Amortized complexity in layman's terms?

Question

Can someone explain amortized complexity in layman\'s terms? I\'ve been having a hard time finding a precise definition online and I don\'t know how it entirely relates to

Answer 1

The principle of "amortized complexity" is that although something may be quite complex when you do it, since it's not done very often, it's considered "not complex". For example, if you create a binary tree that needs balancing from time to time - say once every 2^n insertions - because although balancing the tree is quite complex, it only happens once in every n insertions (e.g once at insertion number 256, then again at 512th, 1024th, etc). On all other insertions, the complexity is O(1) - yes, it takes O(n) once every n insertions, but it's only 1/n probability - so we multiply O(n) by 1/n and get O(1). So that is said to be "Amortized complexity of O(1)" - because as you add more elements, the time consumed for rebalancing the tree is minimal.