Merge pull request kodecocodes#117 from vinayjn/master

Replaced Array2D with swift 2d array

Author: Chris Pilcher

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)

Combinatorics/Combinatorics.swift

@@ -100,21 +100,22 @@ func quickBinomialCoefficient(n: Int, _ k: Int) -> Int {
   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]
 }

Combinatorics/README.markdown

@@ -366,26 +366,26 @@ The following code calculates Pascal's triangle in order to find the `C(n, k)` y
 
 ```swift
 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]
 }
 ```
 
-This uses [Array2D](../Array2D/) as helper code because Swift doesn't have a built-in two-dimensional array. The algorithm itself is quite simple: the first loop fills in the 1s at the outer edges of the triangle. The other loops calculate each number in the triangle by adding up the two numbers from the previous row.
+The algorithm itself is quite simple: the first loop fills in the 1s at the outer edges of the triangle. The other loops calculate each number in the triangle by adding up the two numbers from the previous row.
 
 Now you can calculate `C(66, 33)` without any problems: