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Questions by SomnathKayal

3 votes
2 answers
1
A better guess on upper bound
It's a question from Cormen book Exercise 4.4-5 and is described like this: Use a recursion tree to determine a good asymptotic upper bound on the recurrence $T(n)=T(n-1)+T(\frac{n}{2})+n$
It's a question from Cormen book Exercise 4.4-5 and is described like this:Use a recursion tree to determine a good asymptotic upper bound on the recurrence $T(n)=T(n-1)+...
2 votes
1 answer
2
Solve recurrence using Master theorem
$T(a)=0 \hspace{0.2cm} if \hspace{0.2cm} a=1$ $T(a)=2T(a/2) + ak \hspace{0.2cm} if \hspace{0.2cm} a=2^{p}, p>0$ where $a=\frac{n}{k}$ Answer: $\Theta (n \log (\frac{n}{k}))$, This is while (n/k) is power of 2. How can I solve it using master theorem?
$T(a)=0 \hspace{0.2cm} if \hspace{0.2cm} a=1$$T(a)=2T(a/2) + ak \hspace{0.2cm} if \hspace{0.2cm} a=2^{p}, p>0$where $a=\frac{n}{k}$Answer: $\Theta (n \log (\frac{n}{k}))$...
1 votes
1 answer
8
Find a formula when m is a positive integer?
$(a) \sum_{k = 0}^{m} \left \lfloor \sqrt k \right \rfloor$ $(b) \sum_{k = 0}^{m} \left \lfloor \sqrt {k^{3}} \right \rfloor$ Is there any quick way to find the formula for complex expression?
$(a) \sum_{k = 0}^{m} \left \lfloor \sqrt k \right \rfloor$$(b) \sum_{k = 0}^{m} \left \lfloor \sqrt {k^{3}} \right \rfloor$Is there any quick way to find the formula for...
1 votes
1 answer
9
What are the values of the sum?
$\sum_{j \in S} 1$ where S = {1, 3, 5, 7}. if we have $\sum_{j = 1}^{n} 1$ then the answer will be n. But what happens if this a set?
$\sum_{j \in S} 1$ where S = {1, 3, 5, 7}.if we have $\sum_{j = 1}^{n} 1$ then the answer will be n. But what happens if this a set?