Problem Detail: Some confusion about time-complexity and A*. According to A* Wiki the time-complexity is exponential in the depth of the solution (shortest path): The time complexity of A* depends on the heuristic. In the worst case of an unbounded search Read More …
Category: Uncategorized
[Solved]: Let A,B be languages. If A is decidable and B undecidable, then A reducible to B
Problem Detail: So I’m learning for an upcoming exam and there’s a specific problem which I can’t show: Let A be decidable and B undecidable, then $A le B$ Can someone give me a hint how to solve that? Furthermore, does Read More …
[Solved]: Linear time algorithm for finding $k$ shortest paths from $s$ to $t$
Problem Detail: Definition. Given a graph $G=(V,E)$ and two vertices $s$ and $t$, the $k$-shortest-paths problem is finding the $k$ shortest simple paths between $s$ and $t$ in $G$. Note that the length of these paths is not necessarily equal, Read More …
[Solved]: implementation of queue using stack with REVERSE
Problem Detail: Suppose a stack implementation supports an instruction REVERSE, which reverses the order of elements on the stack, in addition to the PUSH and POP instructions. I’m looking for implementation of queue where ENQUEUE takes a sequence of three Read More …
[Solved]: Examples of processes / problems that cannot be tackled by Turing Machines
Problem Detail: I know that there are problems that cannot be solved by any algorithm, such as the Halting problem. I also know that some processes cannot be even adequately approximated by any Turing Machine (equivalently, any digital computer), meaning that Read More …
[Solved]: Relation between hardware and software
Problem Detail: I’m very interested in computing and programming. I have done a lot of programming with different languages although I have a question nobody was able to answer until now. I question myself how is software related to hardware. to Read More …
[Solved]: How “coplanar” is a set of points?
Problem Detail: Assume that we have 10 points. If all those points are on the same plane, they all are coplanar. But some of them might be at a different place. That disrupts the structure of the plane if we were Read More …
[Solved]: How to purge a linked list in $mathcal{O}(nlog n)$ time?
Problem Detail: I was wondering how to remove duplicate values from a linked list in $mathcal{O}(nlg n)$ time. I have an idea that by using merge sort when we want to compare elements for choosing the small one, if they are Read More …
[Solved]: Kth largest subset for small K
Problem Detail: The $K$th Largest Subset problem is often given as an example of an NP-hard problem. However, the assumption is that $K$ is unconstrained, and can be as large as $2^n$. Clearly, if $K le 3$ the solution in $O(n)$ Read More …
[Solved]: Equivalence of Kolmogorov-Complexity definitions
Problem Detail: There are many ways to define the Kolmogorov-Complexity, and usually, all these definitions they are equivalent up to an additive constant. That is if $K_1$ and $K_2$ are kolmogorov complexity functions (defined via different languages or models), then there Read More …
