I think I haven't understood what you are trying to say.
This is what I thought, 10 files - 100 of which can fit in memory which means that
all the 10 can be loaded into memory at once.
10 open operations for 10 files
load data in to memory from all the 10 files
10 close operations for 10 files
sort everything in memory itself
1 - open for output file
flush sorted data from memory to output file
1 - close for output file
For the above example, its 2 * ( n + 1 ) close and open operations
So, in this case this doesn't tally with what you have said.
Apologies again, if I haven't understood what you meant.
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