Question Detail: I have a high-level understanding of the $P=NP$ problem and I understand that if it were absolutely “proven” to be true with a provided solution, it would open the door for solving numerous problems within the realm of computer Read More …
Author: ignougroup
Hierarchical Paging
Question Detail: Suppose I have a system with 32-bit logical and 16-bit physical address spaces, and the page size is 512 bytes. For simplicity, ignore the valid/invalid bits in the page table. How many sections will the logical address be divided Read More …
What determines the "speed" of a programming language?
Question Detail: Suppose a program was written in two distinct languages, let them be language X and language Y, if their compilers generate the same byte code, why I should use language X instead of the language Y? What defines that Read More …
Proving a binary heap has $lceil n/2 rceil$ leaves
Question Detail: I’m trying to prove that a binary heap with $n$ nodes has exactly $leftlceil frac{n}{2} rightrceil$ leaves, given that the heap is built in the following way: Each new node is inserted via percolate up. This means that each Read More …
Examples of context-free languages with a non-context-free complements
Question Detail: Context-free languages are not closed under complementation. In the lectures we have been given the same argument as here on Wikipedia. But this only shows that one of the three languages $A$, $B$, and $overline A cup overline B$ Read More …
Formalization of the shortest path algorithm to a linear program
Question Detail: I’m trying to understand a formalization of the shortest path algorithm to a linear programming problem: For a graph $G=(E,V)$, we defined $F(v)={e in E mid t(e)=v }$ and $B(v)={ e in E mid h(e)=v}$ where $t(e)$ is a Read More …
In-place algorithm for interleaving an array
Question Detail: You are given an array of $2n$ elements $$a_1, a_2, dots, a_n, b_1, b_2, dots b_n$$ The task is to interleave the array, using an in-place algorithm such that the resulting array looks like $$b_1, a_1, b_2, a_2, dots Read More …
If the speed of electrical charge hasn’t changed, how have computers become faster?
Question Detail: Everyone knows computing speed has drastically increased since their invention, and it looks set to continue. But one thing is puzzling me: if you ran an electrical current through a material today, it would travel at the same speed Read More …
Are there any problems that get easier as they increase in size?
Question Detail: This may be a ridiculous question, but is it possible to have a problem that actually gets easier as the inputs grow in size? I doubt any practical problems are like this, but maybe we can invent a degenerate Read More …
Calculating Floating point Operations Per Second(FLOPS) and Integer Operations Per Second(IOPS)
Question Detail: I am trying to learn some basic benchmarking. I have a loop in my Java program like, float a=6.5f; int b=3; for(long j=0; j<999999999; j++){ var = a*b+(a/b); }//end of for My processor takes around 0.431635 second to process Read More …
