This is a greedy algorithms questions that supposedly involves Huffman coding. This problem should be solved through the following:

1. A verbal or graphic description of the algorithm developed to solve the problem.
2. Proof of correctness.
3. Pseudo-code of the algorithm.
4. Analysis of runtime.

We are given n sorted arrays such that array i has length m. We would like to merge these arrays into a single sorted array of length 1 mi. We are given the MERGE procedure, which (m + mj) time. can merge two arrays of length m; and m; in We would like to find a schedule to merge these n arrays into a single array by making n 1 calls to the MERGE procedure on pairs of arrays. Here, a schedule refers to a tree that specifies the order in which we should merge the arrays. For example, if we have m 80, m = = 20, m3 100, and m4= 10 then the optimal schedule is to merge the second and fourth arrays to obtain an array of length 30, then merge this array with the first array to obtain an array of length 110, and finally merge this array with the third array to obtain the final array of length 210. Develop an efficient algorithm to compute the most efficient schedule for merging the n input arrays. =