Clear solution step by step please.

Implement an efficient algorithm in Java to solve the following problem: You are given n ropes of different lengths (expressed as integers), and you are asked to connect them to form a single rope with the minimum cost. The cost of connecting two ropes is equal to the sum of their lengths. Given a sequence of rope lengths, the expected outputs are a sequence of rope connection operations and the total cost. Use one of your implementations of the Min-priority Queue ADT in your solution. a) Give a brief description of your implementation, explaining why a priority queue is needed for an efficient algorithm. [8] b) What is the output for this instance of the problem 4,8,3,1,6,9,12,7,2 ? [1]