Changed Array2d to Swift standard 2d array in playground

Author: vinayjn

Combinatorics/Combinatorics.playground/Contents.swift

@@ -2,13 +2,13 @@
 
 /* Calculates n! */
 func factorial(n: Int) -> Int {
-  var n = n
-  var result = 1
-  while n > 1 {
-    result *= n
-    n -= 1
-  }
-  return result
+    var n = n
+    var result = 1
+    while n > 1 {
+        result *= n
+        n -= 1
+    }
+    return result
 }
 
 factorial(5)
@@ -17,17 +17,17 @@ factorial(20)
 
 
 /*
-  Calculates P(n, k), the number of permutations of n distinct symbols
-  in groups of size k.
-*/
+ Calculates P(n, k), the number of permutations of n distinct symbols
+ in groups of size k.
+ */
 func permutations(n: Int, _ k: Int) -> Int {
-  var n = n
-  var answer = n
-  for _ in 1..<k {
-    n -= 1
-    answer *= n
-  }
-  return answer
+    var n = n
+    var answer = n
+    for _ in 1..<k {
+        n -= 1
+        answer *= n
+    }
+    return answer
 }
 
 permutations(5, 3)
@@ -37,22 +37,22 @@ permutations(9, 4)
 
 
 /*
-  Prints out all the permutations of the given array.
-  Original algorithm by Niklaus Wirth.
-  See also Dr.Dobb's Magazine June 1993, Algorithm Alley
-*/
+ Prints out all the permutations of the given array.
+ Original algorithm by Niklaus Wirth.
+ See also Dr.Dobb's Magazine June 1993, Algorithm Alley
+ */
 func permuteWirth<T>(a: [T], _ n: Int) {
-  if n == 0 {
-    print(a)   // display the current permutation
-  } else {
-    var a = a
-    permuteWirth(a, n - 1)
-    for i in 0..<n {
-      swap(&a[i], &a[n])
-      permuteWirth(a, n - 1)
-      swap(&a[i], &a[n])
+    if n == 0 {
+        print(a)   // display the current permutation
+    } else {
+        var a = a
+        permuteWirth(a, n - 1)
+        for i in 0..<n {
+            swap(&a[i], &a[n])
+            permuteWirth(a, n - 1)
+            swap(&a[i], &a[n])
+        }
     }
-  }
 }
 
 let letters = ["a", "b", "c", "d", "e"]
@@ -66,30 +66,30 @@ permuteWirth(xyz, 2)
 
 
 /*
-  Prints out all the permutations of an n-element collection.
-
-  The initial array must be initialized with all zeros. The algorithm
-  uses 0 as a flag that indicates more work to be done on each level
-  of the recursion.
-
-  Original algorithm by Robert Sedgewick.
-  See also Dr.Dobb's Magazine June 1993, Algorithm Alley
-*/
+ Prints out all the permutations of an n-element collection.
+ 
+ The initial array must be initialized with all zeros. The algorithm
+ uses 0 as a flag that indicates more work to be done on each level
+ of the recursion.
+ 
+ Original algorithm by Robert Sedgewick.
+ See also Dr.Dobb's Magazine June 1993, Algorithm Alley
+ */
 func permuteSedgewick(a: [Int], _ n: Int, inout _ pos: Int) {
-  var a = a
-  pos += 1
-  a[n] = pos
-  if pos == a.count - 1 {
-    print(a)              // display the current permutation
-  } else {
-    for i in 0..<a.count {
-      if a[i] == 0 {
-        permuteSedgewick(a, i, &pos)
-      }
+    var a = a
+    pos += 1
+    a[n] = pos
+    if pos == a.count - 1 {
+        print(a)              // display the current permutation
+    } else {
+        for i in 0..<a.count {
+            if a[i] == 0 {
+                permuteSedgewick(a, i, &pos)
+            }
+        }
     }
-  }
-  pos -= 1
-  a[n] = 0
+    pos -= 1
+    a[n] = 0
 }
 
 print("\nSedgewick permutations:")
@@ -100,35 +100,35 @@ permuteSedgewick(numbers, 0, &pos)
 
 
 /*
-  Calculates C(n, k), or "n-choose-k", i.e. how many different selections
-  of size k out of a total number of distinct elements (n) you can make.
-*/
+ Calculates C(n, k), or "n-choose-k", i.e. how many different selections
+ of size k out of a total number of distinct elements (n) you can make.
+ */
 func combinations(n: Int, _ k: Int) -> Int {
-  return permutations(n, k) / factorial(k)
+    return permutations(n, k) / factorial(k)
 }
 
 combinations(3, 2)
 combinations(28, 5)
 
 print("\nCombinations:")
 for i in 1...20 {
-  print("\(20)-choose-\(i) = \(combinations(20, i))")
+    print("\(20)-choose-\(i) = \(combinations(20, i))")
 }
 
 
 
 /*
-  Calculates C(n, k), or "n-choose-k", i.e. the number of ways to choose
-  k things out of n possibilities.
-*/
+ Calculates C(n, k), or "n-choose-k", i.e. the number of ways to choose
+ k things out of n possibilities.
+ */
 func quickBinomialCoefficient(n: Int, _ k: Int) -> Int {
-  var result = 1
+    var result = 1
 
-  for i in 0..<k {
-    result *= (n - i)
-    result /= (i + 1)
-  }
-  return result
+    for i in 0..<k {
+        result *= (n - i)
+        result /= (i + 1)
+    }
+    return result
 }
 
 quickBinomialCoefficient(8, 2)
@@ -138,47 +138,48 @@ quickBinomialCoefficient(30, 15)
 
 /* Supporting code because Swift doesn't have a built-in 2D array. */
 struct Array2D<T> {
-  let columns: Int
-  let rows: Int
-  private var array: [T]
-  
-  init(columns: Int, rows: Int, initialValue: T) {
-    self.columns = columns
-    self.rows = rows
-    array = .init(count: rows*columns, repeatedValue: initialValue)
-  }
-  
-  subscript(column: Int, row: Int) -> T {
-    get { return array[row*columns + column] }
-    set { array[row*columns + column] = newValue }
-  }
+    let columns: Int
+    let rows: Int
+    private var array: [T]
+    
+    init(columns: Int, rows: Int, initialValue: T) {
+        self.columns = columns
+        self.rows = rows
+        array = .init(count: rows*columns, repeatedValue: initialValue)
+    }
+    
+    subscript(column: Int, row: Int) -> T {
+        get { return array[row*columns + column] }
+        set { array[row*columns + column] = newValue }
+    }
 }
 
 /*
-  Calculates C(n, k), or "n-choose-k", i.e. the number of ways to choose
-  k things out of n possibilities.
+ Calculates C(n, k), or "n-choose-k", i.e. the number of ways to choose
+ k things out of n possibilities.
+ 
+ Thanks to the dynamic programming, this algorithm from Skiena allows for
+ the calculation of much larger numbers, at the cost of temporary storage
+ space for the cached values.
+ */
 
-  Thanks to the dynamic programming, this algorithm from Skiena allows for
-  the calculation of much larger numbers, at the cost of temporary storage
-  space for the cached values.
-*/
 func binomialCoefficient(n: Int, _ k: Int) -> Int {
-  var bc = Array2D(columns: n + 1, rows: n + 1, initialValue: 0)
-  
-  for i in 0...n {
-    bc[i, 0] = 1
-    bc[i, i] = 1
-  }
-  
-  if n > 0 {
-    for i in 1...n {
-      for j in 1..<i {
-        bc[i, j] = bc[i - 1, j - 1] + bc[i - 1, j]
-      }
+    var bc = Array(count: n + 1, repeatedValue: Array(count: n + 1, repeatedValue: 0))
+    
+    for i in 0...n {
+        bc[i][0] = 1
+        bc[i][i] = 1
     }
-  }
-  
-  return bc[n, k]
+    
+    if n > 0 {
+        for i in 1...n {
+            for j in 1..<i {
+                bc[i][j] = bc[i - 1][j - 1] + bc[i - 1][j]
+            }
+        }
+    }
+    
+    return bc[n][k]
 }
 
 binomialCoefficient(30, 15)