List (Sequence)

AKA: Sequence, \(a_n\) where n is the nth element, (1,2,3, ….)

Distinct from: Set

Measure of:

Description: A list is a collection of objects with a specific ordering and where the same object can appear more than once. Call each object an element, and its location its index or rank. An index is a natural number counting upward from the first element in the list. Whether counting begins at 0 or 1 depends on local conventions.

Formalization:

Algorithm:

Cites: Wikipedia Wikidata Encyclopedia Of Math Wolfram PlanetMath

R

Documentation:

list: Lists – Generic and Dotted Pairs

Examples:

example_list = list(1,2,3)
example_list

[[1]]
[1] 1

[[2]]
[1] 2

[[3]]
[1] 3

Sorting a list in R Sorting or Ordering Vectors

You can specify auto, shell, quick, or radix algorithms. Auto typically chooses radix. Radix applies to lexigraphical data, e.g. string and numbers. Radix has \(O(nw)\) time where \(n\) is the number of keys and \(w\) is the length of the keys.

Fast, stable and scalable true radix sorting

*Radix because it’s fast for R’s use case

*It is stable. Stable sorts preserve the original order of two elements if they are equal by the sorting criteria.

temp <- 5:1
sort(temp)

[1] 1 2 3 4 5

Python

Documentation:

More on Lists

Examples:

example_list =  [1,2,3]
example_list

[1, 2, 3]

The ‘range’ function returns a generator for integers from between start to (stop-1). It’ll do reverse as well but you have to pass a third decrement term. The Python range() Function (Guide)

[q for q in range(5,10)]

[5, 6, 7, 8, 9]

[q for q in range(10,5,-1)]

[10, 9, 8, 7, 6]

Python lists have to ways to sort, in palce with “sort” or returning a new list with “sorted”. Sorting HOW TO

Python uses Timsort whose best case is \(O(n)\) and worst and average case are both \(O(nlog(n))\)

temp=[q for q in range(10,5,-1)]
temp

[10, 9, 8, 7, 6]

temp.sort()
temp

[6, 7, 8, 9, 10]

temp=[q for q in range(10,5,-1)]
sorted(temp)

[6, 7, 8, 9, 10]

SQL

library(DBI)
# Create an ephemeral in-memory RSQLite database
con <- dbConnect(RSQLite::SQLite(), dbname = ":memory:")
dbListTables(con)

character(0)

dbWriteTable(con, "mtcars", mtcars)
dbListTables(con)

[1] "mtcars"

create table StatisticalNumbers(
 value int
)

SELECT * FROM mtcars LIMIT 5;

5 records

mpg	cyl	disp	hp	drat	wt	qsec	vs	am	gear	carb
21.0	6	160	110	3.90	2.620	16.46	0	1	4	4
21.0	6	160	110	3.90	2.875	17.02	0	1	4	4
22.8	4	108	93	3.85	2.320	18.61	1	1	4	1
21.4	6	258	110	3.08	3.215	19.44	1	0	3	1
18.7	8	360	175	3.15	3.440	17.02	0	0	3	2