# Tagged Questions

Mathematical questions about Algorithms, including the analysis of algorithms, combinatorial algorithms, proofs of correctness, invariants, and semantic analyses. See also (computational-mathematics) and (computational-complexity).

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### Do irrational number contain infinite/every patterns of sequences?

I guess the question is "does an 'infinite' number of patterns imply 'every' number of patterns?" For instance, if you could quickly calculate the decimal sequence of π, could you not (in ...
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### What does it mean to “have a multiplicative inverse of modulo 10!”?

Here's the question: What's the smallest integer > 1 that has a multiplicative inverse modulo 10! (that is, 10 factorial)? What does that mean? I understand that: We say that x is the ...
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### What does it mean for a function to be polynomially bounded

There is a definition in my notes and says, When functions are polynomially bounded, the initial conditions (the value on small inputs) do not make a difference for the solution in ...
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### Non overlapping areas algorithm

One of my fellow members on stackoverflow has posted a question thread which concerns how to write a mathematical equation to calculate the exposed areas of a window from a group of windows (like on ...
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### How can I prove big-oh relation between $\log_2(\log_2 n)$ and $\sqrt{\log_2 n}$

How can I prove big-O relation between $f=\log_2(\log_2 n)$ and $g=\sqrt{\log_2 n}\,$? I want to find the constants, $c, N$ such that $\ g(x) \leq cf(x)$ for all $x>N$.
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### permutation search game

Arrange the natural numbers $1$ through $n$ in a random order (the order is unknown and has a uniform distribution). Now make a sequence of guesses as to which number is in which slot, one number and ...
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### Algorithm for generating homeomorphically irreducible trees of size n

In this video they talk about generating all the homeomorphically irreducible trees of size 10. I was wondering if there is a generating algorithm for generating all the homeomorphically irreducible ...
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### What is the complexity (\Theta version) of the function $\sum = 3i^{\frac{3}{2}}$

What is the complexity ($\Theta$ version) of the function $$\sum\limits_{i=1}^n 3i^{\frac 3 2}$$ I think that it is just $\Theta(n^3)$ because the $n^3$ grows faster then the constant or the square ...
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### How can I find the value of $a^n+b^n$, given the value of $a+b$, $ab$, and $n$?

I have been given the value of $a+b$ , $ab$ and $n$. I've to calculate the value of $a^n+b^n$. How can I do it? I would like to find out a general solution. Because the value of $n$ , $a+b$ and $ab$ ...