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+16 votes

The minimum number of record movements required to merge five files A (with $10$ records), B (with $20$ records), C (with $15$ records), D (with $5$ records) and E (with $25$ records) is:

  1. $165$
  2. $90$
  3. $75$
  4. $65$
asked in Algorithms by Loyal (6.1k points)
edited by | 2.3k views

Notice difference with respect to question -->

4 Answers

+23 votes
Best answer

Arrange files in increasing order of records

D  A   C   B   E

$5$ $10$ $15$ $20$ $25$


              $30$                           $45$

    $15$           $15$ (C)    $20$ (B)      $25$ (E)

$5$ (D)     $10$ (A)

No of movements$=15+30+45+75=165$

answered by Boss (31.3k points)
edited by
Hi Pooja

I am not able to follow how did you get 45 ?

Could u please explain it for me.

Thanks in advance.

# Update:Understood.! First three files u merged and then u merged last two files and then clubbed u merged the two!

"This is different from another greedy problem in which we simply merge the files one into another in after arranging them in ascending order."

In the above solved question, we have used to "MERGE" procedure from merge sort which takes one element of each array compare them and put them in the final or output array.

  • Movement of record is analogous to the movement of elements of arrays which we merge and no. of element get moved in MERGE producer are "all" i.e m+n.
  • Comparisons would be just m+n-1 as last element remaining does not need any comparison to put it into the output array.
Why isn't this like- When we are merging the file with 5 records with another file of 10 records then the least no of records(i.e one with #records=5) among them would be moved to another file. Thus reducing no of movements to just 5? Why there is a need to use another file?
+2 votes
Sort the files: 5, 10, 15, 20, 25.
Merge the smallest two records 15, 15, 20, 25
Merge 30, 20, 25
Sort 20, 25, 30
Merge 45, 30
75. So C is the answer
answered by Loyal (6.1k points)
Your answer is not correct.Correct ans is 165 !
whats the diffrence between no.of movement  and comparisions ?????????

if you will count no of comparison it will come out to be 165-4=161 and nos of movement= 165, because no of comparison on merging two nodes will be m+n-1, but the record movement will be m+n..because you have to move entire records of both nodes to newly created node
0 votes
(a) 165
answered by (25 points)
0 votes

No of movements=15+30+45+75=165

answered by Loyal (9.1k points)

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