Methods with return values in Python - Time & Space Complexity

Time Complexity: Methods with return values

O(n)

Understanding Time Complexity

When we use methods that return values, it is important to see how long they take to run as the input grows.

We want to know how the time to get the return value changes when the input gets bigger.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

def sum_list(numbers):
    total = 0
    for num in numbers:
        total += num
    return total

result = sum_list([1, 2, 3, 4, 5])
print(result)

This method adds up all numbers in a list and returns the total sum.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Looping through each number in the list once.
• How many times: Exactly once for each item in the input list.

How Execution Grows With Input

As the list gets longer, the method takes longer because it adds each number one by one.

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

Pattern observation: The time grows directly with the number of items. Double the items, double the work.

Final Time Complexity

Time Complexity: O(n)

This means the time to get the return value grows in a straight line with the input size.

Common Mistake

[X] Wrong: "Since the method just returns a value, it must be very fast no matter the input size."

[OK] Correct: The method still does work inside, like looping through the list, so bigger inputs take more time.

Interview Connect

Understanding how methods with return values scale helps you explain your code clearly and shows you know how to write efficient programs.

Self-Check

"What if the method used recursion instead of a loop? How would the time complexity change?"

Practice

1. What does a method with a return statement do in Python?

easy

A. It sends a value back to where the method was called.

B. It prints a value on the screen.

C. It stops the program immediately.

D. It creates a new variable automatically.

Solution

1. Step 1: Understand the purpose of return

   The return statement sends a value back from the method to the caller.

2. Step 2: Differentiate from printing or stopping

   Printing shows output but does not send a value back; stopping ends execution.

3. Final Answer:

   It sends a value back to where the method was called. -> Option A

4. Quick Check:

   Method return = sends value back [OK]

Hint: Return sends value back, print shows it only [OK]

Common Mistakes:

• Confusing return with print
• Thinking return stops the program
• Believing return creates variables

2. Which of the following is the correct syntax for a method that returns the sum of two numbers a and b?

easy

A. def add(a, b): return a - b

B. def add(a, b): print(a + b)

C. def add(a, b): return a + b

D. def add(a, b): a + b

Solution

1. Step 1: Identify correct return usage

   The method must use return to send back the sum a + b.

2. Step 2: Check each option

   The version with return a - b returns the difference. The version with print(a + b) prints but returns None. The version with just a + b lacks return. Only def add(a, b): return a + b correctly returns the sum.

3. Final Answer:

   def add(a, b): return a + b -> Option C

4. Quick Check:

   Return sum = def add(a, b): return a + b [OK]

Hint: Return must be followed by value to send back [OK]

Common Mistakes:

• Using print instead of return
• Omitting return keyword
• Returning wrong expression

3. What is the output of this code?

def multiply(x, y):
    return x * y

result = multiply(3, 4)
print(result)

medium

A. 7

B. 12

C. 34

D. None

Solution

1. Step 1: Understand the method call

   The method multiply returns the product of 3 and 4, which is 12.

2. Step 2: Print the returned value

   The variable result stores 12, so print(result) outputs 12.

3. Final Answer:

   12 -> Option B

4. Quick Check:

   3 * 4 = 12 [OK]

Hint: Multiply inputs, return result, print shows it [OK]

Common Mistakes:

• Adding instead of multiplying
• Printing None by missing return
• Confusing string concatenation with multiplication

4. Find the error in this method and choose the correct fix:

def greet(name):
    print("Hello, " + name)

message = greet("Alice")
print(message)

medium

A. Remove the argument name from the method.

B. Add print before calling greet.

C. Change message to greet in the last print.

D. Change print to return inside the method.

Solution

1. Step 1: Identify the problem with return value

   The method prints but does not return a value, so message is None.

2. Step 2: Fix by returning the greeting string

   Replace print with return to send the greeting back.

3. Final Answer:

   Change print to return inside the method. -> Option D

4. Quick Check:

   Return greeting to assign message [OK]

Hint: Use return to get value, not print [OK]

Common Mistakes:

• Expecting print to return a value
• Removing needed parameters
• Changing variable names incorrectly

5. You want to write a method that returns a dictionary with keys as numbers from 1 to n and values as their squares. Which method below correctly does this?

hard

A. def squares(n):
result = {}
for i in range(1, n+1):
result[i] = i * i
return result

B. def squares(n):
result = []
for i in range(n):
result.append(i * i)
return result

C. def squares(n):
return {i: i + i for i in range(1, n)}

D. def squares(n):
for i in range(1, n+1):
print(i * i)

Solution

1. Step 1: Understand the requirement

   The method must return a dictionary with keys 1 to n and values as squares.

2. Step 2: Check each option

   The loop building result = {}, setting result[i] = i * i for i in range(1, n+1), and returning result is correct. Returning a list fails. The comprehension {i: i + i for i in range(1, n)} uses doubles instead of squares and misses key n. Printing without returning fails.

3. Final Answer:

   def squares(n): result = {} for i in range(1, n+1): result[i] = i * i return result -> Option A

4. Quick Check:

   Return dict with squares = def squares(n): result = {} for i in range(1, n+1): result[i] = i * i return result [OK]

Hint: Return dict with keys and squares using loop [OK]

Common Mistakes:

• Returning list instead of dict
• Using wrong range limits
• Printing instead of returning