I've gotten this question for an assignment in our introduction to computer science. And I have absolutely no idea on how to solve it. Help very much appreciated!!

This may sound like a clichÃ©, but my girlfriend just left me, so I can't think straight even though how hard I try, and I have to deliver this by tommorow..

Question:

Design an algorithm for finding the cubic root of a positive integer,

rounded down to the nearest integer. Thus, given input N, a positive

integer, you should find a positive integer m such m^3 is smaller or equal to N, but (m + 1)^3 > N. Use the binary search idea.

(a) Express the algorithm in pseudocode.

(b) Find a fundamental operation and use big theta notation to ex-

press how long your algorithm takes. Express this as a function

of the positive integer N which is input, and also as a function of

the length of N (the number of bits in N). State any assumption

you make about how long it takes to multiply two integers, one of

length s and one of length t.