## Class MyersDiff<S extends Sequence>

• Type Parameters:
`S` - type of sequence.

```public class MyersDiff<S extends Sequence>
extends Object```
Diff algorithm, based on "An O(ND) Difference Algorithm and its Variations", by Eugene Myers.

The basic idea is to put the line numbers of text A as columns ("x") and the lines of text B as rows ("y"). Now you try to find the shortest "edit path" from the upper left corner to the lower right corner, where you can always go horizontally or vertically, but diagonally from (x,y) to (x+1,y+1) only if line x in text A is identical to line y in text B.

Myers' fundamental concept is the "furthest reaching D-path on diagonal k": a D-path is an edit path starting at the upper left corner and containing exactly D non-diagonal elements ("differences"). The furthest reaching D-path on diagonal k is the one that contains the most (diagonal) elements which ends on diagonal k (where k = y - x).

Example:

```    H E L L O   W O R L D
____
L     \___
O         \___
W             \________
```

Since every D-path has exactly D horizontal or vertical elements, it can only end on the diagonals -D, -D+2, ..., D-2, D.

Since every furthest reaching D-path contains at least one furthest reaching (D-1)-path (except for D=0), we can construct them recursively.

Since we are really interested in the shortest edit path, we can start looking for a 0-path, then a 1-path, and so on, until we find a path that ends in the lower right corner.

To save space, we do not need to store all paths (which has quadratic space requirements), but generate the D-paths simultaneously from both sides. When the ends meet, we will have found "the middle" of the path. From the end points of that diagonal part, we can generate the rest recursively.

This only requires linear space.

The overall (runtime) complexity is:

```     O(N * D^2 + 2 * N/2 * (D/2)^2 + 4 * N/4 * (D/4)^2 + ...)
= O(N * D^2 * 5 / 4) = O(N * D^2),
```

(With each step, we have to find the middle parts of twice as many regions as before, but the regions (as well as the D) are halved.)

So the overall runtime complexity stays the same with linear space, albeit with a larger constant factor.

• ### Field Summary

Fields
Modifier and Type Field Description
`protected HashedSequence<S>` `a`
The first text to be compared.
`protected HashedSequence<S>` `b`
The second text to be compared.
`protected HashedSequenceComparator<S>` `cmp`
Comparison function for sequences.
`protected EditList` `edits`
The list of edits found during the last call to `calculateEdits(Edit)`
`static DiffAlgorithm` `INSTANCE`
Singleton instance of MyersDiff.
• ### Method Summary

All Methods
Modifier and Type Method Description
`protected void` ```calculateEdits​(int beginA, int endA, int beginB, int endB)```
Calculates the differences between a given part of A against another given part of B
`static void` `main​(String[] args)`
Main method
• ### Methods inherited from class java.lang.Object

`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`
• ### Field Detail

• #### INSTANCE

`public static final DiffAlgorithm INSTANCE`
Singleton instance of MyersDiff.
• #### cmp

`protected HashedSequenceComparator<S extends Sequence> cmp`
Comparison function for sequences.
• #### a

`protected HashedSequence<S extends Sequence> a`
The first text to be compared. Referred to as "Text A" in the comments
• #### b

`protected HashedSequence<S extends Sequence> b`
The second text to be compared. Referred to as "Text B" in the comments
• ### Method Detail

• #### calculateEdits

```protected void calculateEdits​(int beginA,
int endA,
int beginB,
int endB)```
Calculates the differences between a given part of A against another given part of B
Parameters:
`beginA` - start of the part of A which should be compared (0<=beginA<sizeof(A))
`endA` - end of the part of A which should be compared (beginA<=endA<sizeof(A))
`beginB` - start of the part of B which should be compared (0<=beginB<sizeof(B))
`endB` - end of the part of B which should be compared (beginB<=endB<sizeof(B))
• #### main

`public static void main​(String[] args)`
Main method
Parameters:
`args` - two filenames specifying the contents to be diffed