Editing Longest common subsequence (section)

=== Example ===
Let <math>X</math> be “<code>XMJYAUZ</code>” and <math>Y</math> be “<code>MZJAWXU</code>”. The longest common subsequence between <math>X</math> and <math>Y</math> is “<code>MJAU</code>”. The table <code>C</code> shown below, which is generated by the function <code>LCSLength</code>, shows the lengths of the longest common subsequences between prefixes of <math>X</math> and <math>Y</math>. The <math>i</math>th row and <math>j</math>th column shows the length of the LCS between <math>X_{1..i}</math> and <math>Y_{1..j}</math>.

{| class="wikitable" style="text-align: center;"
|-
! colspan="2" rowspan="2" |
! 0 !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7
|-
! ε !! M !! Z !! J !! A !! W !! X !! U
|-
! 0 !! ε
| style="background:yellow" | '''0''' || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
! 1 !! X
| style="background:yellow" | 0 || 0 || 0 || 0 || 0 || 0 || 1 || 1
|-
! 2 !! M
| 0 || style="background:yellow" | '''1''' || style="background:yellow" | 1 || 1 || 1 || 1 || 1 || 1
|-
! 3 !! J
| 0 || 1 || 1 || style="background:yellow" | '''2''' || 2 || 2 || 2 || 2
|-
! 4 !! Y
| 0 || 1 || 1 || style="background:yellow" | 2 || 2 || 2 || 2 || 2
|-
! 5 !! A
| 0 || 1 || 1 || 2 || style="background:yellow" | '''3''' || style="background:yellow" | 3 || style="background:yellow" | 3 || 3
|-
! 6 !! U
| 0 || 1 || 1 || 2 || 3 || 3 || 3 || style="background:yellow" | '''4'''
|-
! 7 !! Z
| 0 || 1 || 2 || 2 || 3 || 3 || 3 || style="background: yellow" | 4
|}

The <span style="background: yellow">highlighted</span> numbers show the path the function <code>backtrack</code> would follow from the bottom right to the top left corner, when reading out an LCS. If the current symbols in <math>X</math> and <math>Y</math> are equal, they are part of the LCS, and we go both up and left (shown in '''bold'''). If not, we go up or left, depending on which cell has a higher number. This corresponds to either taking the LCS between <math>X_{1..i-1}</math> and <math>Y_{1..j}</math>, or <math>X_{1..i}</math> and <math>Y_{1..j-1}</math>.