Lulu Arrays — Unions, Intersections, Differences

Introduction

If you have imported the lulu.Array class as

local Array = require 'lulu.Array'

Then, you can use the following methods to combine Arrays:

Array:union(...)
Returns a new Array that has all the values from the arguments (without any duplicates).
Any non-table argument will be treated as single element array.

Array:intersection(...)
Returns a new Array that holds the common values from the arguments (without any duplicates).
Any non-table argument will be treated as single element array.

Array:difference(other, symmetric)
Returns a new Array that holds the elements of self that are not in other where other can be an Array or a plain Lua array.

These methods only consider each clement’s value when looking for commonality and differences. This contrasts with the table.union, table.intersection and table.difference methods which consider both the element index and the value.

Generally a:difference(b) ~= b:difference(a).

We sometimes refer to a:difference(b) as \(a - b\).

By default, the boolean symmetric argument is false. You can set it to true to get the symmetric difference between \(a\) and \(b\): \[ a - b \cup b - a. \] That is the array of the elements that occurs only in one of a or b.

Example

local a1 = Array{1,2,3,4}
local a2 = Array{3,4,5,6}
putln("a1:                          %t", a1)
putln("a2:                          %t", a2)
putln("Union         a1,  a2:       %t", a1:union(a2))
putln("Append        a1,  a2:       %t", a1:append(a2))
putln("Intersection  a1,  a2:       %t", a1:intersection(a2))
putln("Difference    a1 - a2:       %t", a1:difference(a2))
putln("Difference    a2 - a1:       %t", a2:difference(a1))
putln("Symmetric difference a1, a2: %t", a1:difference(a2, true))
putln("Symmetric difference a2, a1: %t", a2:difference(a1, true))

Outputs:

a1:                          [1, 2, 3, 4]
a2:                          [3, 4, 5, 6]
Union         a1,  a2:       [1, 2, 3, 4, 5, 6]
1Append        a1,  a2:       [1, 2, 3, 4, 3, 4, 5, 6]
Intersection  a1,  a2:       [3, 4, 5, 6]
Difference    a1 - a2:       [1, 2]
Difference    a2 - a1:       []
Symmetric difference a1, a2: [1, 2]
Symmetric difference a2, a1: [1, 2]

1: The Array:append method just appends a2 to a1 which means there is duplication in this example.

Now look at the same example using table.union, table.intersection and table.difference.

local a1 = Array{1,2,3,4}
local a2 = Array{3,4,5,6}
putln("a1:                          %t", a1)
putln("a2:                          %t", a2)
putln("Union         a1,  a2:       %t", table.union(a1, a2))
putln("Intersection  a1,  a2:       %t", table.intersection(a1, a2))
putln("Difference    a1 - a2:       %t", table.difference(a1, a2))
putln("Difference    a2 - a1:       %t", table.difference(a2, a1))
putln("Symmetric difference a1, a2: %t", table.difference(a1, a2, true))
putln("Symmetric difference a1, a2: %t", table.difference(a2, a1, true))

Outputs

a1:                          [1, 2, 3, 4]
a2:                          [3, 4, 5, 6]
1Union         a1,  a2:       {{1, 3}, {2, 4}, {3, 5}, {4, 6}}
2Intersection  a1,  a2:       {}
Difference    a1 - a2:       {1, 2, 3, 4}
Difference    a2 - a1:       {3, 4, 5, 6}
Symmetric difference a1, a2: {{1, 3}, {2, 4}, {3, 5}, {4, 6}}
Symmetric difference a1, a2: {{3, 1}, {4, 2}, {5, 3}, {6, 4}}

1: There are multiple values for the index keys 1,2,3 and 4.
2: The common values are not at the same index position in the two arrays so the intersection is empty as far as table is concerned.

Introduction

Example

See Also