The question actually belongs to optimal merge..Let us see through the given question how we do optimal merge..It is similar to Huffman Coding..In each step , here also we pick up 2 files which have 1st and 2nd minimum no of records or sizes whatever we say.
a) So in this case we have 1st 2 minimums = 40 and 50 and the files corresponding to them are F4 and F6..Now on merging these 2 , we get resultant new merged file having 40 + 50 = 90 records.Now this file is also considered for comparision.
b) Now we have minimum out of the nodes : 70 and 90 and corresponding to 70 we have F3 , hence next file that will come in the sequence is F3 and weight of the merged file hence = 70 + 90 = 160..
c) Next F1 is merged so no of merges now becomes = 160 + 100 = 260
d) Then F2 is merged so no of merges now becomes = 260 + 200 = 460
e) And finally F5 is merged so no of merges now becomes = 460 + 250 = 710
Hence total no of merge operations that are performed = 90 + 160 + 260 + 460 + 710
= 1680
So average no of merges per file = 1680 / 6
= 280
Hence option D) should be the correct option for 1st part and option C) for the 2nd part since it is closest to 280 and approximate is being asked..
