Author: ignougroup

Problem Detail: I have been told than $n^{1000001} = O(1.000001^n)$. If that’s the case, there must be some value $n$ at which $1.000001^n$ exceeds $n^{1000001}$. However, when I consult Wolfram Alpha, I get a negative value for when that occurs. http://www.wolframalpha.com/input/?i=1.000001%5Ex+%3D+x%5E1000001 Read More …

Problem Detail: Dynamic programming algorithm for Knapsack is stated to have complexity $mathcal O (nW)$. However, I’ve also seen the complexity stated as $mathcal O (n^2V)$, where $V=max v_i$. (Here $n$ is the number of items and $W$ the weight limit). Read More …

Problem Detail: I have to generate a grammar for the language $L = { w in { a, b}^* mid |w| in 2mathbb{N}, w neq w^R}$ and give the type of the language. I’ve generated the grammar $qquad begin{align} S &to Read More …

Problem Detail: I was wondering if finding if a graph has k or more isolated nodes is a NP-Complete problem. I found the following problem: Prove that the following problem is NP-Complete. Given a set of T transactions: $T = {t_1,t_2,dots,t_m}$ Read More …

Problem Detail: In a lecture a professor mentioned that modern computers don’t have as much computational power as a Turing machine because they don’t have infinite memory, and since no computer can have infinite memory the Turing machine is therefore unattainable Read More …

Problem Detail: I’ve learned today that algorithm analysis differs based on computational model. It is something I’ve never thought about or heard of. An example given to me, that illustrated it further, by User @chi was: E.g. consider the task: given Read More …

Problem Detail: As I have understood from all the internet sources I can get to, when you declare and initialize a variable in java, you are allocating this data, say an 8-byte float, in a particular memory cell in the RAM, Read More …

Problem Detail: I’ve seen circuit level implementations of ALU’s before, but how are NOT/AND/ADD performed mechanically? Asked By : Wuschelbeutel Kartoffelhuhn Answered By : slebetman Babbage’s arithmetic unit (ALU) for the Analytical Engine was originally called the mill. It wasn’t constructed out of Read More …

Problem Detail: I have a binary heap with $n$ elements. I want to get the $k$ largest elements in this heap, in $O(k log k)$ time. How do I do it? (Calling deletemax $k$ times yields a $O(k log n)$ complexity. Read More …