Recursive enumerations in Swift - Time & Space Complexity

Time Complexity: Recursive enumerations

O(n)

Understanding Time Complexity

When using recursive enumerations, it is important to understand how the number of steps grows as the data structure gets bigger.

We want to know how the time to process these recursive values changes with their size.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

indirect enum List {
  case end
  case node(Int, List)
}

func length(_ list: List) -> Int {
  switch list {
  case .end:
    return 0
  case let .node(_, tail):
    return 1 + length(tail)
  }
}
    

This code defines a recursive list and a function to count how many elements it has.

Identify Repeating Operations

• Primary operation: Recursive calls to length for each node in the list.
• How many times: Once for every element until the end of the list is reached.

How Execution Grows With Input

Each element in the list causes one recursive call, so the work grows directly with the number of elements.

Input Size (n)	Approx. Operations
10	10 calls
100	100 calls
1000	1000 calls

Pattern observation: The number of steps grows in a straight line with the size of the list.

Final Time Complexity

Time Complexity: O(n)

This means the time to count elements grows directly in proportion to the number of elements.

Common Mistake

[X] Wrong: "Recursive enumerations always cause exponential time because of recursion."

[OK] Correct: Here, each recursive call processes one element only once, so the time grows linearly, not exponentially.

Interview Connect

Understanding how recursion works with data structures like recursive enums helps you explain and reason about code clearly in interviews.

Self-Check

"What if the list was a tree with two recursive branches instead of one? How would the time complexity change?"

Practice

1. What does the indirect keyword do in a Swift recursive enumeration?

easy

A. It allows the enum to refer to itself recursively.

B. It makes the enum immutable.

C. It converts the enum into a class.

D. It prevents the enum from being used in switch statements.

Solution

1. Step 1: Understand the role of indirect

   The indirect keyword tells Swift that the enum cases can hold references to the enum itself, enabling recursion.

2. Step 2: Identify what recursion means in enums

   Recursion means an enum case can contain another instance of the same enum, which requires indirect to avoid infinite size.

3. Final Answer:

   It allows the enum to refer to itself recursively. -> Option A

4. Quick Check:

   indirect enables recursion = C [OK]

Hint: Remember: indirect means self-reference allowed [OK]

Common Mistakes:

• Thinking indirect makes enum immutable
• Confusing indirect with class conversion
• Believing indirect disables switch usage

2. Which of the following is the correct syntax to declare a recursive enum case in Swift?

easy

A. enum Tree { case leaf(Int); indirect case node(Tree, Tree) }

B. enum Tree { case leaf(Int); case node(Tree, Tree) }

C. enum Tree { indirect case leaf(Int); case node(Tree, Tree) }

D. indirect enum Tree { case leaf(Int); case node(Tree, Tree) }

Solution

1. Step 1: Recall how to declare recursive enums

   Swift allows marking the whole enum as indirect to enable recursion for all cases.

2. Step 2: Check each option's syntax

   The syntax indirect enum Tree { case leaf(Int); case node(Tree, Tree) } correctly enables recursion by marking the whole enum indirect. Other options either lack the keyword, apply it only to non-recursive cases (leaving recursive case without), or contain syntax errors such as missing the case keyword.

3. Final Answer:

   indirect enum Tree { case leaf(Int); case node(Tree, Tree) } -> Option D

4. Quick Check:

   Whole enum indirect = A [OK]

Hint: Use 'indirect enum' for all recursive cases [OK]

Common Mistakes:

• Omitting indirect keyword
• Placing indirect only on some cases incorrectly
• Using indirect outside enum declaration

3. Given the recursive enum below, what is the output of print(tree.countLeaves())?

indirect enum Tree {
    case leaf(Int)
    case node(Tree, Tree)

    func countLeaves() -> Int {
        switch self {
        case .leaf(_): return 1
        case let .node(left, right):
            return left.countLeaves() + right.countLeaves()
        }
    }
}

let tree = Tree.node(.leaf(1), Tree.node(.leaf(2), .leaf(3)))

medium

A. 1

B. 2

C. 3

D. 4

Solution

1. Step 1: Understand the tree structure

   The tree is: node(leaf(1), node(leaf(2), leaf(3))). It has three leaves: 1, 2, and 3.

2. Step 2: Count leaves recursively

   The countLeaves function returns 1 for each leaf and sums counts for nodes. So total leaves = 1 + (1 + 1) = 3.

3. Final Answer:

   3 -> Option C

4. Quick Check:

   Leaves counted = 3 [OK]

Hint: Count leaf nodes recursively for total leaves [OK]

Common Mistakes:

• Counting nodes instead of leaves
• Misunderstanding recursive calls
• Forgetting to sum both sides

4. Identify the error in this recursive enum declaration:

enum List {
    case end
    case node(Int, List)
}

medium

A. Missing indirect keyword for recursion.

B. Enum cases cannot have associated values.

C. The enum must be a class to be recursive.

D. The case end should have an associated value.

Solution

1. Step 1: Check for recursion support

   The enum List has a case node(Int, List) which refers to itself, so it is recursive.

2. Step 2: Verify use of indirect

   Swift requires marking recursive enums or cases with indirect. This enum lacks it, causing a compile error.

3. Final Answer:

   Missing indirect keyword for recursion. -> Option A

4. Quick Check:

   Recursive enum needs indirect = B [OK]

Hint: Add indirect to recursive enums or cases [OK]

Common Mistakes:

• Ignoring indirect keyword requirement
• Thinking recursion needs classes
• Assuming all enum cases need associated values

5. How would you modify this recursive enum to safely calculate the depth of a tree, returning 0 for leaves and the maximum depth for nodes?

indirect enum Tree {
    case leaf(Int)
    case node(Tree, Tree)

    func depth() -> Int {
        // Your code here
    }
}

hard

A. Return 1 for leaf, and sum depths of left and right nodes.

B. Return 0 for leaf, and 1 + max depth of left and right nodes.

C. Return 0 for leaf, and sum depths of left and right nodes.

D. Return 1 for leaf, and 1 + min depth of left and right nodes.

Solution

1. Step 1: Define depth for leaf nodes

   Leaves have depth 0 because they have no children.

2. Step 2: Define depth for node cases

   Nodes have depth 1 plus the maximum depth of their two child trees.

3. Final Answer:

   Return 0 for leaf, and 1 + max depth of left and right nodes. -> Option B

4. Quick Check:

   Depth = 0 for leaf, max + 1 for node = A [OK]

Hint: Depth = 0 leaf, 1 + max child depth node [OK]

Common Mistakes:

• Using sum instead of max for node depth
• Returning 1 for leaf depth incorrectly
• Using min instead of max for node depth