Polymorphism through functions in Python - Time & Space Complexity

Time Complexity: Polymorphism through functions

O(n)

Understanding Time Complexity

Let's explore how the time needed to run a function changes when it can work with different types of inputs.

We want to see how the function's work grows as the input size grows.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

def process(items):
    result = []
    for item in items:
        result.append(str(item))
    return result

values = [1, 2, 3, 4, 5]
print(process(values))

This function takes a list of items and converts each item to a string, collecting the results.

Identify Repeating Operations

• Primary operation: Looping through each item in the input list.
• How many times: Once for every item in the list.

How Execution Grows With Input

As the list gets bigger, the function does more work by converting more items.

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

Pattern observation: The work grows directly with the number of items.

Final Time Complexity

Time Complexity: O(n)

This means the time to finish grows in a straight line with the input size.

Common Mistake

[X] Wrong: "Polymorphism makes the function slower because it handles different types."

[OK] Correct: The function still processes each item once; the type difference does not add extra loops or steps.

Interview Connect

Understanding how functions handle different inputs without extra cost shows you know how to write flexible and efficient code.

Self-Check

"What if the function called another function inside the loop that itself loops over the item? How would the time complexity change?"

Practice

1.

What does polymorphism through functions mean in Python?

easy

A. Functions cannot be reused with different inputs

B. Multiple functions have the same name but different parameters

C. Functions can only accept one specific data type

D. A single function works with different data types

Solution

1. Step 1: Understand polymorphism concept

   Polymorphism means one function can handle different types of inputs.

2. Step 2: Relate to function behavior

   In Python, a single function can accept various data types and behave accordingly.

3. Final Answer:

   A single function works with different data types -> Option D

4. Quick Check:

   Polymorphism = single function, many types [OK]

Hint: Think: one function, many input types [OK]

Common Mistakes:

• Confusing polymorphism with function overloading
• Believing functions accept only one data type
• Mixing polymorphism with inheritance

2.

Which of the following is the correct way to check a variable's type inside a function for polymorphism?

def process(value):
    # What to use here?
    pass

easy

A. if type(value) == int:

B. if value is int:

C. if isinstance(value, int):

D. if value == int:

Solution

1. Step 1: Recall Python type checking methods

   Using isinstance() is the recommended way to check type in Python.

2. Step 2: Compare options

   if isinstance(value, int): uses isinstance(value, int), which correctly checks if value is an int or subclass.

3. Final Answer:

   if isinstance(value, int): -> Option C

4. Quick Check:

   Use isinstance() for type checks [OK]

Hint: Use isinstance() to check types safely [OK]

Common Mistakes:

• Using 'type() == int' which fails with subclasses
• Using 'is' or '==' incorrectly for type comparison
• Not checking type at all

3.

What is the output of this code?

def describe(value):
    if isinstance(value, int):
        return f"Integer: {value}"
    elif isinstance(value, str):
        return f"String: {value}"
    else:
        return "Unknown type"

print(describe(10))
print(describe('hello'))
print(describe(3.14))

medium

A. Integer: 10\nString: hello\nUnknown type

B. Integer: 10\nString: hello\nFloat: 3.14

C. Unknown type\nUnknown type\nUnknown type

D. Integer: 10\nUnknown type\nUnknown type

Solution

1. Step 1: Check input 10

   10 is int, so returns 'Integer: 10'.

2. Step 2: Check input 'hello'

   'hello' is str, so returns 'String: hello'.

3. Step 3: Check input 3.14

   3.14 is float, not int or str, so returns 'Unknown type'.

4. Final Answer:

   Integer: 10 String: hello Unknown type -> Option A

5. Quick Check:

   Type checks match outputs [OK]

Hint: Match isinstance checks to output lines [OK]

Common Mistakes:

• Assuming float is handled like int or str
• Ignoring else case output
• Mixing output order

4.

Find the error in this polymorphic function and fix it:

def process(value):
    if isinstance(value, int):
        return value * 2
    elif isinstance(value, str):
        return value + value
    else:
        return value / 2

print(process('abc'))
print(process([1, 2, 3]))

medium

A. No error; code runs fine

B. Error: Cannot divide list by 2; fix by handling list separately

C. Error: Missing return statement for int type

D. Error: Cannot multiply string by 2; fix by converting to int

Solution

1. Step 1: Analyze input 'abc'

   String input returns 'abcabc' by concatenation, no error.

2. Step 2: Analyze input [1, 2, 3]

   List input goes to else: value / 2, but dividing list by 2 causes TypeError.

3. Step 3: Fix the error

   Need to add a check for list type or avoid dividing list by 2.

4. Final Answer:

   Error: Cannot divide list by 2; fix by handling list separately -> Option B

5. Quick Check:

   List / 2 causes error [OK]

Hint: Check operations valid for each type [OK]

Common Mistakes:

• Assuming all types support division
• Not testing with different input types
• Ignoring TypeError exceptions

5.

Write a polymorphic function combine that accepts either two strings or two lists and returns their concatenation. What is the output of this code?

def combine(a, b):
    if isinstance(a, str) and isinstance(b, str):
        return a + b
    elif isinstance(a, list) and isinstance(b, list):
        return a + b
    else:
        return None

print(combine('Hi, ', 'there!'))
print(combine([1, 2], [3, 4]))
print(combine('Hello', [1, 2]))

hard

A. 'Hi, there!'\n[1, 2, 3, 4]\nNone

B. 'Hi, there!'\n[1, 2]\n[3, 4]

C. None\nNone\nNone

D. 'Hi, there!'\nNone\nNone

Solution

1. Step 1: Check first call combine('Hi, ', 'there!')

   Both are strings, so returns concatenation 'Hi, there!'.

2. Step 2: Check second call combine([1, 2], [3, 4])

   Both are lists, so returns concatenated list [1, 2, 3, 4].

3. Step 3: Check third call combine('Hello', [1, 2])

   Types differ, so returns None.

4. Final Answer:

   'Hi, there!' [1, 2, 3, 4] None -> Option A

5. Quick Check:

   Type checks control output [OK]

Hint: Check types of both inputs before combining [OK]

Common Mistakes:

• Not checking both inputs' types
• Trying to combine different types directly
• Returning wrong default for mismatched types