Questions tagged [factorial]

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2
votes
2answers
75 views

Efficient way to reduce a binomial coefficient as a fraction

Here is the full problem. You need to calculate Euler's totient function of a binomial coefficient $C_n^k$. Input The first line contains two integers: $n$ and $k$ $(0 \le k \le n \le 500000)$. ...
-2
votes
2answers
79 views

prove that log((n^2)!)= o(log((n!)^2))

i have a question - how i can prove that: $\log((n^2)!) =\theta (log((n!)^2))$ i try something like that: $\log((n^2)!) = 2*(log(n)!)=\theta(2*(log(n)!)=\theta(n\ log(n)) $ $\ \theta(log(n!)^2)=\...
2
votes
1answer
377 views

Solving recurrence relation with minimum and factorial

I need to solve the following recurrence relation, where $T(n,m)$ is defined over $\Bbb N_+\times\Bbb N_+$. $T(n,m)=\begin{cases} 1, & n=1\text{ or }m\leq 2(n-1)!\\ \min\limits_{a,b,c\geq 1,\ c\...
1
vote
1answer
120 views

Recurrence with Minimum

I need to solve the following recurrece: $T(n,m)=\begin{cases} 1, & m\leq 2(n-1)!\\ \min\limits_{a,b\geq 1\\a\cdot b\leq (n-1)!}{T(n-1,a)+T(n-1,b)+T(n,m-ab)}, & \text{else} \end{cases}$ Note:...
7
votes
1answer
435 views

Asymptotics question

Is $\frac {n!} {2!\cdot 4!\cdot 8!\dots (n/2)!}=O(4^n)$? I am really stuck and I tend to believe it's true, but I don't know how to prove it. Any help would be appreciated!
0
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0answers
29 views

Where f(n) = n! belongs to? P, co-P, NPComplete or NPHard? [duplicate]

Where f(n) = n! belongs to? P, co-P, NPComplete or NPHard?
4
votes
1answer
2k views

Why is the complexity of factorial a function of n?

When we compute the complexity of calculating factorial of a number $n$ why is it in terms of $n$ instead of the number of the number of bits occupied by the number of bits occupied by $n$ (like we do ...
2
votes
0answers
649 views

Can factorial be done in O(1) and proof?

The typical way to compute the factorial would take $O(n)$ because it calls itself recursively. However, there are many other ways to compute the factorial function based off the gamma function, ...
0
votes
1answer
456 views

Complexity calculation using a recurrence relation [duplicate]

I just can't solve this problem, I'm new to reccurences. I have this recurrence $T(n)=n*T(n-1)$ $T(1)=1$ The second term will be: $T(n-1)=(n-1)*T(n-2)$ And so on. It's complexity is O(n!) but i ...
1
vote
0answers
411 views

How to get from factorial to a y-combinator?

In one of his conference talks Jim Weirich derives the applicative form of the y-combinator by refactoring a partial definition of factorial. The starting point in his talk is different than what ...
1
vote
1answer
95 views

Generating all factorials up to $n$: faster than naive approach?

I'm aware of prime decomposition and parallel approaches to calculating one factorial; however, if I want the factorials of all numbers up to $n$, is there anything more efficient than the naive ...