GATE CSE
First time here? Checkout the FAQ!
x
+1 vote
77 views

Let $T(a, b)$ be the function with two arguments (both nonnegative integral powers of 2) defined by the following reccurence:

  • $ T(a, b) = T \biggl( \frac{a}{2}, b \biggl) +T\biggl( a, \frac{b}{2} \biggl) \quad \quad \text{ if } a, b \geq 2$;
  • $ T(a, 1) = T \biggl( \frac{a}{2}, 1 \biggl) \quad \quad \quad \text{ if } a \geq 2$;
  • $ T(1, b) = T \biggl( 1, \frac{b}{2} \biggl) \quad \quad \quad \text{ if } b \geq 2$;
  • $T(1, 1)=1$.

What is $T(2^r, 2^s)$?

  1. $rs$
  2. $r+s$
  3. $\begin{pmatrix} 2^r+2^s \\ 2^r \end{pmatrix}$
  4. $\begin{pmatrix} r+s \\ r \end{pmatrix}$
  5. $2^{r-s}$ if $r \geq s$, otherwise $2^{s-r}$
asked in Set Theory & Algebra by Veteran (76k points)   | 77 views

1 Answer

0 votes
Its better to take an example and trace.

The answer comes out to be (d).
answered by Active (1k points)  

Related questions



Top Users Mar 2017
  1. rude

    5246 Points

  2. sh!va

    3054 Points

  3. Rahul Jain25

    2920 Points

  4. Kapil

    2732 Points

  5. Debashish Deka

    2602 Points

  6. 2018

    1574 Points

  7. Vignesh Sekar

    1440 Points

  8. Bikram

    1432 Points

  9. Akriti sood

    1420 Points

  10. Sanjay Sharma

    1128 Points

Monthly Topper: Rs. 500 gift card

21,553 questions
26,902 answers
61,258 comments
23,269 users