Is there a defined set of steps or principles on how to reduce time complexity of algorithms?
Just something to remember: You said &quot;could you make it faster (time complexity)&quot;. What counts in practice is the resources used for practical cases. Reducing the runtime by a factor ten may be extremely valuable, but doesn't reduce time complexity. It is in practice more valuable than reducing time complexity by a factor log log n.
Next thing to remember: In many cases &quot;could you make it faster&quot; has the valid response &quot;Probably, but I wouldn't bother&quot;. Making it faster takes time in money. The first step is to figure out whether it's worth the effort. Especially in an interview.
One method that works very well is called &quot;brute force and ignorance&quot;. It doesn't care about algorithms, but about making the identical code run faster. Removing all unneeded overhead. Check for cache usage and so on.
And the other method is finding better algorithms. O (n*n) can often be changed to O (n log n), which is massively better. And with really complicated algorithms, you may find some heuristics that improves it. For example, optimisation algorithms tend to work a lot better if you manage to start with a good solution that may be good enough to allow you showing that many other solutions cannot be optimal.
But general principles? No.