There is a squirrel named that lives in a tree with n branches,and she wants to find the lowest possible branch that when an acornis dropped it will break open, however, once an acorn is broken itcannot be dropped again, given the constraints below, please helpcome up with solutions fitting these runtimes.

a) Suppose that the squirrel has two acorns. Give a procedure so that she can identify the correct branch using O(Vn) drops [We are expecting: Pseudocode AND a short English description of your algorithm, and a justification of the number of drops. If it helps you may assume that n is a perfect square.] b) Suppose that the squirrel has kO(1) acorns. Give a procedure so that she can identify the correct branch sing O(n1/k) drops [We are expecting: Pseudocode AND a short English description of your algorithm, and a justification of the number of drops. If it helps you Tnany assurne that n is of the form n = m for some integer m.] c) What happens to your algorithm in part (b) when k = [log(n)1 + 1? Is it O(log(n), like in part (a)? Is it 0(n 1/k) when k = rlog(n)1+ 1, like in part (b We are expecting: A sentence of the form “the number of drops of my algorithm in part (b) when k-Под(n)1 + 1 is 0( )”, along with justification. Also, two yes/no answers to the two yes/no questions (you should justify your answers but do not need to include a formal proof). d) k acorns, for k = 0(1)? Either give a proof that she can’t do better, or give an algorithm with asymptotically fewer drops Is Θ(n 1/k) drops is the best thatthe squirrel can do with Show transcribed image text a) Suppose that the squirrel has two acorns. Give a procedure so that she can identify the correct branch using O(Vn) drops [We are expecting: Pseudocode AND a short English description of your algorithm, and a justification of the number of drops. If it helps you may assume that n is a perfect square.] b) Suppose that the squirrel has kO(1) acorns. Give a procedure so that she can identify the correct branch sing O(n1/k) drops [We are expecting: Pseudocode AND a short English description of your algorithm, and a justification of the number of drops. If it helps you Tnany assurne that n is of the form n = m for some integer m.] c) What happens to your algorithm in part (b) when k = [log(n)1 + 1? Is it O(log(n), like in part (a)? Is it 0(n 1/k) when k = rlog(n)1+ 1, like in part (b We are expecting: A sentence of the form “the number of drops of my algorithm in part (b) when k-Под(n)1 + 1 is 0( )”, along with justification. Also, two yes/no answers to the two yes/no questions (you should justify your answers but do not need to include a formal proof). d) k acorns, for k = 0(1)? Either give a proof that she can’t do better, or give an algorithm with asymptotically fewer drops Is Θ(n 1/k) drops is the best thatthe squirrel can do with