Numeric values (int and float behavior) in Python - Time & Space Complexity

Time Complexity: Numeric values (int and float behavior)

O(n^2)

Understanding Time Complexity

When working with numbers in Python, it helps to know how the time to do math grows as numbers get bigger.

We want to see how long it takes to add or multiply numbers as their size changes.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

num1 = 12345678901234567890
num2 = 98765432109876543210
result = num1 * num2
print(result)
    

This code multiplies two very large integers and prints the result.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Multiplying digits of large numbers internally.
• How many times: The multiplication process repeats roughly proportional to the number of digits in the numbers.

How Execution Grows With Input

As the numbers get more digits, the time to multiply grows more than just adding more digits.

Input Size (digits)	Approx. Operations
10	About 100 steps
100	About 10,000 steps
1000	About 1,000,000 steps

Pattern observation: Doubling digits roughly squares the work needed for multiplication.

Final Time Complexity

Time Complexity: O(n^2)

This means multiplying two numbers takes time roughly proportional to the square of their digit count.

Common Mistake

[X] Wrong: "Multiplying numbers always takes the same time no matter how big they are."

[OK] Correct: Bigger numbers have more digits, so the computer must do more steps to multiply them.

Interview Connect

Understanding how number size affects calculation time helps you explain efficiency clearly and shows you know what happens behind the scenes.

Self-Check

"What if we used floating-point numbers instead of integers? How would the time complexity change?"

Practice

1.

Which of the following is an example of a float in Python?

1. 42
2. 3.14
3. -7
4. 0

easy

A. 42

B. 3.14

C. -7

D. 0

Solution

1. Step 1: Understand what a float is

   A float is a number with a decimal point, like 3.14.

2. Step 2: Identify the float among options

   Only 3.14 has a decimal point, so it is a float.

3. Final Answer:

   3.14 -> Option B

4. Quick Check:

   Float = 3.14 [OK]

Hint: Floats always have a decimal point [OK]

Common Mistakes:

• Choosing integers as floats
• Confusing negative numbers with floats
• Ignoring decimal points

2.

Which of the following is the correct way to convert the float 5.7 to an integer in Python?

easy

A. float(5.7)

B. int(5,7)

C. int('5.7')

D. int(5.7)

Solution

1. Step 1: Recall how to convert float to int

   Use the int() function with a float value as argument.

2. Step 2: Check each option

   int(5.7) correctly converts float 5.7 to int 5. int('5.7') causes error, int(5,7) is invalid syntax.

3. Final Answer:

   int(5.7) -> Option D

4. Quick Check:

   int(5.7) = 5 [OK]

Hint: Use int() directly on float to convert [OK]

Common Mistakes:

• Trying int() on string with decimal
• Using wrong syntax like int(5,7)
• Using float() instead of int()

3.

What is the output of the following code?

x = 7 / 2
print(type(x))
print(x)

medium

A. <class 'int'>\n3.5

B. <class 'int'>\n3

C. <class 'float'>\n3.5

D. SyntaxError

Solution

1. Step 1: Understand division operator in Python 3

   Division with / always returns a float, even if numbers divide evenly.

2. Step 2: Evaluate the code

   7 / 2 = 3.5, which is a float. So type(x) is <class 'float'> and x is 3.5.

3. Final Answer:

   <class 'float'>\n3.5 -> Option C

4. Quick Check:

   7 / 2 = 3.5 float [OK]

Hint: Division / always returns float in Python 3 [OK]

Common Mistakes:

• Assuming integer division with /
• Confusing type output format
• Expecting 3 instead of 3.5

4.

Find the error in this code snippet:

num = 4.8
num_int = int(num)
print(num_int + ' is the integer value')

medium

A. Cannot add int and str directly

B. No error, code runs fine

C. Syntax error in print statement

D. Cannot convert float to int

Solution

1. Step 1: Check conversion from float to int

   int(4.8) converts float 4.8 to int 4 without error.

2. Step 2: Check print statement

   Adding int and string directly causes a TypeError in Python.

3. Final Answer:

   Cannot add int and str directly -> Option A

4. Quick Check:

   int + str causes TypeError [OK]

Hint: Convert int to str before adding to string [OK]

Common Mistakes:

• Thinking int() conversion fails
• Ignoring type mismatch in addition
• Assuming print syntax error

5.

You have a list of mixed numbers: nums = [1, 2.5, 3, 4.75, 5]. You want to create a new list with all numbers converted to integers by dropping decimals. Which code correctly does this?

hard

A. new_nums = [int(n) for n in nums]

B. new_nums = [float(n) for n in nums]

C. new_nums = [str(int(n)) for n in nums]

D. new_nums = [round(n) for n in nums]

Solution

1. Step 1: Understand the goal

   We want to convert all numbers to int by dropping decimals, not rounding.

2. Step 2: Evaluate each option

   C uses int() which drops decimals correctly. A converts to string, not int. B converts to float, not int. D rounds numbers, which changes values.

3. Final Answer:

   new_nums = [int(n) for n in nums] -> Option A

4. Quick Check:

   int() drops decimals, list comprehension applies to all [OK]

Hint: Use int() in list comprehension to drop decimals [OK]

Common Mistakes:

• Using round() instead of int()
• Converting to string instead of int
• Using float() which keeps decimals