Problem Detail: I have an algorithmic problem. Given an array (or a set) $T$ of $n$ nonnegative integers. Find the maximal set $S$ of $T$ such that for all $ain S$, $ageqslant |S|$. For example: If $T$=[1, 3, 4, 1, 3, Read More …
Author: ignougroup
[Solved]: Maximum Independent Subset of 2D Grid Subgraph
Problem Detail: In the general case finding a Maximum Independent Subset of a Graph is NP-Hard. However consider the following subset of graphs: Create an $N times N$ grid of unit square cells. Build a graph $G$ by creating a vertex Read More …
[Solved]: Can I construct a Turing machine that accepts only its own encoding?
Problem Detail: Is the set $S$ = $lbrace M mid M text{ is a Turing machine and }L(M)=lbrace langle Mranglerbracerbrace$ empty? In other words is there a Turing machine $M$ that only accepts its own encoding? What about a Turing machine Read More …
[Solved]: Dynamic programming VS Greedy Algroithms
Problem Detail: I have two True or False questions in my practice test that are related but I am unsure about: 1. If an optimization problem can be solved using a greedy algorithm, there must be a solution for this optimization Read More …
[Solved]: What is the difference between the semantic and syntactic views of function types?
Problem Detail: Edit: My original question referred to nonconstructive and constructive definitions of function types. I changed the terminology in the question and the title to semantic and syntactic, which the answer indicates is the correct terminology for this distinction. I Read More …
[Solved]: Time Complexity of Universal Turing Machine Simulations and the Time Hierarchy Theorem
Problem Detail: I have a little problem to understand the proof of the Time Hierarchy Theorem (Hennie and Stearns, 1966) that ensures the existence of a language acceptable in $U(n)$ but not acceptable in $T(n)$ for any functions $T(n),U(n)$, such that Read More …
[Solved]: Breadth First Search with cost
Problem Detail: Looking for some tutorials / references that discuss Breadth First Search that takes into consideration the cost of paths, but could not find much information. Could someone refer a tutorial? Asked By : Roberta Rocha Answered By : Carlos Linares López Read More …
[Solved]: A polynomial reduction from any NP-complete problem to bounded PCP
Problem Detail: Text books everywhere assume that the Bounded Post Correspondence Problem is NP-complete (no more than $N$ indexes allowed with repetitions). However, nowhere is one shown a simple (as in, something that an undergrad can understand) polynomial time reduction from Read More …
[Solved]: How to apply the pumping lemma to ${0^m 1^n mid 2n leq m leq 3n, m,n geq 0 }$?
Problem Detail: I’m not really sure the how you would go about proving this language isn’t regular with the pumping lemma: $L= {0^m 1^n | 2n leq m leq 3n, m,n geq 0 }$ Does this indicate that $S = 2$, Read More …
[Solved]: Probabilty that quicksort partition creates an imbalanced partition
Problem Detail: I have come across this question: Let 0<α<.5 be some constant (independent of the input array length n). Recall the Partition subroutine employed by the QuickSort algorithm, as explained in lecture. What is the probability that, with a randomly Read More …
