Hi, please provide me a detailed answer for the problem below, thank you!

6. Consider the following problem: Input: a natural number n. Output: [n1/3]. Design a binary-search style algorithm to solve the above problem. (a) (2 pts) Explain your algorithm in plain English. (b) (5 pts) Explain your algorithm in pseudocode. (c) (5 pts) Briefly argue correctness. (d) (3 pts) Let A(n) denote the number of additions that your algorithm uses. Asymptotically, what is A(n) =? Justify your