Show that a divide-and-conquer algorithm based on Equality 3.6 has an exponential time complexity. | Numerade

SOLVED:When a divide-and-conquer algorithm divides an instance of size n of a problem into subinstances each of size n / c, the recurrence relation is typically given by T(n)=a T((n)/(c))+g(n) for n>1 T(1)=d where g(n) is the cost of the dividing and combining processes, and d is a constant. Let n=c^k (a) Show that T(c^k)=d × d^k+∑j=1^k[a^k-j× g(c^j)] (b) Solve the recurrence relation given that g(n) ∈Θ(n)

Divide-and-Conquer Algorithm | Definition, Approach & Example - Video | Study.com