorithm? An algorithm is a detailed sequence of instructions, often abstract, designed to solve a specific task