Least computationally expensive bitwise addition

I am familiar with the oft-cited method of bitwise addition using XOR and left shift for the carry, applied recursively. I was wondering if this is the least computationally expensive way to achieve simple addition modulo 2^n using bitwise operators. Answer AttributionSource : Link , Question Author : Brad Thomas , Answer Author : Community

What’s the most time efficient way to find the number of nodes reachable from each root and no other root?

Suppose there are n nodes. These nodes are connected by m unique directed edges. Sets of these edges may form cycles. Each node has an associated quantity. r of these nodes are selected as root nodes. A node a can be said to reach node b if a is b or there exists a directed … Read more

Understanding recursion tree for withdrawal formula

T(n)=T(n−a)+T(a)+cn Now the solution says that the height of the tree (h) is: h=⌊n/a⌋ And I don’t understand why. Maybe I didn’t understand the withdrawal formula as needed. Answer Your recurrence expands into a recurrence tree in the following way. Each node has a label. If the label n is a or smaller, then the … Read more

Can we make at most 3 comparisons in the closest points algorithm instead of 7?

Let’s say I am using the divide and conquer algorithm outlined here, but I only want to return the minimum distance. I understand why that algorithm puts an upper-bound at 7 but I think that can be trimmed down further. I can’t come up with a geometry of points where if you are comparing them … Read more

Which of the query approaches are more efficient?

There are two relations, registered(participant,topic) and fee(participant,amount). The primary key for registered is (participant, topic) and the primary key for fee is participant. The premise is that of an academic conference. The relation registered stores the names of the participants and the names of the topics registered by them. On the other hand, the fee … Read more

How do we determine how much time a multi-tape DTM saves over a one-tape DTM?

Note: This is a part of a homework question Were asked to construct a multi-tape Turing Machine for language {anbncn∣n≥0} Then it says “Discuss how much time your machines saves over a one-tape DTM using the same algorithm” Any hint? Here’s my algorithm: (1) Cut-and-paste c’s to tape 3 (2) Cut-and-paste b’s to tape 2 … Read more