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Generalized solution to creating k-sized sub/supersets from a given set

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0

$begingroup$

In this code for a Set Game, using nested for-loops seems inevitable. But suppose there were more properties to provide for the Card initializer, the pyramid of nested loops would grow even bigger.

A possible solution could be to generate all the possible k-sized sub/supersets from the initial set, and then loop through them:

func combinations<C: Collection>(sized k: Int, from collection: C) -> [[C.Element]] 
 var result: [[C.Element]] = [[]]
 var lastCount = 1
 while result[result.count - 1].count < k 
 for i in result.indices.suffix(lastCount) 
 for element in collection 
 result.append(result[i] + [element])
 
 
 lastCount *= collection.count
 
 return Array(result.suffix(lastCount))

A deck of cards would be created like so:

struct Card 
 let number: Int
 let symbol: Int
 let color: Int
 let shading: Int


var deck: [Card] = combinations(sized: 4, from: 1..<3)
 .map Card(number : $0[0],
 symbol : $0[1],
 color : $0[2],
 shading : $0[3])

The advantage of this approach is that it could be used to concoct subsets as well as supersets :

for comb in combinations(sized: 5, from: ["a", "b", "c"]) 
 print(comb.joined()) //"aaaaa", "aaaab", ... , "ccccc"
 

//Or if you're feeling artsy
combinations(sized: 2, from: [UIColor.red, UIColor.green, UIColor.blue])

The one limitation is that it quickly goes slow for higher k or collection.count since this is an O(n^k) algorithm I believe (n being the collection count). Is there a better way?

Feedback on all aspects of the code is welcome, such as (but not limited to):

• Efficiency,


• Readability,


• Naming.

performance swift

share|improve this question

edited 20 mins ago

ielyamani

asked 26 mins ago

ielyamaniielyamani

372213

$endgroup$

add a comment | 

0

$begingroup$

In this code for a Set Game, using nested for-loops seems inevitable. But suppose there were more properties to provide for the Card initializer, the pyramid of nested loops would grow even bigger.

A possible solution could be to generate all the possible k-sized sub/supersets from the initial set, and then loop through them:

func combinations<C: Collection>(sized k: Int, from collection: C) -> [[C.Element]] 
 var result: [[C.Element]] = [[]]
 var lastCount = 1
 while result[result.count - 1].count < k 
 for i in result.indices.suffix(lastCount) 
 for element in collection 
 result.append(result[i] + [element])
 
 
 lastCount *= collection.count
 
 return Array(result.suffix(lastCount))

A deck of cards would be created like so:

struct Card 
 let number: Int
 let symbol: Int
 let color: Int
 let shading: Int


var deck: [Card] = combinations(sized: 4, from: 1..<3)
 .map Card(number : $0[0],
 symbol : $0[1],
 color : $0[2],
 shading : $0[3])

The advantage of this approach is that it could be used to concoct subsets as well as supersets :

for comb in combinations(sized: 5, from: ["a", "b", "c"]) 
 print(comb.joined()) //"aaaaa", "aaaab", ... , "ccccc"
 

//Or if you're feeling artsy
combinations(sized: 2, from: [UIColor.red, UIColor.green, UIColor.blue])

The one limitation is that it quickly goes slow for higher k or collection.count since this is an O(n^k) algorithm I believe (n being the collection count). Is there a better way?

Feedback on all aspects of the code is welcome, such as (but not limited to):

• Efficiency,


• Readability,


• Naming.

performance swift

share|improve this question

edited 20 mins ago

ielyamani

asked 26 mins ago

ielyamaniielyamani

372213

$endgroup$

add a comment | 

$begingroup$

In this code for a Set Game, using nested for-loops seems inevitable. But suppose there were more properties to provide for the Card initializer, the pyramid of nested loops would grow even bigger.

A possible solution could be to generate all the possible k-sized sub/supersets from the initial set, and then loop through them:

func combinations<C: Collection>(sized k: Int, from collection: C) -> [[C.Element]] 
 var result: [[C.Element]] = [[]]
 var lastCount = 1
 while result[result.count - 1].count < k 
 for i in result.indices.suffix(lastCount) 
 for element in collection 
 result.append(result[i] + [element])
 
 
 lastCount *= collection.count
 
 return Array(result.suffix(lastCount))

A deck of cards would be created like so:

struct Card 
 let number: Int
 let symbol: Int
 let color: Int
 let shading: Int


var deck: [Card] = combinations(sized: 4, from: 1..<3)
 .map Card(number : $0[0],
 symbol : $0[1],
 color : $0[2],
 shading : $0[3])

The advantage of this approach is that it could be used to concoct subsets as well as supersets :

for comb in combinations(sized: 5, from: ["a", "b", "c"]) 
 print(comb.joined()) //"aaaaa", "aaaab", ... , "ccccc"
 

//Or if you're feeling artsy
combinations(sized: 2, from: [UIColor.red, UIColor.green, UIColor.blue])

The one limitation is that it quickly goes slow for higher k or collection.count since this is an O(n^k) algorithm I believe (n being the collection count). Is there a better way?

Feedback on all aspects of the code is welcome, such as (but not limited to):

• Efficiency,


• Readability,


• Naming.

performance swift

share|improve this question

edited 20 mins ago

ielyamani

asked 26 mins ago

ielyamaniielyamani

372213

$endgroup$

func combinations<C: Collection>(sized k: Int, from collection: C) -> [[C.Element]] 
 var result: [[C.Element]] = [[]]
 var lastCount = 1
 while result[result.count - 1].count < k 
 for i in result.indices.suffix(lastCount) 
 for element in collection 
 result.append(result[i] + [element])
 
 
 lastCount *= collection.count
 
 return Array(result.suffix(lastCount))

struct Card 
 let number: Int
 let symbol: Int
 let color: Int
 let shading: Int


var deck: [Card] = combinations(sized: 4, from: 1..<3)
 .map Card(number : $0[0],
 symbol : $0[1],
 color : $0[2],
 shading : $0[3])

for comb in combinations(sized: 5, from: ["a", "b", "c"]) 
 print(comb.joined()) //"aaaaa", "aaaab", ... , "ccccc"
 

//Or if you're feeling artsy
combinations(sized: 2, from: [UIColor.red, UIColor.green, UIColor.blue])

share|improve this question

edited 20 mins ago

ielyamani

asked 26 mins ago

ielyamaniielyamani

372213

share|improve this question

edited 20 mins ago

ielyamani

asked 26 mins ago

ielyamaniielyamani

372213

asked 26 mins ago

ielyamaniielyamani

372213

asked 26 mins ago

ielyamaniielyamani

372213