I have been asked to construct a 2-3-4 tree from a sequence of elements in a top down and bottom up approach. I was able to do this as its quite straight forward.
Next, I was asked to analyse the running-time of the algorithms and also find out what the complexity of the problem is i.e. how fast can a 2-3-4 tree be constructed from a given sequence of elements? This is where it gets confusing for me, so far I understand the complexity to be O(logn) since the algorithm does not need to traverse the entire tree to insert new elements. However, how do I analyse the running time of the algorithm? I always thought running time and complexity to be sort of the same thing.