Category: Uncategorized

Problem Detail: Given $n$ arrays of size $k$ each, we want to show that at least $Omega(nk log k)$ comparisons are needed to sort all arrays (indepentent of each other). My proof is a simple modification of the decision tree argument Read More …

Problem Detail: The following example was given in an online lecture I was watching. A phone directory is 1000 pages long, and we have to find the name “Zurich Smith”. The algorithm is as follows: Split the phone directory into half. Read More …

Problem Detail: My question here is dealing with the residual that I get. We are trying to prove $T(n) = 3T(n/3) + n$ is $O(n*log n)$. So where I get is $T(n) le cn[log n – log 3] + n$. So Read More …

Problem Detail: Given three matrices $A, B,C in mathbb{Z}^{n times n}$ we want to test whether $AB neq C$. Assume that the arithmetic operations $+$ and $-$ take constant time when applied to numbers from $mathbb{Z}$. How can I state an Read More …

Problem Detail: I’m trying to prove/disprove two statements. I just want to make sure with you I’m on the right line. These are the following statements: Preface : Let A[n] be an array of min-heap (a min-heap represented by an array], Read More …

Problem Detail: I’m studying for an exam on software testing and in my notes I found this: Many more paths than branches. A pragmatic compromise will be needed I cannot understand the difference between paths and branches; each time I work Read More …

Problem Detail: This language I think is not accepted by a deterministic one counter but accepted by a non-deterministic one counter : $L = {a^{i}b^{j}c^{k} mid (i=j) vee (j=k) text{ such that } igeq0, jgeq0, kgeq0}$ But how to prove this Read More …

Problem Detail: I’ve read that, incorporating many words(spatial locality) per cache blocks leads to lower miss rate. Is it the case always? One possibility of such approach is to make a single cache block of size equal to the size of Read More …

Problem Detail: I’m not sure how to word this because I’m not familiar with this, but I’m sure a process like this is rather common. Basically, I’ve got members signing up for our website, and each one is assigned a normal Read More …

Problem Detail: Recently I am reading a document [1]. In this document, Prof. Cook provides a brief proof of $mathbf{P} subseteq mathbf{NP}$, which is only one sentence: It is trivial to show that $mathbf{P} subseteq mathbf{NP}$, since for each language $L$ Read More …