forked from M3-Academy/challenge-algorithms-v2.0
405 lines
15 KiB
Markdown
405 lines
15 KiB
Markdown
# diff-sequences
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Compare items in two sequences to find a **longest common subsequence**.
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The items not in common are the items to delete or insert in a **shortest edit script**.
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To maximize flexibility and minimize memory, you write **callback** functions as configuration:
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**Input** function `isCommon(aIndex, bIndex)` compares items at indexes in the sequences and returns a truthy/falsey value. This package might call your function more than once for some pairs of indexes.
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- Because your function encapsulates **comparison**, this package can compare items according to `===` operator, `Object.is` method, or other criterion.
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- Because your function encapsulates **sequences**, this package can find differences in arrays, strings, or other data.
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**Output** function `foundSubsequence(nCommon, aCommon, bCommon)` receives the number of adjacent items and starting indexes of each common subsequence. If sequences do not have common items, then this package does not call your function.
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If N is the sum of lengths of sequences and L is length of a longest common subsequence, then D = N – 2L is the number of **differences** in the corresponding shortest edit script.
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[_An O(ND) Difference Algorithm and Its Variations_](http://xmailserver.org/diff2.pdf) by Eugene W. Myers is fast when sequences have **few** differences.
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This package implements the **linear space** variation with optimizations so it is fast even when sequences have **many** differences.
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## Usage
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To add this package as a dependency of a project, do either of the following:
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- `npm install diff-sequences`
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- `yarn add diff-sequences`
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To use `diff` as the name of the default export from this package, do either of the following:
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- `var diff = require('diff-sequences').default; // CommonJS modules`
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- `import diff from 'diff-sequences'; // ECMAScript modules`
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Call `diff` with the **lengths** of sequences and your **callback** functions:
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```js
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const a = ['a', 'b', 'c', 'a', 'b', 'b', 'a'];
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const b = ['c', 'b', 'a', 'b', 'a', 'c'];
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function isCommon(aIndex, bIndex) {
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return a[aIndex] === b[bIndex];
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}
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function foundSubsequence(nCommon, aCommon, bCommon) {
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// see examples
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}
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diff(a.length, b.length, isCommon, foundSubsequence);
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```
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## Example of longest common subsequence
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Some sequences (for example, `a` and `b` in the example of usage) have more than one longest common subsequence.
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This package finds the following common items:
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| comparisons of common items | values | output arguments |
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| :------------------------------- | :--------- | --------------------------: |
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| `a[2] === b[0]` | `'c'` | `foundSubsequence(1, 2, 0)` |
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| `a[4] === b[1]` | `'b'` | `foundSubsequence(1, 4, 1)` |
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| `a[5] === b[3] && a[6] === b[4]` | `'b', 'a'` | `foundSubsequence(2, 5, 3)` |
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The “edit graph” analogy in the Myers paper shows the following common items:
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| comparisons of common items | values |
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| :------------------------------- | :--------- |
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| `a[2] === b[0]` | `'c'` |
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| `a[3] === b[2] && a[4] === b[3]` | `'a', 'b'` |
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| `a[6] === b[4]` | `'a'` |
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Various packages which implement the Myers algorithm will **always agree** on the **length** of a longest common subsequence, but might **sometimes disagree** on which **items** are in it.
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## Example of callback functions to count common items
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```js
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// Return length of longest common subsequence according to === operator.
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function countCommonItems(a, b) {
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let n = 0;
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function isCommon(aIndex, bIndex) {
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return a[aIndex] === b[bIndex];
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}
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function foundSubsequence(nCommon) {
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n += nCommon;
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}
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diff(a.length, b.length, isCommon, foundSubsequence);
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return n;
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}
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const commonLength = countCommonItems(
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['a', 'b', 'c', 'a', 'b', 'b', 'a'],
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['c', 'b', 'a', 'b', 'a', 'c'],
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);
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```
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| category of items | expression | value |
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| :----------------- | ------------------------: | ----: |
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| in common | `commonLength` | `4` |
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| to delete from `a` | `a.length - commonLength` | `3` |
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| to insert from `b` | `b.length - commonLength` | `2` |
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If the length difference `b.length - a.length` is:
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- negative: its absolute value is the minimum number of items to **delete** from `a`
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- positive: it is the minimum number of items to **insert** from `b`
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- zero: there is an **equal** number of items to delete from `a` and insert from `b`
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- non-zero: there is an equal number of **additional** items to delete from `a` and insert from `b`
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In this example, `6 - 7` is:
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- negative: `1` is the minimum number of items to **delete** from `a`
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- non-zero: `2` is the number of **additional** items to delete from `a` and insert from `b`
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## Example of callback functions to find common items
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```js
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// Return array of items in longest common subsequence according to Object.is method.
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const findCommonItems = (a, b) => {
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const array = [];
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diff(
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a.length,
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b.length,
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(aIndex, bIndex) => Object.is(a[aIndex], b[bIndex]),
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(nCommon, aCommon) => {
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for (; nCommon !== 0; nCommon -= 1, aCommon += 1) {
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array.push(a[aCommon]);
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}
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},
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);
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return array;
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};
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const commonItems = findCommonItems(
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['a', 'b', 'c', 'a', 'b', 'b', 'a'],
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['c', 'b', 'a', 'b', 'a', 'c'],
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);
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```
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| `i` | `commonItems[i]` | `aIndex` |
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| --: | :--------------- | -------: |
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| `0` | `'c'` | `2` |
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| `1` | `'b'` | `4` |
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| `2` | `'b'` | `5` |
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| `3` | `'a'` | `6` |
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## Example of callback functions to diff index intervals
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Instead of slicing array-like objects, you can adjust indexes in your callback functions.
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```js
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// Diff index intervals that are half open [start, end) like array slice method.
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const diffIndexIntervals = (a, aStart, aEnd, b, bStart, bEnd) => {
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// Validate: 0 <= aStart and aStart <= aEnd and aEnd <= a.length
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// Validate: 0 <= bStart and bStart <= bEnd and bEnd <= b.length
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diff(
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aEnd - aStart,
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bEnd - bStart,
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(aIndex, bIndex) => Object.is(a[aStart + aIndex], b[bStart + bIndex]),
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(nCommon, aCommon, bCommon) => {
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// aStart + aCommon, bStart + bCommon
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},
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);
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// After the last common subsequence, do any remaining work.
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};
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```
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## Example of callback functions to emulate diff command
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Linux or Unix has a `diff` command to compare files line by line. Its output is a **shortest edit script**:
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- **c**hange adjacent lines from the first file to lines from the second file
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- **d**elete lines from the first file
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- **a**ppend or insert lines from the second file
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```js
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// Given zero-based half-open range [start, end) of array indexes,
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// return one-based closed range [start + 1, end] as string.
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const getRange = (start, end) =>
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start + 1 === end ? `${start + 1}` : `${start + 1},${end}`;
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// Given index intervals of lines to delete or insert, or both, or neither,
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// push formatted diff lines onto array.
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const pushDelIns = (aLines, aIndex, aEnd, bLines, bIndex, bEnd, array) => {
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const deleteLines = aIndex !== aEnd;
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const insertLines = bIndex !== bEnd;
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const changeLines = deleteLines && insertLines;
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if (changeLines) {
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array.push(`${getRange(aIndex, aEnd)}c${getRange(bIndex, bEnd)}`);
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} else if (deleteLines) {
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array.push(`${getRange(aIndex, aEnd)}d${String(bIndex)}`);
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} else if (insertLines) {
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array.push(`${String(aIndex)}a${getRange(bIndex, bEnd)}`);
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} else {
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return;
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}
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for (; aIndex !== aEnd; aIndex += 1) {
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array.push(`< ${aLines[aIndex]}`); // delete is less than
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}
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if (changeLines) {
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array.push('---');
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}
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for (; bIndex !== bEnd; bIndex += 1) {
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array.push(`> ${bLines[bIndex]}`); // insert is greater than
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}
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};
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// Given content of two files, return emulated output of diff utility.
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const findShortestEditScript = (a, b) => {
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const aLines = a.split('\n');
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const bLines = b.split('\n');
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const aLength = aLines.length;
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const bLength = bLines.length;
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const isCommon = (aIndex, bIndex) => aLines[aIndex] === bLines[bIndex];
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let aIndex = 0;
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let bIndex = 0;
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const array = [];
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const foundSubsequence = (nCommon, aCommon, bCommon) => {
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pushDelIns(aLines, aIndex, aCommon, bLines, bIndex, bCommon, array);
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aIndex = aCommon + nCommon; // number of lines compared in a
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bIndex = bCommon + nCommon; // number of lines compared in b
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};
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diff(aLength, bLength, isCommon, foundSubsequence);
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// After the last common subsequence, push remaining change lines.
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pushDelIns(aLines, aIndex, aLength, bLines, bIndex, bLength, array);
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return array.length === 0 ? '' : `${array.join('\n')}\n`;
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};
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```
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## Example of callback functions to format diff lines
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Here is simplified code to format **changed and unchanged lines** in expected and received values after a test fails in Jest:
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```js
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// Format diff with minus or plus for change lines and space for common lines.
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const formatDiffLines = (a, b) => {
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// Jest depends on pretty-format package to serialize objects as strings.
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// Unindented for comparison to avoid distracting differences:
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const aLinesUn = format(a, {indent: 0 /*, other options*/}).split('\n');
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const bLinesUn = format(b, {indent: 0 /*, other options*/}).split('\n');
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// Indented to display changed and unchanged lines:
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const aLinesIn = format(a, {indent: 2 /*, other options*/}).split('\n');
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const bLinesIn = format(b, {indent: 2 /*, other options*/}).split('\n');
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const aLength = aLinesIn.length; // Validate: aLinesUn.length === aLength
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const bLength = bLinesIn.length; // Validate: bLinesUn.length === bLength
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const isCommon = (aIndex, bIndex) => aLinesUn[aIndex] === bLinesUn[bIndex];
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// Only because the GitHub Flavored Markdown doc collapses adjacent spaces,
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// this example code and the following table represent spaces as middle dots.
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let aIndex = 0;
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let bIndex = 0;
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const array = [];
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const foundSubsequence = (nCommon, aCommon, bCommon) => {
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for (; aIndex !== aCommon; aIndex += 1) {
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array.push(`-·${aLinesIn[aIndex]}`); // delete is minus
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}
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for (; bIndex !== bCommon; bIndex += 1) {
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array.push(`+·${bLinesIn[bIndex]}`); // insert is plus
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}
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for (; nCommon !== 0; nCommon -= 1, aIndex += 1, bIndex += 1) {
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// For common lines, received indentation seems more intuitive.
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array.push(`··${bLinesIn[bIndex]}`); // common is space
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}
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};
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diff(aLength, bLength, isCommon, foundSubsequence);
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// After the last common subsequence, push remaining change lines.
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for (; aIndex !== aLength; aIndex += 1) {
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array.push(`-·${aLinesIn[aIndex]}`);
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}
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for (; bIndex !== bLength; bIndex += 1) {
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array.push(`+·${bLinesIn[bIndex]}`);
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}
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return array;
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};
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const expected = {
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searching: '',
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sorting: {
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ascending: true,
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fieldKey: 'what',
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},
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};
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const received = {
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searching: '',
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sorting: [
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{
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descending: false,
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fieldKey: 'what',
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},
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],
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};
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const diffLines = formatDiffLines(expected, received);
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```
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If N is the sum of lengths of sequences and L is length of a longest common subsequence, then N – L is length of an array of diff lines. In this example, N is 7 + 9, L is 5, and N – L is 11.
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| `i` | `diffLines[i]` | `aIndex` | `bIndex` |
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| ---: | :--------------------------------- | -------: | -------: |
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| `0` | `'··Object {'` | `0` | `0` |
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| `1` | `'····"searching": "",'` | `1` | `1` |
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| `2` | `'-···"sorting": Object {'` | `2` | |
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| `3` | `'-·····"ascending": true,'` | `3` | |
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| `4` | `'+·····"sorting": Array ['` | | `2` |
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| `5` | `'+·······Object {'` | | `3` |
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| `6` | `'+·········"descending": false,'` | | `4` |
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| `7` | `'··········"fieldKey": "what",'` | `4` | `5` |
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| `8` | `'········},'` | `5` | `6` |
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| `9` | `'+·····],'` | | `7` |
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| `10` | `'··}'` | `6` | `8` |
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## Example of callback functions to find diff items
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Here is simplified code to find changed and unchanged substrings **within adjacent changed lines** in expected and received values after a test fails in Jest:
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```js
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// Return diff items for strings (compatible with diff-match-patch package).
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const findDiffItems = (a, b) => {
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const isCommon = (aIndex, bIndex) => a[aIndex] === b[bIndex];
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let aIndex = 0;
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let bIndex = 0;
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const array = [];
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const foundSubsequence = (nCommon, aCommon, bCommon) => {
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if (aIndex !== aCommon) {
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array.push([-1, a.slice(aIndex, aCommon)]); // delete is -1
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}
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if (bIndex !== bCommon) {
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array.push([1, b.slice(bIndex, bCommon)]); // insert is 1
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}
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aIndex = aCommon + nCommon; // number of characters compared in a
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bIndex = bCommon + nCommon; // number of characters compared in b
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array.push([0, a.slice(aCommon, aIndex)]); // common is 0
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};
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diff(a.length, b.length, isCommon, foundSubsequence);
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// After the last common subsequence, push remaining change items.
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if (aIndex !== a.length) {
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array.push([-1, a.slice(aIndex)]);
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}
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if (bIndex !== b.length) {
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array.push([1, b.slice(bIndex)]);
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}
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return array;
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};
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const expectedDeleted = ['"sorting": Object {', '"ascending": true,'].join(
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'\n',
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);
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const receivedInserted = [
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'"sorting": Array [',
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'Object {',
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'"descending": false,',
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].join('\n');
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const diffItems = findDiffItems(expectedDeleted, receivedInserted);
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```
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| `i` | `diffItems[i][0]` | `diffItems[i][1]` |
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| --: | ----------------: | :---------------- |
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| `0` | `0` | `'"sorting": '` |
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| `1` | `1` | `'Array [\n'` |
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| `2` | `0` | `'Object {\n"'` |
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| `3` | `-1` | `'a'` |
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| `4` | `1` | `'de'` |
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| `5` | `0` | `'scending": '` |
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| `6` | `-1` | `'tru'` |
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| `7` | `1` | `'fals'` |
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| `8` | `0` | `'e,'` |
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The length difference `b.length - a.length` is equal to the sum of `diffItems[i][0]` values times `diffItems[i][1]` lengths. In this example, the difference `48 - 38` is equal to the sum `10`.
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| category of diff item | `[0]` | `[1]` lengths | subtotal |
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| :-------------------- | ----: | -----------------: | -------: |
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| in common | `0` | `11 + 10 + 11 + 2` | `0` |
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| to delete from `a` | `–1` | `1 + 3` | `-4` |
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| to insert from `b` | `1` | `8 + 2 + 4` | `14` |
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Instead of formatting the changed substrings with escape codes for colors in the `foundSubsequence` function to save memory, this example spends memory to **gain flexibility** before formatting, so a separate heuristic algorithm might modify the generic array of diff items to show changes more clearly:
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| `i` | `diffItems[i][0]` | `diffItems[i][1]` |
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| --: | ----------------: | :---------------- |
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| `6` | `-1` | `'true'` |
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| `7` | `1` | `'false'` |
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| `8` | `0` | `','` |
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For expected and received strings of serialized data, the result of finding changed **lines**, and then finding changed **substrings** within adjacent changed lines (as in the preceding two examples) sometimes displays the changes in a more intuitive way than the result of finding changed substrings, and then splitting them into changed and unchanged lines.
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