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<H1>merge</H1>
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(definition)

<P>
<strong>Definition:</strong>
Combine two or more sorted sequences of data into a single sorted  sequence.
<P><strong>See also</strong>
<a href="nonitermerge.html" tppabs="http://hissa.nist.gov/dads/HTML/nonitermerge.html"><em>noniterative merge</em></a>, <a href="simplemerge.html" tppabs="http://hissa.nist.gov/dads/HTML/simplemerge.html"><em>simple merge</em></a>, <a href="idealmerge.html" tppabs="http://hissa.nist.gov/dads/HTML/idealmerge.html"><em>ideal merge</em></a>, <a href="twowaymrgsrt.html" tppabs="http://hissa.nist.gov/dads/HTML/twowaymrgsrt.html"><em>two-way merge sort</em></a>, <a href="threewaymsrt.html" tppabs="http://hissa.nist.gov/dads/HTML/threewaymsrt.html"><em>three-way merge sort</em></a>, <a href="kwaymergsort.html" tppabs="http://hissa.nist.gov/dads/HTML/kwaymergsort.html"><em>k-way merge sort</em></a>, <a href="balancmrgsrt.html" tppabs="http://hissa.nist.gov/dads/HTML/balancmrgsrt.html"><em>balanced merge sort</em></a>, <a href="nonbalncmsrt.html" tppabs="http://hissa.nist.gov/dads/HTML/nonbalncmsrt.html"><em>nonbalanced merge sort</em></a>.
<P><em>Note:
Formally the input is two sequences, A={a<sub>1</sub>,  ..., a<sub>n</sub>} and B={b<sub>1</sub>,  ..., b<sub>m</sub>}, each sorted according to some <a href="totalorder.html" tppabs="http://hissa.nist.gov/dads/HTML/totalorder.html"><em>total order</em></a>, <=.  The output is a single sequence, merge(A,B), which is a sorted permutation of {a<sub>1</sub>,  ..., a<sub>n</sub>, b<sub>1</sub>,  ..., b<sub>m</sub>}. <P> The method defines merge(A, B) as (1) A if B is empty, (2) B if A is empty, (3) {a<sub>1</sub>}.merge({a<sub>2</sub>,  ..., a<sub>n</sub>}, B) if a<sub>1</sub> <= b<sub>1</sub>, and (4) {b<sub>1</sub>}.merge(A, {b<sub>2</sub>,  ..., b<sub>m</sub>}) otherwise.  Here are symbol "." stands for concatenation, for example, {a<sub>1</sub>,  ..., a<sub>n</sub>}.{b<sub>1</sub>,  ..., b<sub>m</sub>} = {a<sub>1</sub>,  ..., a<sub>n</sub>, b<sub>1</sub>,  ..., b<sub>m</sub>}. <P> Formalization by Mustafa Ege &lt;ege@eti.cc.hun.edu.tr&gt;.</em>
<P>Author: <a href="terms.html#authorASK" tppabs="http://hissa.nist.gov/dads/terms.html#authorASK">ASK</a>

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Entry modified Tue Jun  8 12:08:39 1999.<BR>
HTML page formatted Wed Dec 22 09:35:50 1999.

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