Basic Algorithms and O Values

The efficiency of an algorithm is measured in two ways. The time complexity and space complexity. Big O accomplishes this. Most of what people know about Big O can be summed up in this: we want it to be small.

Many people have heard of Big O notation, but when I first learned about it, I did not feel like it was taught well enough for me to apply it to my existing knowledge of algorithms. The O in Big O simply refers to "order of magnitude". Big O simply is the worst case scenario of performance for the algorithm, and can be used to describe either time OR space that it takes one algorithm to complete.

A note about time and space:

Some algorithms for instance, will execute quickly, but they take up a lot of space because of the data structures involved. Other algorithms execute slowly but do not take up much space at all. A good example of the former would be a hash map or many large arrays, due to the need to store every value in the array. An example of the latter would be an algorithm that counts from 1 to a very large number. At any given time, the space is very small because it only needs to process a single number at a time, but the length to reach the very large number might be significant enough to slow the whole thing down. We value time and space together, because computers have limited space, and people have limited time. Simply put, code that takes large amounts of both are bad if it can be avoided.

Often when space isn't a problem, with modern computers, time becomes the more important factor. Sometimes loops can be cause for concern, because a formula exists that negates the need to run every operation in the loop, which takes that much extra time.