5. Diff

The diff(3m) module will compute the shortest edit script (SES) of two sequences. This algorithm is perhaps best known as the one used in GNU diff(1) although GNU diff employs additional optimizations specific to line oriented input such as source code files whereas this implementation is more generic. Formally, this implementation of the SES solution uses the dynamic programming algorithm described by Myers [1] with the Hirschberg linear space refinement. The objective is to compute the minimum set of edit operations necessary to transform a sequence A of length N into B of length M. This can be performed in O(N+M*D^2) expected time where D is the edit distance (number of elements deleted and inserted to transform A into B). Thus the algorithm is particularly fast and uses less space if the difference between sequences is small. The interface is generic such that sequences can be anything that can be indexed and compared with user supplied functions including arrays of structures, linked lists, arrays of pointers to strings in a file, etc.

[1] E. Myers, ``An O(ND) Difference Algorithm and Its Variations,'' Algorithmica 1, 2 (1986), 251-266. http://www.cs.arizona.edu/people/gene/PAPERS/diff.ps

Example 2. Printing the Edit Script
The below code computes and prints the edit script of two 8 bit encoded character strings a and b. Note that off and len for DIFF_INSERT operations reference sequence b whereas matches and deletes reference sequence a.

  int d, sn, i;
  struct varray *ses = varray_new(sizeof(struct diff_edit), NULL);
  d = diff(a, 0, n, b, 0, m, NULL, NULL, NULL, 0, ses, &sn, NULL);
  for (i = 0; i < sn; i++) {
  	struct diff_edit *e = varray_get(ses, i);
  	switch (e->op) {
  		case DIFF_MATCH:
  			printf("MAT: ");
  			fwrite(a + e->off, 1, e->len, stdout);
  		case DIFF_DELETE:
  			printf("DEL: ");
  			fwrite(a + e->off, 1, e->len, stdout);
  		case DIFF_INSERT:
  			printf("INS: ");
  			fwrite(b + e->off, 1, e->len, stdout);


Diff definitions

#include <mba/diff.h> typedef const void *(*idx_fn)(const void *s, int idx, void *context); typedef int (*cmp_fn)(const void *e1, const void *e2, void *context); typedef enum { DIFF_MATCH = 1, DIFF_DELETE, DIFF_INSERT } diff_op; struct diff_edit { short op; /* DIFF_MATCH, DIFF_DELETE or DIFF_INSERT */ int off; /* off into a if MATCH or DELETE, b if INSERT */ int len; };
The idx_fn is a pointer to a function that returns the element the numeric index specified by idx in the sequence s. The cmp_fn (actually defined in hashmap(3m)) is a pointer to a function that returns zero if the sequence elements e1 and e2 are equal and non-zero otherwise. The context parameter specified with the diff call is always supplied to both callbacks.

Each element in the ses varray is a struct diff_edit structure and represents an individual match, delete, or insert operation in the edit script. The op member is DIFF_MATCH, DIFF_DELETE or DIFF_INSERT. The off and len members indicate the offset and length of the subsequence that matches or should be deleted from sequence a or inserted from sequence b.

The diff function

#include <mba/diff.h> int diff(const void *a, int aoff, int n, const void *b, int boff, int m, idx_fn idx, cmp_fn cmp, void *context, int dmax, struct varray *ses, int *sn, struct varray *buf);
The diff(3m) function computes the minimum edit distance between the sequences a (from aoff for length n) and b (from boff for length m) and optionally collects the edit script necessary to transform a into b storing the result in the varray identified by the ses parameter. The idx paremeter is a pointer to an idx_fn that returns the element at the numeric index in a sequence. The cmp parameter is a pointer to a cmp_fn function that returns zero if the two elements e1 and e2 are equal and non-zero otherwise. The supplied context parameter will be passed directly to both functions with each invokation. If idx and cmp are NULL a and b will be compared as continuous sequences of unsigned char (i.e. raw memory diff).

If the ses parameter is not NULL it must be a varray(3m) with a membsize of sizeof(struct diff_edit). Each struct diff_edit element in the varray(3m) starting from 0 will be populated with the op, off, and len that together constitute the edit script. The number of struct diff_edit elements in the edit script is written to the integer pointed to by the sn parameter. If the ses or sn parameter is NULL, the edit script will not be collected.

If the dmax parameter is not 0, the calculation will stop as soon as it is determined that the edit distance of the two sequences equals or exceeds the specified value. A value of 0 indicates that there is no limit.

If the buf parameter is not NULL it must be a varray(3m) with membsize of sizeof(int) and will be used as temporary storage for the dynamic programming tables. If buf is NULL storage will be temporarily allocated and freed with malloc(3) and free(3).
The diff(3m) function returns the edit distance between the two sequences a and b or dmax if the edit distance has been determined to meet or exceed the specified dmax value. If an error occurs -1 is returned and errno is set to indicate the error.

Copyright 2004 Michael B. Allen <mba2000 ioplex.com>