# Background

This question is similar to this one. I have provided all of the information needed below. If you are familiar with the other challenge then note that we are ranking all defenses instead of seeing the effectiveness of a single attack. This is important because it means that the tables are inverses of each other and the goal of this challenge is to be without user input.

In Pokemon there are 18 types:

Normal    Fighting  Flying  Poison  Ground  Rock
Bug       Ghost     Steel   Fire    Water   Grass
Electric  Psychic   Ice     Dragon  Dark    Fairy


Pokemon have either one or two unique types that define them (a "type combination"). For example, a Bulbasaur has the type combination Grass/Poison (it has two types, Grass and Poison) and a Charmander has the type combination Fire (having just one type). The order of types does not matter (i.e. Grass/Poison is the same as Poison/Grass).

These types all have strengths and weaknesses:

• A type can be weak to another type. Fire is weak against Water. This results in Fire having a 2× multiplier against Water.
• A type can be resistant to another type. Water is resistant to Water. This results in Water having a 0.5× multiplier against Water.
• A type can be immune to another type. Flying is immune to Ground. This results in Flying having a 0× multiplier against Ground.

Anything else receives a standard 1× multiplier. Normal against Normal would result in a 1× multiplier is an example of this. These strengths and weaknesses can be compounded or negated as well. For example, Fire is weak to Water but a Fire/Water dual type would have a 1× multiplier against Water since the weakness from Fire would negate the resistance from Water. For a full table and a further explanation, see below.

# Objective

The goal here is to output a list of all types combinations, sorted in the order of their defensive ability, and listing their numbers of (resistances+immunities), weaknesses, and the ratio between those. Specifically, the sort order is as follows: type combinations with the best ratio of (resistances+immunities) to weaknesses are listed first, and if there is a tie, type combinations with the most resistances and immunities will win the tiebreak. You can produce this list via any means (an obvious method is to do a type effectiveness calculation against each type combination, but you are allowed to store precalculated or partially precalculated output in your program if doing so would make it shorter.)

# Type effectiveness table

For a human readable table, see the Pokemon database. Note: the columns of this list are what we are considering. But just in case, here is the table I'm thinking of in a compressed computer-friendly matrix of effectiveness. I've multiplied every value by 2 so we don't have to deal with pesky decimals:

           Attacking type
(same order)
Nor   222222422222202222
Fir   214211224221422211
D  Wat   211441222222222212
e  Ele   222122224122222212
f  Gra   241114241424222222
e  Ice   242221422222422242
n  Fig   222222222441122124
d  Poi   222212114241222221
i  Gro   224044212222122222
n  Fly   222414120221422222
g  Psy   222222122214242422
Bug   242212121422422222
T  Roc   114242414122222242
y  Gho   022222012221242422
p  Dra   211114222222224224
e  Dar   222222422204212124
Ste   142211404111121211
Fai   222222142221220142


# Example

If this problem had requested only output for single-type type combinations, then a valid output would look like this:

Steel -> 11/3 = 3.66
Electric -> 3/1 = 3
Poison -> 5/2 = 2.5
Fire -> 6/3 = 2
Water -> 4/2 = 2
Ghost -> 4/2 = 2
Fairy -> 4/2 = 2
Fly -> 4/3 = 1.333
Dragon -> 4/3 = 1.333
Fighting -> 3/3 = 1
Normal -> 1/1 = 1
Ground -> 3/3 = 1
Psychic -> 2/2 = 1
Bug -> 3/3 = 1
Dark -> 3/3 = 1
Grass -> 4/5 = 0.8
Rock -> 4/5 = 0.8
Ice -> 1/4 = 0.25


However, your program will also need to list all of the dual-type combinations in the output, so its output will be considerably longer.

Best of luck! Shortest code in bytes wins.

• Related. – Martin Ender Nov 20 '16 at 22:06
• And welcome to PPCG! :) – Martin Ender Nov 20 '16 at 22:06
• I think this has the obvious problem that the answer is smaller than the data needed to solve the question, and thus a winning solution will just hardcode the output. In order to solve the issue, you probably need to change the challenge to take the type effectiveness matrix as input at runtime. – user62131 Nov 20 '16 at 22:17
• @ais523 I believe compressing the matrix is supposed to be the core of the challenge, and in principle I see nothing wrong with that (although in this case, unfortunately, this exact table has been the subject of a challenge before). – Martin Ender Nov 20 '16 at 22:21
• @MartinEnder It's more than related... If you go over the introduction it's 100% copied and then altered to not look like it's copied. It follows the exact same structure, the starting types are in the same order, formatted the same. It's just blatant plagiarizing without mentioning it and trying to hide it. – orlp Nov 21 '16 at 12:37

## Python 2, 784 bytes

i=['Normal','222222422222202222'],['Fire','214211224221422211'],['Water','211441222222222212'],['Electric','222122224122222212'],['Grass','241114241424222222'],['Ice','242221422222422242'],['Fighting','222222222441122124'],['Poison','222212114241222221'],['Ground','224044212222122222'],['Flying','222414120221422222'],['Psychic','222222122214242422'],['Bug','242212121422422222'],['Rock','114242414122222242'],['Ghost','022222012221242422'],['Dragon','211114222222224224'],['Dark','222222422204212124'],['Steel','142211404111121211'],['Fairy','222222142221220142']
L=[]
for x,X in i:
for y,Y in i[i.index([x,X]):]:
S=W=0.
for a,b in zip(X,Y):A=int(a)*int(b);W+=A>4;S+=A<4
L+=[([x+'/'+y,x][x==y]+' -> %d/%d'%(S,W),S/W)]
for l in sorted(L, key=lambda l:-l[1]):print'%s = %.2f'%l


Outputs:

Bug/Steel -> 9/1 = 9.00
Steel/Fairy -> 11/2 = 5.50
Normal/Ghost -> 5/1 = 5.00
Water/Ground -> 5/1 = 5.00
Grass/Steel -> 10/2 = 5.00
Poison/Dark -> 5/1 = 5.00
Poison/Steel -> 10/2 = 5.00
Flying/Steel -> 10/2 = 5.00
Dragon/Steel -> 10/2 = 5.00
Normal/Steel -> 12/3 = 4.00
Electric/Poison -> 8/2 = 4.00
Electric/Steel -> 12/3 = 4.00
Ghost/Dark -> 4/1 = 4.00
Water/Steel -> 11/3 = 3.67
Dark/Steel -> 11/3 = 3.67
Steel -> 11/3 = 3.67
Fire/Steel -> 10/3 = 3.33
Fire/Ground -> 6/2 = 3.00
Water/Flying -> 6/2 = 3.00
Electric -> 3/1 = 3.00
Electric/Flying -> 6/2 = 3.00
Electric/Fairy -> 6/2 = 3.00
Ice/Steel -> 9/3 = 3.00
Fighting/Steel -> 9/3 = 3.00
Rock/Steel -> 9/3 = 3.00
Ghost/Steel -> 12/4 = 3.00
Fire/Electric -> 8/3 = 2.67
Water/Poison -> 8/3 = 2.67
Normal/Poison -> 5/2 = 2.50
Water/Electric -> 5/2 = 2.50
Poison -> 5/2 = 2.50
Ground/Flying -> 5/2 = 2.50
Ground/Steel -> 10/4 = 2.50
Psychic/Steel -> 10/4 = 2.50
Fire/Flying -> 7/3 = 2.33
Water/Fairy -> 7/3 = 2.33
Electric/Ghost -> 7/3 = 2.33
Normal/Electric -> 4/2 = 2.00
Normal/Fairy -> 4/2 = 2.00
Fire -> 6/3 = 2.00
Fire/Poison -> 8/4 = 2.00
Fire/Bug -> 6/3 = 2.00
Fire/Fairy -> 8/4 = 2.00
Water -> 4/2 = 2.00
Water/Ghost -> 8/4 = 2.00
Electric/Bug -> 4/2 = 2.00
Fighting/Poison -> 6/3 = 2.00
Poison/Fairy -> 6/3 = 2.00
Psychic/Ghost -> 4/2 = 2.00
Ghost -> 4/2 = 2.00
Ghost/Fairy -> 4/2 = 2.00
Dragon/Fairy -> 8/4 = 2.00
Fairy -> 4/2 = 2.00
Fire/Ghost -> 9/5 = 1.80
Normal/Fire -> 7/4 = 1.75
Fire/Rock -> 7/4 = 1.75
Fire/Dark -> 7/4 = 1.75
Poison/Dragon -> 7/4 = 1.75
Normal/Water -> 5/3 = 1.67
Fire/Water -> 5/3 = 1.67
Fire/Dragon -> 5/3 = 1.67
Water/Bug -> 5/3 = 1.67
Electric/Fighting -> 5/3 = 1.67
Ghost/Dragon -> 8/5 = 1.60
Fire/Fighting -> 6/4 = 1.50
Water/Dragon -> 3/2 = 1.50
Electric/Dragon -> 6/4 = 1.50
Electric/Dark -> 6/4 = 1.50
Poison/Ground -> 6/4 = 1.50
Poison/Flying -> 6/4 = 1.50
Poison/Rock -> 6/4 = 1.50
Poison/Ghost -> 6/4 = 1.50
Ground/Fairy -> 6/4 = 1.50
Flying/Dragon -> 6/4 = 1.50
Rock/Fairy -> 6/4 = 1.50
Fire/Psychic -> 7/5 = 1.40
Water/Fighting -> 7/5 = 1.40
Water/Dark -> 7/5 = 1.40
Grass/Fairy -> 7/5 = 1.40
Fighting/Dragon -> 7/5 = 1.40
Dragon/Dark -> 7/5 = 1.40
Normal/Flying -> 4/3 = 1.33
Fire/Grass -> 4/3 = 1.33
Fighting/Dark -> 4/3 = 1.33
Poison/Psychic -> 4/3 = 1.33
Ground/Dragon -> 4/3 = 1.33
Flying -> 4/3 = 1.33
Dragon -> 4/3 = 1.33
Dark/Fairy -> 4/3 = 1.33
Normal/Dragon -> 5/4 = 1.25
Water/Rock -> 5/4 = 1.25
Electric/Ground -> 5/4 = 1.25
Electric/Psychic -> 5/4 = 1.25
Electric/Rock -> 5/4 = 1.25
Grass/Poison -> 5/4 = 1.25
Fighting/Bug -> 5/4 = 1.25
Fighting/Ghost -> 5/4 = 1.25
Poison/Bug -> 5/4 = 1.25
Flying/Dark -> 5/4 = 1.25
Water/Psychic -> 6/5 = 1.20
Grass/Ghost -> 6/5 = 1.20
Ground/Ghost -> 6/5 = 1.20
Flying/Rock -> 6/5 = 1.20
Flying/Ghost -> 6/5 = 1.20
Flying/Fairy -> 6/5 = 1.20
Bug/Ghost -> 6/5 = 1.20
Bug/Fairy -> 6/5 = 1.20
Normal -> 1/1 = 1.00
Normal/Fighting -> 4/4 = 1.00
Normal/Ground -> 4/4 = 1.00
Normal/Psychic -> 2/2 = 1.00
Normal/Bug -> 3/3 = 1.00
Normal/Rock -> 5/5 = 1.00
Normal/Dark -> 3/3 = 1.00
Fire/Ice -> 4/4 = 1.00
Water/Grass -> 3/3 = 1.00
Electric/Grass -> 4/4 = 1.00
Grass/Fighting -> 6/6 = 1.00
Grass/Dark -> 7/7 = 1.00
Ice/Poison -> 5/5 = 1.00
Ice/Ghost -> 5/5 = 1.00
Ice/Fairy -> 4/4 = 1.00
Fighting -> 3/3 = 1.00
Fighting/Flying -> 5/5 = 1.00
Fighting/Fairy -> 5/5 = 1.00
Ground -> 3/3 = 1.00
Ground/Bug -> 4/4 = 1.00
Ground/Rock -> 6/6 = 1.00
Ground/Dark -> 6/6 = 1.00
Psychic/Dragon -> 6/6 = 1.00
Psychic/Fairy -> 3/3 = 1.00
Bug -> 3/3 = 1.00
Bug/Dragon -> 5/5 = 1.00
Bug/Dark -> 5/5 = 1.00
Rock/Ghost -> 6/6 = 1.00
Rock/Dark -> 7/7 = 1.00
Dark -> 3/3 = 1.00
Grass/Psychic -> 6/7 = 0.86
Fighting/Rock -> 6/7 = 0.86
Normal/Grass -> 5/6 = 0.83
Grass/Bug -> 5/6 = 0.83
Fighting/Ground -> 5/6 = 0.83
Ground/Psychic -> 5/6 = 0.83
Rock/Dragon -> 5/6 = 0.83
Grass -> 4/5 = 0.80
Grass/Flying -> 4/5 = 0.80
Flying/Psychic -> 4/5 = 0.80
Flying/Bug -> 4/5 = 0.80
Rock -> 4/5 = 0.80
Electric/Ice -> 3/4 = 0.75
Grass/Ground -> 3/4 = 0.75
Ice/Flying -> 3/4 = 0.75
Ice/Bug -> 3/4 = 0.75
Psychic/Rock -> 5/7 = 0.71
Grass/Dragon -> 4/6 = 0.67
Ice/Rock -> 4/6 = 0.67
Ice/Dark -> 4/6 = 0.67
Fighting/Psychic -> 2/3 = 0.67
Psychic -> 2/3 = 0.67
Psychic/Bug -> 4/6 = 0.67
Bug/Rock -> 2/3 = 0.67
Ice/Dragon -> 3/5 = 0.60
Grass/Ice -> 4/7 = 0.57
Normal/Ice -> 2/4 = 0.50
Water/Ice -> 2/4 = 0.50
Grass/Rock -> 2/4 = 0.50
Ice/Fighting -> 3/6 = 0.50
Psychic/Dark -> 1/2 = 0.50
Ice/Ground -> 2/5 = 0.40
Ice/Psychic -> 2/6 = 0.33
Ice -> 1/4 = 0.25

• Awesome. Exactly what I wanted. Thanks mate! – Devin White Nov 29 '16 at 13:40