Constant Space: O(1)

Grokking Algorithm Complexity and Big-O

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Constant Space: O(1)

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Constant Space Complexity $O(1)$ describes algorithms that require a fixed amount of memory, regardless of the input size. This means that no matter how large the input gets, the algorithm only uses a constant, limited amount of additional memory.

Constant space complexity is common in algorithms that use a fixed number of variables or operate in-place on the input data without needing extra memory for structures like arrays or lists.

Key Characteristics

In an algorithm with $O(1)$ space complexity:

Memory usage remains constant, regardless of the size of the input.
The algorithm typically only requires a fixed number of variables or performs operations in-place on the input.

In an algorithm with $O(1)$ space complexity:

Code Example: Swapping Two Variables

The following function swaps two variables without using additional memory, demonstrating an algorithm with $O(1)$ space complexity.

Python3

. . . .

Explanation:
- The swap function swaps the values of a and b using arithmetic operations instead of an extra variable.
- This function only requires the memory for a and b, regardless of their values, so it uses $O(1)$ space.

Examples of $O(1)$ operations

Accessing Array Elements: Retrieving a specific element in an array by index doesn’t require additional memory.
Updating a Single Variable: Modifying a counter or assigning a value to a variable requires constant space.
In-Place Operations: Algorithms that modify data directly in the input array without using extra memory (e.g., reversing an array in place) use $O(1)$ space.

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Table of Contents

Contents are not accessible

Key Characteristics

Code Example: Swapping Two Variables

Examples of O(1) operations

Examples of $O(1)$ operations