Question

For each of the following problems write a recurrence relation describing the running time of each of the following algorithms and determine the asymptotic complexity of the function defined by the recurrence relation. Justify your solution using substitution and carefully computing lower and upper bounds for the sums. Simplify and express your answer as Θ(n k ) or Θ(n k (log n)) wherever possible. If the algorithm takes exponential time, then just give exponential lower bounds.

5. func5 (A,n) /* A = array of n integers 1 if (n 1) then return Al 3 x = A [n/2] + A[n] 5 x =x+ func5 (A, 2n/3) 2 4 6 return (r)

Answer 1

We clear explained each line with the complexity, for constant line complexity will be o(1) or constant both same.

If we call any function then complexity will be depends upon the function call , if n is divided in n/2 parts then TC will be

T(n/2) if divided in 4 parts the it will be T(n/4) so on ...

In this problem n is divided in 2n/3 parts so TC will be T(n/3) .

k- hms ㄦ

ケ叹!chon leie aj ler So\.my the ,< c u γχ ne 3