Mastering Big O Notation: Time Complexity and Run Time Demystified - Part 2
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"Big O notation" is a mathematical notation used in computer science to describe the performance or complexity of an algorithm. Specifically, it's used to describe the worst-case scenario, or the maximum amount of time that an algorithm could potentially take to complete.
In Big O notation:
O(1) refers to constant time complexity. It doesn't matter how large the input is, the time taken is always the same. An example is accessing an element from an array by its index.
O(N) refers to linear time complexity. The time taken grows proportionally with the size of the input. An example is searching for a specific item in an unsorted list.
O(log N) refers to logarithmic time complexity. The time taken increases logarithmically with the input size. An example is a binary search in a sorted list.
O(N log N) refers to linearithmic time complexity. The time taken increases linearly and logarithmically with the input size. An example is the quicksort or mergesort algorithm.
O(N^2) refers to quadratic time complexity. The time taken grows with the square of the input size. An example is a simple bubble sort algorithm.
O(2^N) refers to exponential time complexity. The time taken doubles with each addition to the input data set. An example is the naive recursive calculation of Fibonacci numbers.
O(N!) refers to factorial time complexity. The time taken grows factorially with the input size. An example is the brute-force search algorithm for the travelling salesman problem.
Remember that Big O notation gives an upper bound of the complexity in the worst-case scenario, helping us to understand how the time complexity scales when the size of the input increases.
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