amortized-analysis

So when a dynamic array is doubled in size each time an element is added, I understand how the time complexity for expanding is O(n) n being the elements. What about if the the array is copied and moved to a new array that is only 1 size bigger when it is full? (instead of doubling) When we resize by some constant C, it the time complexity always O(n)? templatetypedef If you grow by some fixed constant C, then no, the runtime will not be O(n). Instead, it will be Θ(n 2 ). To see this, think about what happens if you do a sequence of C consecutive operations. Of those operations, C - 1 of them

Such structures are necessary for real-time applications - for example user interfaces. (Users don't care if clicking a button takes 0.1s or 0.2s, but they do care if the 100th click forces an outstanding lazy computation and takes 10s to proceed.) I was reading Okasaki's thesis Purely functional data structures and he describes an interesting general method for converting lazy data structures with amortized bounds into structures with the same worst-case bounds for every operation . The idea is to distribute computations so that at each update some portion of unevaluated thunks is forced. I

Here's a breakdown on the union/find algorithm for disjoint set forests on wikipedia : Barebone disjoint-set forests... ( O(n) ) ... with union by rank ... (now improved to O(log(n) ) ... with path compression (now improved to O(a(n)) , effectively O(1) ) Implementing union by rank necessitates that each node keeps a rank field for comparison purposes. My question is, is union by rank worth this additional space? What happens if I skip union by rank and just do path compression instead? Is it good enough? What is the amortized complexity now? A comment is made that implies that union by rank

I am currently reading amortized analysis. I am not able to fully understand how it is different from normal analysis we perform to calculate average or worst case behaviour of algorithms. Can someone explain it with an example of sorting or something ? Amortized analysis gives the average performance (over time) of each operation in the worst case. In a sequence of operations the worst case does not occur often in each operation - some operations may be cheap, some may be expensive Therefore, a traditional worst-case per operation analysis can give overly pessimistic bound. For example, in a

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 the analysis of algorithms. Anything useful, even if externally referenced, would be highly appreciated. Amortized complexity is the total expense per operation, evaluated over a sequence of operations. The idea is to guarantee the total expense of the entire sequence, while permitting individual operations to be much more expensive than the amortized cost. Example: The behavior of C++ std::vector<> . When push_back() increases

How is it different from asymptotic analysis? When do you use it, and why? I've read some articles that seem to have been written well, like these: http://www.ugrad.cs.ubc.ca/~cs320/2010W2/handouts/aa-nutshell.pdf http://www.cs.princeton.edu/~fiebrink/423/AmortizedAnalysisExplained_Fiebrink.pdf but I've still not understood fully these concepts. So, can anyone please simplify it for me? Amortized analysis doesn't naively multiply the number of invocations with the worst case for one invocation. For example, for a dynamic array that doubles in size when needed, normal asymptotic analysis would