# Tagged Questions

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### Alternative to Hungarian Algorithm to determine minimum cost?

Is there a graphic calculator (CAS technology) method to solve minimum cost problems/allocations that are normally completed with the Hungarian Algorithm... Hungarian Algorithm is time consuming, ...
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### Is there a quick way to obtain $a,b$ in $ax+by = z$ where $x,y,z$ are fixed and $x+1 = y$?

Suppose that all numbers are postive integers. Let $x,y,z$ be fixed/given and $x+1=y$. Then would there be a quick way to find set of solutions $(a,b)$ that satisfy $ax+by=z$? "Quick" would be ...
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### Unrolling and rerolling with a different thickness

I have two rolls, the main one with two layers of material and the secondary one with just one of them. As the main one unrolls it loses one layer of thickness, and simultaneously the second one has ...
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### Refresh summation formulas

I am trying to refresh on algorithm analysis. I am looking for a refresher on summation formulas. E.g. I can derive the $$\sum_{i = 0}^{N-1}i$$ to be N(N-1)/2 but I am rusty on the and more complex ...
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### Reaching a proof

I'm trying to solve this problem: Link. After reading the problem, I realized that to start off, we can imagine the problem only in the positive axis, working only with $|x|$. Then, we want the ...
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### Richardson's theorem for constants

It's known that there is no algorithm for deciding for any elementary function is it identically zero or not (http://en.wikipedia.org/wiki/Richardson%27s_theorem ). But if I consider only constants - ...
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### What is the point of the median?

It seems like the purpose of the median is to ignore a specific type of data point. More specifically, it is used to make outliers have a lower weight than other data points on an average. Why not ...
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### simple maths problem

N locations are numbered from 0 to N-1. Given a int[] containing N elements. The i-th (0-based index) element of array is the number of persons who live near location i.One car can move to one ...
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### Question Understanding Simple Algebra With Regards to Computational Complexity

Initial Disclaimer: I decided not to post this on Stack Overflow as my problem lies with understanding the mathematics of this problem, but does not relate to theory at all. I am studying Parallel ...
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### Maximizing an algebraic expression using brackets

It's a riddle of sorts: given a list of numbers $\alpha_1 \dots \alpha_n$ and operators $o_1 \dots o_{n-1}$ which can be only $\times\, \mbox{or}\, +$ if the above is a specific algebraic expression ...
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### Is there a known algorithm for approximating all the real and imaginary zeros of any well behaved equation of a single variable?

Does there currently exist a general algorithm (or set of algorithms used together) that will approximate all the zeros of any well behaved non-differential equation of a single variable which has a ...
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### What is the Mirror/PingPong clamp mode algorithm?

I do programming as a hobby, and in a dynamic system various numerical values inevitably change. Those values can be greater than or less than the expected range, in which case they need to be ...
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### How can I optimise the power series calculation of the exponential function?

In an answer to the question Fastest way to calculate $e^x$ upto arbitrary number of decimals? there is a description of a method by which the number of terms needed to calcluate $e^x$ to a given ...
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### pandigital rational approximations to the golden ratio and the base of the natural logarithm

Steven Stadnicki suggested in a comment that I post the following as a question. The golden ration $\phi$ is given by $$\phi = \frac{1+\sqrt{5}}{2} \approx 1.618033988.$$ A rational approximation is ...
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### Rounding to the nearest term in a geometric progression

Consider the following progression: where i is ith number within the progression. I would like to devise an equation that will round input value to the nearest number from this progression. For ...
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### Smallest value of n for two algoritms with a certain running time

If one algorithm has a running time of $100n^2$ and another of $2^n$; how can I find the smallest value of $n$ such that the former is faster than the latter? I could do: $100n^2 < 2^n$ then ...
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### Celsius to Fahrenheit back and forth conversion with rounding.

Recently I've encountered some problem with conversion Celsius and Fahrenheit scales. Let's assume that I have value of 44 degrees in Fahrenheit scale, I convert this to the Celsius which gives me ...
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### Accounting for changing radius of a paper roll to always unroll the same amount of paper

So I'm building a Post-Turing Machine that's running a 5-state busy beaver. It has a 300ft roll of receipt paper at each end simulating an infinite tape. Hypothetically the tape is divided into ...
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### Algorithm for root function $[2^{n-1}]$

I am attempting to convert this function $[2^{n-1}]$ into a root function to return original value. Thus far all my attempts have ended in abject failure. Base : 1 2 3 4 5 6 7 8 9 Result : ...
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### Maximize $f(p)=(k-p)^2+(p-1)^2$

From a computer algorithms analysis (quicksort), its given that $f(p)=(k-p)^2+(p-1)^2$ is maximized when $p=1, p=k$. But how do they get that?
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### Algorithms for “solving” $\sqrt{2}$

The very first words out of my mouth need to be this... "Solving" is the wrong term since I am speaking about irrational numbers. I just don't know which word is the correct word... So that can be ...