Big O Simply Explained

in #whereinlast month

Big O Notation is a must known concept in software engineer algorithm complexity analysis. You will be asked the Big O during your software engineer interview, for sure.

Big O notation is a simplification and approximation for assessing algorithmic efficiency for memory and time based on the algorithm inputs. The important bit there is "inputs". You use the bigO to try and figure out how an algorithm will scale with large inputs. Often people use "n" as a variable for big O, but this is really just a variable that needs to be defined, perhaps a variable for one of your inputs. In this case "n" is n = s.length. If you have multiple inputs in which you are looping on, your big O needs to factor those in. In your example, the only variable we care about on the loop is "s.length".

Often in the real world when assessing algorithms you really care about constant O(1), logarithmic O(logn), linear O(n) and exponential O(n^x). Usually any exponential function just doesn't scale. It is fine to use for things where n is small or maybe not a critical function in something that needs to be performant but its worth considering. I haven't seen in many cases where exponential algorithms are broken down more finitely but I am sure it does happen on some systems where a complex graph problem is the core problem of a solution.

With that said, big O is strictly a way to categorize and bucketize algorithms. There are some algorithms with quite complex big O notations if there is multiple inputs being looped on in some form or manner. If you think about it from a math perspective, if you have a 2d chart where x axis is your input "n" and the y axis is time. What shape shape does your algorithm make on the chart with different "n" inputs.

If your algorithm is constant, logarithmic, linear, or exponential, it always makes the same shape. O(n) and O(50000n) make the same shape. So we classify these as being the same, linear.

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