Editing Subsequence (section)

== Common subsequence ==

Given two sequences <math>X</math> and <math>Y,</math> a sequence <math>Z</math> is said to be a ''common subsequence'' of <math>X</math> and <math>Y,</math> if <math>Z</math> is a subsequence of both <math>X</math> and <math>Y.</math>  For example, if
<math display=block>X = \langle A,C,B,D,E,G,C,E,D,B,G \rangle \qquad \text{ and}</math>
<math display=block>Y = \langle B,E,G,J,C,F,E,K,B \rangle \qquad \text{ and}</math>
<math display=block>Z = \langle B,E,E \rangle.</math>
then <math>Z</math> is said to be a common subsequence of <math>X</math> and <math>Y.</math>

This would {{em|not}} be the ''[[Longest-common subsequence problem|longest common subsequence]]'', since <math>Z</math> only has length 3, and the common subsequence <math>\langle B,E,E,B \rangle</math> has length&nbsp;4. The longest common subsequence of <math>X</math> and <math>Y</math> is <math>\langle B,E,G,C,E,B \rangle.</math>