https://metool.online/_assets/js/how-text-diff-algorithms-work.en.BXHo1N1b.js

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2const e=`<blockquote>
3<p>Text diff looks like &quot;mark differences red and green&quot;—the hard part is: <strong>after inserting one line, every line below shifts—how do you know they are unchanged, just offset?</strong> Diff's core is not character comparison but finding a <strong>minimum-cost edit path from A to B</strong>.</p>
4</blockquote>
5<p><img src="/blog/how-text-diff-algorithms-work/cover.webp" alt="Finding the shortest edit path between two texts on an edit graph grid"></p>
6<h2>What Problem Is Diff Actually Solving?</h2>
7<p>Diff asks for the <strong>shortest edit sequence from text A to text B</strong>: the fewest insert and delete operations to turn A into B. Why not compare character by character? Insert a line at row 3 and naive comparison misaligns everything below—each line looks &quot;changed&quot; while a human sees only a downward shift with identical content.</p>
8<p>Modeling &quot;minimum edits&quot; lets the algorithm recognize <strong>&quot;these lines are unchanged, just pushed down by the insert.&quot;</strong> That pairs with <strong>longest common subsequence (LCS)</strong>: the longer the LCS of A and B, the fewer edits needed—two views of the same coin.</p>
9<h2>How Does LCS Locate the Unchanged Parts?</h2>
10<p>LCS is the <strong>longest subsequence appearing in both texts in original order, not necessarily contiguous</strong>. It is what A and B share unchanged; A-only parts are deletes, B-only parts are adds. Classic approach: dynamic programming—</p>
11<ul>
12<li>Table <code>dp[i][j]</code> = LCS length of first i units of A and first j of B;</li>
13<li>If units match, <code>dp[i][j] = dp[i-1][j-1] + 1</code>; else max of cell above and left;</li>
14<li>Backtrack the table to recover common vs add/delete regions.</li>
15</ul>
16<p>Intuitive and easy to implement—but time and space are O(N×M) for lengths N, M. Large texts blow up the table—that is the main weakness.</p>
17<h2>Why Is Myers Faster and More Common?</h2>
18<p>Myers treats diff as <strong>shortest path on an edit graph</strong>—often much faster than naive DP when differences are small, which is why Git uses it. Key insight: real versions usually differ in <strong>few places</strong>—difference count D is small. Myers runs in roughly <strong>O(ND)</strong> (N total length, D edit distance); when D ≪ N, behavior is nearly linear.</p>
19<table>
20<thead>
21<tr>
22<th>Dimension</th>
23<th>LCS dynamic programming</th>
24<th>Myers (O(ND))</th>
25</tr>
26</thead>
27<tbody>
28<tr>
29<td>Idea</td>
30<td>Fill 2D table for LCS</td>
31<td>Shortest edit path on edit graph</td>
32</tr>
33<tr>
34<td>Time</td>
35<td>O(N×M)</td>
36<td>~O(ND), D = diff count</td>
37</tr>
38<tr>
39<td>Space</td>
40<td>O(N×M) (optimizable to O(N))</td>
41<td>Linear-space variants O(N)</td>
42</tr>
43<tr>
44<td>Small diffs</td>
45<td>Still fills full table</td>
46<td>Very fast (near linear)</td>
47</tr>
48<tr>
49<td>Large diffs</td>
50<td>Stable but slow</td>
51<td>Degrades toward O(N²)</td>
52</tr>
53<tr>
54<td>Typical use</td>
55<td>Teaching, short text</td>
56<td>Git, most diff tools</td>
57</tr>
58</tbody>
59</table>
60<p>Practical takeaway: <strong>Myers wins when D is small; both slow when diffs dominate</strong>.</p>
61<h2>Line-Level vs Character-Level Diff—How to Choose?</h2>
62<p>Diff granularity matters—wrong unit hurts readability. Three common levels:</p>
63<ul>
64<li><strong>Line-level</strong>: compare whole lines—default for code, config, logs. Clean structure; tells you a line changed, not which character inside.</li>
65<li><strong>Word-level</strong>: words or tokens—better for prose; shows which word changed.</li>
66<li><strong>Character-level</strong>: finest; long text produces noisy micro-fragments and hurts readability.</li>
67</ul>
68<p>Common engineering pattern: <strong>layered</strong>—line diff for structure, then finer diff on paired &quot;modified&quot; lines.</p>
69<h2>How Is Inline Highlighting Implemented?</h2>
70<p>Inline highlight (exact characters changed within one line) is usually <strong>two-level diff</strong>. Level one: line diff yields delete/add operations; when a delete and add pair nearby with enough similarity, classify as <strong>modified line</strong>. Level two: character- or word-level diff on that pair to mark changed fragments precisely.</p>
71<p>Inline highlight is not separate magic—it is <strong>the same algorithm at finer granularity</strong>—which is why it costs more: every modified line pair runs diff again.</p>
72<h2>Limits and Known Boundaries</h2>
73<p>

73Diff is not universal. Common boundaries:</p>
74<ul>
75<li><strong>Large diffs degrade</strong>: when texts are almost entirely different (D ≈ N), Myers approaches O(N²)—large inputs may stutter;</li>
76<li><strong>No semantic equivalence</strong>: only character sequences—rename-with-same-logic or moved code blocks read as delete + add, not &quot;moved unchanged&quot;;</li>
77<li><strong>Line endings and whitespace</strong>: CRLF vs LF, trailing spaces, tab vs space indent all count as diffs—normalize before compare;</li>
78<li><strong>Granularity vs readability</strong>: character diff on long paragraphs fragments output—word or line level often clearer.</li>
79</ul>
80<p>A useful diff result depends on <strong>granularity matching text type and sensible newline/whitespace normalization</strong>—not raw algorithm speed alone.</p>
81<h2>Summary</h2>
82<p>Text diff is not &quot;compare every character&quot; but <strong>find a shortest edit path</strong>: LCS finds shared unchanged content; Myers uses edit-graph shortest path for near-linear behavior when D is small. Line, word, and character levels are granularity choices; inline highlight is line diff then character diff on modified pairs. Understand <strong>shortest edit + granularity + normalization</strong> and you can judge what diff implementation fits which text and scale.</p>
83`;export{e as default};