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stroke-linecap=\"round\" stroke-linejoin=\"round\" stroke-width=\"2\">\u003Cpath d=\"M11.017 2.814a1 1 0 0 1 1.966 0l1.051 5.558a2 2 0 0 0 1.594 1.594l5.558 1.051a1 1 0 0 1 0 1.966l-5.558 1.051a2 2 0 0 0-1.594 1.594l-1.051 5.558a1 1 0 0 1-1.966 0l-1.051-5.558a2 2 0 0 0-1.594-1.594l-5.558-1.051a1 1 0 0 1 0-1.966l5.558-1.051a2 2 0 0 0 1.594-1.594zM20 2v4m2-2h-4\"\u002F>\u003Ccircle cx=\"4\" cy=\"20\" r=\"2\"\u002F>\u003C\u002Fg>",{"left":4,"top":4,"width":5,"height":5,"rotate":4,"vFlip":6,"hFlip":6,"body":44},"\u003Cg fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"round\" stroke-linejoin=\"round\" stroke-width=\"2\">\u003Cpath d=\"M21.42 10.922a1 1 0 0 0-.019-1.838L12.83 5.18a2 2 0 0 0-1.66 0L2.6 9.08a1 1 0 0 0 0 1.832l8.57 3.908a2 2 0 0 0 1.66 0zM22 10v6\"\u002F>\u003Cpath d=\"M6 12.5V16a6 3 0 0 0 12 0v-3.5\"\u002F>\u003C\u002Fg>","\u003Cblockquote>\n\u003Cp>Text diff looks like "mark differences red and green"—the hard part is: \u003Cstrong>after inserting one line, every line below shifts—how do you know they are unchanged, just offset?\u003C\u002Fstrong> Diff's core is not character comparison but finding a \u003Cstrong>minimum-cost edit path from A to B\u003C\u002Fstrong>.\u003C\u002Fp>\n\u003C\u002Fblockquote>\n\u003Cp>\u003Cimg src=\"\u002Fblog\u002Fhow-text-diff-algorithms-work\u002Fcover.webp\" alt=\"Finding the shortest edit path between two texts on an edit graph grid\">\u003C\u002Fp>\n\u003Ch2>What Problem Is Diff Actually Solving?\u003C\u002Fh2>\n\u003Cp>Diff asks for the \u003Cstrong>shortest edit sequence from text A to text B\u003C\u002Fstrong>: 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 "changed" while a human sees only a downward shift with identical content.\u003C\u002Fp>\n\u003Cp>Modeling "minimum edits" lets the algorithm recognize \u003Cstrong>"these lines are unchanged, just pushed down by the insert."\u003C\u002Fstrong> That pairs with \u003Cstrong>longest common subsequence (LCS)\u003C\u002Fstrong>: the longer the LCS of A and B, the fewer edits needed—two views of the same coin.\u003C\u002Fp>\n\u003Ch2>How Does LCS Locate the Unchanged Parts?\u003C\u002Fh2>\n\u003Cp>LCS is the \u003Cstrong>longest subsequence appearing in both texts in original order, not necessarily contiguous\u003C\u002Fstrong>. It is what A and B share unchanged; A-only parts are deletes, B-only parts are adds. Classic approach: dynamic programming—\u003C\u002Fp>\n\u003Cul>\n\u003Cli>Table \u003Ccode>dp[i][j]\u003C\u002Fcode> = LCS length of first i units of A and first j of B;\u003C\u002Fli>\n\u003Cli>If units match, \u003Ccode>dp[i][j] = dp[i-1][j-1] + 1\u003C\u002Fcode>; else max of cell above and left;\u003C\u002Fli>\n\u003Cli>Backtrack the table to recover common vs add\u002Fdelete regions.\u003C\u002Fli>\n\u003C\u002Ful>\n\u003Cp>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.\u003C\u002Fp>\n\u003Ch2>Why Is Myers Faster and More Common?\u003C\u002Fh2>\n\u003Cp>Myers treats diff as \u003Cstrong>shortest path on an edit graph\u003C\u002Fstrong>—often much faster than naive DP when differences are small, which is why Git uses it. Key insight: real versions usually differ in \u003Cstrong>few places\u003C\u002Fstrong>—difference count D is small. Myers runs in roughly \u003Cstrong>O(ND)\u003C\u002Fstrong> (N total length, D edit distance); when D ≪ N, behavior is nearly linear.\u003C\u002Fp>\n\u003Ctable>\n\u003Cthead>\n\u003Ctr>\n\u003Cth>Dimension\u003C\u002Fth>\n\u003Cth>LCS dynamic programming\u003C\u002Fth>\n\u003Cth>Myers (O(ND))\u003C\u002Fth>\n\u003C\u002Ftr>\n\u003C\u002Fthead>\n\u003Ctbody>\n\u003Ctr>\n\u003Ctd>Idea\u003C\u002Ftd>\n\u003Ctd>Fill 2D table for LCS\u003C\u002Ftd>\n\u003Ctd>Shortest edit path on edit graph\u003C\u002Ftd>\n\u003C\u002Ftr>\n\u003Ctr>\n\u003Ctd>Time\u003C\u002Ftd>\n\u003Ctd>O(N×M)\u003C\u002Ftd>\n\u003Ctd>~O(ND), D = diff count\u003C\u002Ftd>\n\u003C\u002Ftr>\n\u003Ctr>\n\u003Ctd>Space\u003C\u002Ftd>\n\u003Ctd>O(N×M) (optimizable to O(N))\u003C\u002Ftd>\n\u003Ctd>Linear-space variants O(N)\u003C\u002Ftd>\n\u003C\u002Ftr>\n\u003Ctr>\n\u003Ctd>Small diffs\u003C\u002Ftd>\n\u003Ctd>Still fills full table\u003C\u002Ftd>\n\u003Ctd>Very fast (near linear)\u003C\u002Ftd>\n\u003C\u002Ftr>\n\u003Ctr>\n\u003Ctd>Large diffs\u003C\u002Ftd>\n\u003Ctd>Stable but slow\u003C\u002Ftd>\n\u003Ctd>Degrades toward O(N²)\u003C\u002Ftd>\n\u003C\u002Ftr>\n\u003Ctr>\n\u003Ctd>Typical use\u003C\u002Ftd>\n\u003Ctd>Teaching, short text\u003C\u002Ftd>\n\u003Ctd>Git, most diff tools\u003C\u002Ftd>\n\u003C\u002Ftr>\n\u003C\u002Ftbody>\n\u003C\u002Ftable>\n\u003Cp>Practical takeaway: \u003Cstrong>Myers wins when D is small; both slow when diffs dominate\u003C\u002Fstrong>.\u003C\u002Fp>\n\u003Ch2>Line-Level vs Character-Level Diff—How to Choose?\u003C\u002Fh2>\n\u003Cp>Diff granularity matters—wrong unit hurts readability. Three common levels:\u003C\u002Fp>\n\u003Cul>\n\u003Cli>\u003Cstrong>Line-level\u003C\u002Fstrong>: compare whole lines—default for code, config, logs. Clean structure; tells you a line changed, not which character inside.\u003C\u002Fli>\n\u003Cli>\u003Cstrong>Word-level\u003C\u002Fstrong>: words or tokens—better for prose; shows which word changed.\u003C\u002Fli>\n\u003Cli>\u003Cstrong>Character-level\u003C\u002Fstrong>: finest; long text produces noisy micro-fragments and hurts readability.\u003C\u002Fli>\n\u003C\u002Ful>\n\u003Cp>Common engineering pattern: \u003Cstrong>layered\u003C\u002Fstrong>—line diff for structure, then finer diff on paired "modified" lines.\u003C\u002Fp>\n\u003Ch2>How Is Inline Highlighting Implemented?\u003C\u002Fh2>\n\u003Cp>Inline highlight (exact characters changed within one line) is usually \u003Cstrong>two-level diff\u003C\u002Fstrong>. Level one: line diff yields delete\u002Fadd operations; when a delete and add pair nearby with enough similarity, classify as \u003Cstrong>modified line\u003C\u002Fstrong>. Level two: character- or word-level diff on that pair to mark changed fragments precisely.\u003C\u002Fp>\n\u003Cp>Inline highlight is not separate magic—it is \u003Cstrong>the same algorithm at finer granularity\u003C\u002Fstrong>—which is why it costs more: every modified line pair runs diff again.\u003C\u002Fp>\n\u003Ch2>Limits and Known Boundaries\u003C\u002Fh2>\n\u003Cp>Diff is not universal. Common boundaries:\u003C\u002Fp>\n\u003Cul>\n\u003Cli>\u003Cstrong>Large diffs degrade\u003C\u002Fstrong>: when texts are almost entirely different (D ≈ N), Myers approaches O(N²)—large inputs may stutter;\u003C\u002Fli>\n\u003Cli>\u003Cstrong>No semantic equivalence\u003C\u002Fstrong>: only character sequences—rename-with-same-logic or moved code blocks read as delete + add, not "moved unchanged";\u003C\u002Fli>\n\u003Cli>\u003Cstrong>Line endings and whitespace\u003C\u002Fstrong>: CRLF vs LF, trailing spaces, tab vs space indent all count as diffs—normalize before compare;\u003C\u002Fli>\n\u003Cli>\u003Cstrong>Granularity vs readability\u003C\u002Fstrong>: character diff on long paragraphs fragments output—word or line level often clearer.\u003C\u002Fli>\n\u003C\u002Ful>\n\u003Cp>A useful diff result depends on \u003Cstrong>granularity matching text type and sensible newline\u002Fwhitespace normalization\u003C\u002Fstrong>—not raw algorithm speed alone.\u003C\u002Fp>\n\u003Ch2>Summary\u003C\u002Fh2>\n\u003Cp>Text diff is not "compare every character" but \u003Cstrong>find a shortest edit path\u003C\u002Fstrong>: 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. 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