# Tagged Questions

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### Algorithm conjecture

This is an algorithm analysis question for computer science. Let f(n) be positive functions. (Dis)prove the following conjecture? $$f(n)+o(f(n))\in\Theta(f(n))$$ o above is the Little O, defined as ...
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### Asymptotic Notations in limits

Can the asymptotic notations, like Big O, be defined using limits? example:- Lim x->infi (f(n)/g(n))=c for defining f(n)=O(g(n)) If not, why??
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### Produce a list of the most-similar units, given various correlations/relationships

I have a database full of units (U1 - U50, U51...) where every unit has the same standard attributes (A1 - A10) and where a % of each attribute defines the amount of that attribute for that particular ...
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### Solve non-linear equations of 3 variables using Newton-Raphson Method iterms of c,s and q.

The three non-linear equations are given by $$c[(6.7 * 10^8) + (1.2 * 10^8)s+(1-q)(2.6*10^8)]-0.00114532=0$$ s[2.001 *c + 835(1-q)]-2.001*c =0 ...
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### MAX-HEAPIFY - why the worst case is when the bottom level is “half full”?

In the 3rd edition of 'Introduction to Algorithms', on page 155, when analysing MAX-HEAPIFY it says: The children's subtrees each have size at most 2n/3 - the worst case occurs when the last row ...
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### Defining a region as a data structure

Is there a way for one to define a curve or region (such as a closed, 2-d disk) as a data structure into the computer, and make an algorithm which detects if a point is a boundary point, limit points, ...
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### Amortized Analysis Problem

I need to find the cost of the problem below but I cannot find a pattern to find the total cost. Problem: The cost of multiplication of n-bit binary number by 2. If a bit changes the cost of that ...
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### asymptotic analysis

For each of the following sentences involving functions f and/or g, find a counterexample to show that it is false: What is meant by counterexamples?
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### Expected error due to the tablemakers' dilemma

[note: to me, this does not seem like a question for m.se, but on mathoverflow it has been retroactively closed, with very little indication of why or what might be corrected... and waiting for ...
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### Is it true that there is no algorithm to approximate the least upper bound?

I just read the following text below from Bishop's Foundations of Contructive Analysis, is it true that there is no such algorithm? The book is from 1967 - I don't know if someone managed to invent ...