Nested functions in Swift - Time & Space Complexity

Time Complexity: Nested functions

O(n²)

Understanding Time Complexity

When we use nested functions, we want to know how the time it takes to run grows as the input gets bigger.

We ask: How does calling a function inside another affect the total work done?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

func outerFunction(_ n: Int) {
    func innerFunction(_ m: Int) {
        for i in 0..

This code defines a function inside another. The outer function calls the inner one multiple times, each time with a different number.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The inner loop inside innerFunction that runs from 0 to m.
• How many times: The outer loop calls innerFunction n times, with m changing from 0 up to n-1.

How Execution Grows With Input

Each time the outer loop runs, the inner loop runs more times than before.

Input Size (n)	Approx. Operations
10	About 45 prints (0+1+2+...+9)
100	About 4,950 prints
1000	About 499,500 prints

Pattern observation: The total work grows roughly like the sum of numbers from 0 to n-1, which grows much faster than just n.

Final Time Complexity

Time Complexity: O(n²)

This means if you double the input size, the work roughly quadruples because of the nested calls.

Common Mistake

[X] Wrong: "Since the inner function runs inside the outer loop, the time is just O(n) because it looks like one loop inside another."

[OK] Correct: The inner loop runs a different number of times each call, adding up to much more than just n times. It's the total sum of all inner loops that matters.

Interview Connect

Understanding how nested functions affect time helps you explain your code clearly and shows you can think about efficiency in real problems.

Self-Check

"What if the inner function always ran a fixed number of times, say 10, no matter the input? How would the time complexity change?"

Practice

1. What is a nested function in Swift?

easy

A. A function that calls itself

B. A function that returns another function

C. A function defined inside another function

D. A function defined outside any class or struct

Solution

1. Step 1: Understand the definition of nested functions

   Nested functions are functions written inside other functions to organize code better.

2. Step 2: Match the definition to the options

   A function defined inside another function correctly describes a function inside another function, which is the definition of nested functions.

3. Final Answer:

   A function defined inside another function -> Option C

4. Quick Check:

   Nested function = function inside function [OK]

Hint: Nested means inside another function [OK]

Common Mistakes:

• Confusing nested with recursive functions
• Thinking nested functions are global
• Mixing nested with returning functions

2. Which of the following is the correct syntax to define a nested function in Swift?

easy

A. func outer() { func inner() { } }

B. func outer() { func inner; }

C. func outer() { inner func() { } }

D. func outer() { func inner() }

Solution

1. Step 1: Review Swift function syntax

   Functions are defined with 'func name() { }'. Nested functions follow the same syntax inside another function.

2. Step 2: Check each option for correct syntax

   func outer() { func inner() { } } uses correct syntax with braces for both outer and inner functions. Others have missing braces or wrong order.

3. Final Answer:

   func outer() { func inner() { } } -> Option A

4. Quick Check:

   Nested function syntax = func inside func with braces [OK]

Hint: Look for 'func' with braces inside another function [OK]

Common Mistakes:

• Omitting braces for inner function
• Using semicolon instead of braces
• Placing 'func' keyword incorrectly

3. What will be the output of the following Swift code?

func greet() {
    func sayHello() {
        print("Hello")
    }
    sayHello()
}
greet()

medium

A. Hello

B. No output

C. Error: sayHello not found

D. HelloHello

Solution

1. Step 1: Understand function calls inside nested functions

   The outer function 'greet' defines 'sayHello' inside it and calls it once.

2. Step 2: Trace the execution

   Calling 'greet()' runs 'sayHello()', which prints "Hello" once.

3. Final Answer:

   Hello -> Option A

4. Quick Check:

   Nested call prints once = Hello [OK]

Hint: Inner function called once inside outer function [OK]

Common Mistakes:

• Thinking inner function runs twice
• Assuming inner function is global
• Expecting no output because inner function is nested

4. Identify the error in this Swift code using nested functions:

func calculate() {
    innerFunc() 
    func innerFunc() {
        print("Inside inner")
    }
}
calculate()

medium

A. No error, code runs fine

B. Missing return type for innerFunc

C. innerFunc cannot be nested inside calculate

D. innerFunc() called before its definition causes error

Solution

1. Step 1: Analyze function call order

   The code calls 'innerFunc()' before it is defined inside 'calculate()'. Swift requires functions to be defined before use.

2. Step 2: Understand Swift's function declaration rules

   Calling a nested function before its declaration causes a compile-time error.

3. Final Answer:

   innerFunc() called before its definition causes error -> Option D

4. Quick Check:

   Call before definition = error [OK]

Hint: Define nested functions before calling them [OK]

Common Mistakes:

• Assuming nested functions can be called before definition
• Thinking missing return type causes error here
• Believing nested functions can't be defined inside

5. How can you use nested functions to create a function that returns another function which adds a fixed number to its input? Choose the correct Swift code.

hard

A. func makeAdder(_ x: Int) -> Int { func adder(y: Int) -> Int { return x + y } return adder(5) }

B. func makeAdder(_ x: Int) -> (Int) -> Int { func adder(y: Int) -> Int { return x + y } return adder }

C. func makeAdder(_ x: Int) -> (Int) -> Int { return func(y: Int) -> Int { x + y } }

D. func makeAdder(_ x: Int) -> (Int) -> Int { func adder(y: Int) -> Int { return y } return adder }

Solution

1. Step 1: Understand the goal

   We want a function that returns another function adding a fixed number 'x' to input 'y'.

2. Step 2: Check each option's logic

   func makeAdder(_ x: Int) -> (Int) -> Int { func adder(y: Int) -> Int { return x + y } return adder } defines nested 'adder' using 'x' and returns it correctly. func makeAdder(_ x: Int) -> Int { func adder(y: Int) -> Int { return x + y } return adder(5) } returns a value, not a function. func makeAdder(_ x: Int) -> (Int) -> Int { return func(y: Int) -> Int { x + y } } has invalid syntax. func makeAdder(_ x: Int) -> (Int) -> Int { func adder(y: Int) -> Int { return y } return adder } returns a function ignoring 'x'.

3. Final Answer:

   func makeAdder(_ x: Int) -> (Int) -> Int { func adder(y: Int) -> Int { return x + y } return adder } -> Option B

4. Quick Check:

   Nested function returns function adding x = func makeAdder(_ x: Int) -> (Int) -> Int { func adder(y: Int) -> Int { return x + y } return adder } [OK]

Hint: Return nested function that uses outer parameter [OK]

Common Mistakes:

• Returning a value instead of a function
• Incorrect nested function syntax
• Ignoring outer function parameter inside nested function