Consider the problem of merging (n) sorted files F, F2,...,Fn of lengths z,z2,...,Zn records into one file F of length z=z, while minimizing the total number of record moves. Only two i=1 files can be merged at one time. Write a pseudocode for an algorithm to obtain the optimal merge pattern. Given the following files and the number of records in each: {F: 14}, {F2: 22}, {F3: 15}, {F4: 20}, {F5: 10}, {F6: 8}, {F7:4}, {F8: 7} 1. Obtain the optimal merge tree for the files. 2. Find the minimum total number of record moves needed to merge the files and the average number of moves per record. (5 points) (10 points) into one file (5 points)