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Results tagged with recurrence-relation
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user 20461
a definition of a sequence where later elements are expressed as a function of earlier elements.
1
vote
1
answer
177
views
What kind of recurrence relations has p < 0?
By the master method,
$T(n) = aT(\frac {n}{b})+\Theta(n^k\log^pn)$
where $p$ is real.
I know $\log^4n=\log(\log(\log(\log n)))$ but how do you calculate something like $\log^pn$ where $p<0$?
3
votes
2
answers
102
views
If $T(n+1)=T(n)+\lfloor \sqrt{n+1} \rfloor$ $\forall n\geq 1$, what is $T(m^2)$?
$T(n+1)=T(n)+\lfloor \sqrt{n+1} \rfloor$ $\forall n\geq 1$
$T(1)=1$
The value of $T(m^2)$ for m ≥ 1 is?
Clearly you cannot apply master theorem because it is not of the form $T(n)=aT(\fra …
2
votes
1
answer
1k
views
How to write recurrence relation for the following scenario?
A program takes as input a balanced binary search tree with n leaf nodes and computes the value of a function $g(x)$ for each node x. If the cost of computing $g(x)$ is min{no. of leaf-nodes in lef …
1
vote
1
answer
120
views
What is the correct representation of Master Theorem?
What I'm taught in my class -
$T(n)=aT(\frac{n}{b})+\theta(n^k\log^pn)$
where $a\geq1$, $b>1$, $k\geq1$ and $p$ is a real number.
if $a>b^k$ then, $T(n)=\theta(n^{\log_ab})$
if $a=b^k$ …
3
votes
2
answers
3k
views
Recurrence relations when function call is made inside loop
int fun (int n)
{
int x=1, k;
if (n==1) return x;
for (k=1; k<n; ++k)
x = x + fun(k) * fun(n – k);
return x;
}
What is the value of fun(5)?
I find it difficult to realize a recurre …