make code 39 barcodes excel The Merge Phase in Software

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The Merge Phase
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We are now ready to merge the merge les The initial sort blocks from of each of the m merge les are brought into memory input bu ers, and their records are compared, starting from the lowest ones
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A Merge Pass The record with the smallest key is placed in a merge output bu er j = 1, and omitted from the merge input This process of selecting the smallest record continues, interrupted only by two conditions: C1 When a merge output bu er is lled, it is written to a merge output le j C2 If a merge input bu er has been processed completely, that merge input block can be ignored during selection When only one merge input bu er contains records, those records are directly copied to the merge output bu er, and the bu er is written out We have now written to the merge output le j = 1 a sequence of sorted records that is m sort blocks long In the case of m = 2 we have merged two input blocks, each from one of the from two source les to create a sorted sequence of two output blocks on one merge output le We then switch to a new merge output le by incrementing j For a two-way merge j alternates between j = 1 and j = 2 A new set of m merge input blocks can be read and processed The merge processing continues for all input sort blocks At the end of the merge input we may not have input blocks for all the bu ers, but this case is treated as if the input bu ers had no records left This merge pass is now complete The input les can be discarded or reused to hold the output of the successor pass Successive Merge Passes The les which were the output of the completed merge pass are reset to become the new input les They now contain sorted sequences of length m sort blocks, and the successor pass has to take this into account For the condition that an input has been completed, C2 in the description of the initial merge pass, the action is now generalized to become: C2 If a merge input bu er has been processed, that bu er is re lled using the next block from the same merge input le until the entire sorted sequence has been read If the sorted sequence is processed completely, the merge input bu er can be ignored during selection When only one merge input sorted sequence remains, the remaining records are directly copied to the merge output les and a new set of sorted sequences can be read The merging of sorted sequences continues to the end of the merge input les Each merge pass processes the output sequences from the prior merge pass With each merge pass the length of the sorted sequences increases by a factor m For a two-way merge the sequences double, redouble, etc
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Data ow in merge-sort
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Merge Termination Eventually the sorted sequence is as large as the source le was This means that we are done Only one merge output le is written, and that le contains the desired output Since we can predict when the nal le is being written we can direct the output to a nal destination An output le can be blocked again to standard form or the results can be used immediately, say, to create an index 3-7-3 Performance of External Sorting The rst phase of a merge-sort requires reading and writing of the entire le content, at a cost of 2TX Since the les are processed sequentially 2TX = 2b btt for b blocks of the source le Parallel operations can reduce that cost, although then the cost of internal sorting must satisfy the condition of Eq 2-22 Each merge pass also requires reading and writing of the entire le contents, at a cost 2TX The selection and copy operations during the merge are simpler than internal sorting, and are easily overlapped with bu ered input and output The number of passes required in the merge phase depends on the size of the initial sort blocks and the power m of the merge For n records of size R we create bs = n/Bfrs sort blocks To merge bs blocks requires logm bs passes
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