Constant Time: O(1)

Grokking Algorithm Complexity and Big-O

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Constant Time: O(1)

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Constant Time Complexity $O(1)$ describes operations or algorithms that take the same amount of time to execute, no matter the size of the input. It’s the fastest time complexity because it remains unaffected by how large or small the input is.

Key Characteristics

In an Algorithm with $O(1)$ time complexity:

Fixed Steps: The algorithm performs a constant number of steps, independent of the input size.
Common Use: This complexity type appears frequently in simple operations that don’t involve iteration over the input, such as lookups or single computations.

Code Example

Here’s a code example that demonstrates $O(1)$ complexity. This example returns the first element of a list.

Python3

. . . .

Explanation: The get_first_element function accesses the first element of arr. Whether arr has 1 element or 1 million elements, it performs a single access and optional check.
Why $O(1)$ ? The number of steps remains the same, regardless of the size of arr.

Examples of $O(1)$ operations

Accessing an element in an array by its index.
Checking a condition or assigning a value.
Returning a specific value without further computation.

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Table of Contents

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Key Characteristics

Code Example

Examples of O(1) operations

Examples of $O(1)$ operations