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+24 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. $65$
in Algorithms by
edited by | 4.2k views

Notice difference with respect to question -->

Can anyone please tell the concept upon which this question is based ?

5 Answers

+26 votes
Best answer
Arrange files in increasing order of records:

$\overset{\boxed5}{\text{D}}\quad \overset{\boxed{10}}{\text{A}}\quad\overset{\boxed{15}}{\text{C}}\quad\overset{\boxed{20}}{\text{B}}\quad\overset{\boxed{25}}{\text{E}}$




$\quad\overset{\boxed{\text{D}}}{5}\qquad\overset{\boxed{\text{A}}} {10}$

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

Correct Answer: $A$
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?
@Mamta , what if there is no space in other file to contain these 5 records :P  ..Actually given question is an example of optimal merge pattern which follows greedy strategy for optimal solution. For this , Files should be sorted and then we merge these sorted files to make one sorted file...In question , it is not mentioned the word "sorted" but I think we should have to assume it.
+5 votes

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

what is the meaning of m and n will you give explanation
@ suneeta m and n are the size of 2 files to which we are merging by using optimal merge pattern of greedy approach
What are those files m, n

for getting the number of comparisons we need to use formula (m+n-1).

here m,n is the size of the file.

for example,



when we merge these two files we need to do the comparison  between the elements of b and a so it takes

10+5-1=14(comparison requires ), here why we subtract 1 bczz we need not to compare the last element.
+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
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
+1 vote

Try to implement it like Huffman coding.

Sorted files 5,10,15,20,25

1) merge min two -- 15,15,20,25 | merges=5+10=15

2) next two -- 30,20,25 -> reordering -- 20,25,30 | merges = merges+15+15=15+(15+15) = 45

3) next two -- 45,30 --> reordering -- 30,45 | merges= merges+ 20+25 = 45+(20+25) = 45+45= 90

4) last two -- 75 | merges = merges+45+30 = 90+(45+30) = 90+75 = 165

so, 165 is the answer

–1 vote
(a) 165

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