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Sorting Really Big Files

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Sorting ReallyBig Files

Sorting Part 3

- Given
- N records in file F
- M records will fit into internal memory
- Use K temp files, where K = N / M

- Create K sorted files from F, then merge them
- Problems
- computers compare 2 values at once, not K values
- merging only 2 of K runs at once creates LOTS of temp files
- in the illustration on the next page, notice that we soon begin merging small runs with big temp files
- too many comparisons

What would these trees look like with 8 runs?

F

F

R1

R2

R1

R2

R3

R4

R5

empty

T1

R3

T1

T2

T3

T2

R4

S1

S2

T3

R5

R1 = Run 1

R2 = Run 2

etc

- We can create that tree using just 4 temp files
- 2 are input and 2 are output, the pairs alternate being input and output files

- Algorithm
Write Run 1 into T1

Write Run 2 into T2

Write Run 3 into T1

Write Run 4 into T2

...

Merge first runs in T1 and T2 into T3

Merge second runs in T1 and T2 into T4

Merge thirds runs in T1 and T2 into T3

...

Merge first runs in T3 and T4 into T1

Merge second runs in T3 and T4 into T2

...

F

T1

T2

T3

T4

T1

T2

T3

T4

- Number of Comparisons:
- N-Way Merge -- O (n log2 n)
- K Temp Files -- O ( n2 )

- Disk Space
- Could the run size be one record?
- In other words, is the internal sort necessary?