When we write computer programs, we want them to run as efficiently as possible. This means we need to understand how much time and space our programs will use. In computer science, we use the terms "time complexity" and "space complexity" to describe these properties of algorithms.
Time complexity
Time complexity refers to how much time an algorithm takes to complete as a function of its input size. In other words, it's a measure of how much computing power an algorithm requires to solve a problem.
Big O notation
To describe time complexity, we use something called "Big O notation". This is a way of expressing how the running time of an algorithm scales with the size of its input. We write it like this:
O(f(n))
where f(n) is some function of the input size. For example, if an algorithm takes n^2 time to complete, we would say its time complexity is O(n^2).
Examples
Here are a few examples of common time complexities, listed from fastest to slowest:
- O(1) - constant time
- O(log n) - logarithmic time
- O(n) - linear time
- O(n log n) - linearithmic time
- O(n^2) - quadratic time
- O(2^n) - exponential time
Space complexity
Space complexity refers to how much memory an algorithm needs to complete as a function of its input size. In other words, it's a measure of how much memory an algorithm requires to solve a problem.
Big O notation (again)
Just like with time complexity, we use Big O notation to describe space complexity. We write it like this:
O(g(n))
where g(n) is some function of the input size. For example, if an algorithm requires n units of memory, we would say its space complexity is O(n).
Examples
Here are a few examples of common space complexities, listed from lowest to highest:
- O(1) - constant space
- O(log n) - logarithmic space
- O(n) - linear space
- O(n^2) - quadratic space
- O(2^n) - exponential space
Conclusion
Understanding time and space complexity is essential for writing efficient algorithms. By analyzing the time and space requirements of our code, we can optimize it for better performance. Remember, faster algorithms mean happier users!
