Problem Detail: Karp’s 21 NP-complete problems show that 0-1 integer linear programming is NP-hard. That is, an integer linear program with binary variables. If we set the $c^T$ vector of the objective $text {maximize } c^Tx$ to all one (unweighted, i.e., Read More …
Category: Uncategorized
[Solved]: Is a 2 address machine more likely to follow a RISC or CISC design?
Problem Detail: The Problem: If I have a 3 address machine, is my machine more likely to follow RISC or CISC design? 2 addresses? 1 address? 0 address. To solve this problem I first looked up the different terms. RISC is Read More …
[Solved]: Efficient way to calculate sum in sliding window?
Problem Detail: Assume you have a grid as below: The square is the sliding window. I want to slide this window over all the possible position such that the window is contained in the grid (i.e the edges of the window Read More …
[Solved]: Number of binary trees with given height
Problem Detail: I was wondering how many binary trees we have with height of $h$ with $n$ nodes(another question is how many binary trees we have with height $ lfloor{lg (n)}rfloor$). Edit: I forgot to add the number of nodes. Asked Read More …
[Solved]: Is there a “natural” undecidable language?
Problem Detail: Is there any “natural” language which is undecidable? by “natural” I mean a language defined directly by properties of strings, and not via machines and their equivalent. In other words, if the language looks like $$ L = { Read More …
[Solved]: Handling dead state in NFA to DFA conversion
Problem Detail: I want to convert below NFA into DFA: I prepared below tables and finally the NFA: NFA However I feel I am wrong here, since original NFA does not have any transitions defined for state C and my final Read More …
[Solved]: Need a practical solution for creating pattern database(5-5-5) for 15-Puzzle
Problem Detail: I have asked this exact question on StackOverflow. I did not get the answer that I was looking for. Please read this question fully before answering. Thank You. For static pattern database(5-5-5), see this(page 290 and 283) OR there Read More …
[Solved]: Can a Big-Oh time complexity contain more than one variable?
Problem Detail: Let us say for instance I am doing string processing that requires some analysis of two strings. I have no given information about what their lengths might end up being, so they come from two distinct families. Would it Read More …
[Solved]: Consistency and completeness imply soundness?
Problem Detail: I understand that soundness implies consistency. Also, I understand that consistency alone does not imply soundness. But shouldn’t consistency + completeness imply soundness? Scott Aaronson in his blog-post hints otherwise. What am I exactly missing? Update: By completeness I Read More …
[Solved]: Shortest path with odd weight
Problem Detail: Let G be a directed graph with non-negative weights. We call a path between two vertices an “odd path” if its weight is odd. We are looking for an algorithm for finding the weight of the shortest odd path Read More …
