Big O Notation -

Big O notation is used to describe the time or space complexity of an algorithm in terms of input size. Here are the common types of Big O complexities, ordered from best (fastest) to worst (slowest) in terms of performance:

Constant Time – O(1)

• Description: The algorithm takes the same amount of time regardless of input size.
• Example: Accessing an element in an array by index.

🔹 Logarithmic Time – O(log n)

• Description: The time grows logarithmically as input size increases.
• Example: Binary search in a sorted array.

🔹 Linear Time – O(n)

• Description: Time increases linearly with input size.
• Example: Looping through an array.

🔹 Linearithmic Time – O(n log n)

• Description: A combination of linear and logarithmic growth.
• Example: Efficient sorting algorithms like Merge Sort, Quick Sort (average case).

🔹 Quadratic Time – O(n²)

• Description: Time increases with the square of the input size.
• Example: Nested loops over the same data, like Bubble Sort.

🔹 Cubic Time – O(n³)

• Description: Time increases with the cube of the input size.
• Example: Triple nested loops, such as in some matrix operations.

🔹 Exponential Time – O(2ⁿ)

• Description: Time doubles with each additional input element.
• Example: Solving the Traveling Salesman Problem using brute force.

🔹 Factorial Time – O(n!)

• Description: Time grows factorially with input size.
• Example: Generating all permutations of a set.