<?php
/**
* Compute edit distance between two scalar sequences. This class uses
* Levenshtein (or Damerau-Levenshtein) to compute the edit distance between
* two inputs. The inputs are arrays containing any scalars (not just strings)
* so it can be used with, e.g., utf8 sequences.
*
* $matrix = id(new PhutilEditDistanceMatrix())
* ->setSequences(str_split('ran'), str_split('rat'));
*
* $cost = $matrix->getEditDistance();
*
* Edit distance computation is slow and requires a large amount of memory;
* both are roughly O(N * M) in the length of the strings.
*
* You can customize the cost of insertions, deletions and replacements. By
* default, each has a cost of 1.
*
* $matrix->setReplaceCost(1);
*
* By default, transpositions are not evaluated (i.e., the algorithm is
* Levenshtein). You can cause transpositions to be evaluated by setting a
* transpose cost (which will change the algorithm to Damerau-Levenshtein):
*
* $matrix->setTransposeCost(1);
*
* You can also provide a cost to alter the type of operation being applied.
* Many strings have several equivalently expensive edit sequences, but one
* some sequences are more readable to humans than others. Providing a small
* cost to alter operation type tends to smooth out the sequence and produce
* long runs of a single operation, which are generally more readable. For
* example, these strings:
*
* (x)
* ((x))
*
* ...have edit strings "issis" and "isssi", which describe edit operations with
* the same cost, but the latter string is more comprehensible to human viewers.
*
* If you set an alter cost, you must call @{method:setComputeString} to enable
* type computation. The alter cost should generally be smaller than `c / N`,
* where `c` is the smallest operational cost and `N` is the length of the
* longest string. For example, if you are using the default costs (insert = 1,
* delete = 1, replace = 1) and computing edit distances for strings of fewer
* than 1,000 characters, you might set the alter cost to 0.001.
*/
final class PhutilEditDistanceMatrix extends Phobject {
private $insertCost = 1;
private $deleteCost = 1;
private $replaceCost = 1;
private $transposeCost = null;
private $alterCost = 0;
private $maximumLength;
private $computeString;
private $applySmoothing = self::SMOOTHING_NONE;
private $reachedMaximumLength;
private $x;
private $y;
private $prefix;
private $suffix;
private $distanceMatrix = null;
private $typeMatrix = null;
const SMOOTHING_NONE = 'none';
const SMOOTHING_INTERNAL = 'internal';
const SMOOTHING_FULL = 'full';
public function setMaximumLength($maximum_length) {
$this->maximumLength = $maximum_length;
return $this;
}
public function getMaximumLength() {
return coalesce($this->maximumLength, $this->getInfinity());
}
public function didReachMaximumLength() {
return $this->reachedMaximumLength;
}
public function setComputeString($compute_string) {
$this->computeString = $compute_string;
return $this;
}
public function getComputeString() {
return $this->computeString;
}
public function setTransposeCost($transpose_cost) {
$this->transposeCost = $transpose_cost;
return $this;
}
public function getTransposeCost() {
return $this->transposeCost;
}
public function setReplaceCost($replace_cost) {
$this->replaceCost = $replace_cost;
return $this;
}
public function getReplaceCost() {
return $this->replaceCost;
}
public function setDeleteCost($delete_cost) {
$this->deleteCost = $delete_cost;
return $this;
}
public function getDeleteCost() {
return $this->deleteCost;
}
public function setInsertCost($insert_cost) {
$this->insertCost = $insert_cost;
return $this;
}
public function getInsertCost() {
return $this->insertCost;
}
public function setAlterCost($alter_cost) {
$this->alterCost = $alter_cost;
return $this;
}
public function getAlterCost() {
return $this->alterCost;
}
public function setApplySmoothing($apply_smoothing) {
$this->applySmoothing = $apply_smoothing;
return $this;
}
public function getApplySmoothing() {
return $this->applySmoothing;
}
public function setSequences(array $x, array $y) {
// NOTE: We strip common prefixes and suffixes from the inputs because
// the runtime of the edit distance algorithm is large and it is common
// to diff similar strings.
$xl = count($x);
$yl = count($y);
$l = min($xl, $yl);
$prefix_l = 0;
$suffix_l = 0;
for ($ii = 0; $ii < $l; $ii++) {
if ($x[$ii] !== $y[$ii]) {
break;
}
$prefix_l++;
}
for ($ii = 1; $ii <= ($l - $prefix_l); $ii++) {
if ($x[$xl - $ii] !== $y[$yl - $ii]) {
break;
}
$suffix_l++;
}
$this->prefix = array_slice($x, 0, $prefix_l);
$this->suffix = array_slice($x, $xl - $suffix_l);
$this->x = array_slice($x, $prefix_l, $xl - ($suffix_l + $prefix_l));
$this->y = array_slice($y, $prefix_l, $yl - ($suffix_l + $prefix_l));
$this->distanceMatrix = null;
return $this;
}
private function requireSequences() {
if ($this->x === null) {
throw new PhutilInvalidStateException('setSequences');
}
}
public function getEditDistance() {
$this->requireSequences();
$x = $this->x;
$y = $this->y;
if (!$x) {
return $this->insertCost * count($y);
}
if (!$y) {
return $this->deleteCost * count($x);
}
$max = $this->getMaximumLength();
if (count($x) > $max || count($y) > $max) {
$this->reachedMaximumLength = true;
return ($this->insertCost * count($y)) + ($this->deleteCost * count($x));
}
if ($x === $y) {
return 0;
}
$matrix = $this->getDistanceMatrix();
return $matrix[count($x)][count($y)];
}
/**
* Return a string representing the edits between the sequences. The string
* has these characters:
*
* - s (same): Same character in both strings.
* - i (insert): Character inserted.
* - d (delete): Character deleted.
* - x (replace): Character replaced.
* - t (transpose): Character transposed.
*/
public function getEditString() {
$this->requireSequences();
$x = $this->x;
$y = $this->y;
if (!$x && !$y) {
return $this->padEditString('');
}
if (!$x) {
return $this->padEditString(str_repeat('i', count($y)));
}
if (!$y) {
return $this->padEditString(str_repeat('d', count($x)));
}
if ($x === $y) {
return $this->padEditString(str_repeat('s', count($x)));
}
$max = $this->getMaximumLength();
if (count($x) > $max || count($y) > $max) {
$this->reachedMaximumLength = true;
return $this->padEditString(
str_repeat('d', count($x)).
str_repeat('i', count($y)));
}
$matrix = $this->getTypeMatrix();
$xx = count($x);
$yy = count($y);
$transposes = array();
$str = '';
while (true) {
$type = $matrix[$xx][$yy];
if (is_array($type)) {
$chr = 't';
$transposes[$type[0]][$type[1]] = true;
$type = $type[2];
} else {
$chr = $type;
}
if (isset($transposes[$xx][$yy])) {
$chr = 't';
}
if ($type == 's' || $type == 'x') {
$xx -= 1;
$yy -= 1;
} else if ($type == 'i') {
$yy -= 1;
} else if ($type == 'd') {
$xx -= 1;
} else {
throw new Exception(pht("Unknown type '%s' in type matrix.", $type));
}
$str .= $chr;
if ($xx <= 0 && $yy <= 0) {
break;
}
}
$str = strrev($str);
// For full smoothing, we pad the edit string before smoothing it, so
// ranges of similar characters at the beginning or end of the string can
// also be smoothed.
// For internal smoothing, we only smooth ranges within the change itself.
$smoothing = $this->getApplySmoothing();
switch ($smoothing) {
case self::SMOOTHING_FULL:
$str = $this->padEditString($str);
$str = $this->applySmoothing($str, true);
break;
case self::SMOOTHING_INTERNAL:
$str = $this->applySmoothing($str, false);
$str = $this->padEditString($str);
break;
case self::SMOOTHING_NONE:
$str = $this->padEditString($str);
break;
default:
throw new Exception(
pht(
'Unknown smoothing type "%s".',
$smoothing));
}
return $str;
}
private function padEditString($str) {
if ($this->prefix) {
$str = str_repeat('s', count($this->prefix)).$str;
}
if ($this->suffix) {
$str = $str.str_repeat('s', count($this->suffix));
}
return $str;
}
private function getTypeMatrix() {
if (!$this->computeString) {
throw new PhutilInvalidStateException('setComputeString');
}
if ($this->typeMatrix === null) {
$this->computeMatrix($this->x, $this->y);
}
return $this->typeMatrix;
}
private function getDistanceMatrix() {
if ($this->distanceMatrix === null) {
$this->computeMatrix($this->x, $this->y);
}
return $this->distanceMatrix;
}
private function computeMatrix(array $x, array $y) {
$xl = count($x);
$yl = count($y);
$m = array();
$infinity = $this->getInfinity();
$use_damerau = ($this->transposeCost !== null);
if ($use_damerau) {
// Initialize the default cost of a transpose.
$m[-1][-1] = $infinity;
// Initialize the character position dictionary for Damerau.
$d = array();
foreach ($x as $c) {
$d[$c] = -1;
}
foreach ($y as $c) {
$d[$c] = -1;
}
// Initialize the transpose costs for Damerau.
for ($xx = 0; $xx <= $xl; $xx++) {
$m[$xx][-1] = $infinity;
}
for ($yy = 0; $yy <= $yl; $yy++) {
$m[-1][$yy] = $infinity;
}
}
// Initialize the top row of the matrix.
for ($xx = 0; $xx <= $xl; $xx++) {
$m[$xx][0] = $xx * $this->deleteCost;
}
// Initialize the left column of the matrix.
$cost = 0;
for ($yy = 0; $yy <= $yl; $yy++) {
$m[0][$yy] = $yy * $this->insertCost;
}
$use_types = ($this->computeString);
if ($use_types) {
$t = array();
for ($xx = 0; $xx <= $xl; $xx++) {
$t[$xx][0] = 'd';
}
for ($yy = 0; $yy <= $yl; $yy++) {
$t[0][$yy] = 'i';
}
$t[0][0] = 's';
}
$alt_cost = $this->getAlterCost();
if ($alt_cost && !$use_types) {
throw new Exception(
pht(
'If you provide an alter cost with %s, you must enable '.
'type computation with %s.',
'setAlterCost()',
'setComputeStrings()'));
}
// Build the edit distance matrix.
for ($xx = 1; $xx <= $xl; $xx++) {
$last_dy = -1;
for ($yy = 1; $yy <= $yl; $yy++) {
if ($use_damerau) {
$dx = $d[$y[$yy - 1]];
$dy = $last_dy;
}
if ($x[$xx - 1] === $y[$yy - 1]) {
$rep_cost = $m[$xx - 1][$yy - 1] + 0;
$rep_type = 's';
} else {
$rep_cost = $m[$xx - 1][$yy - 1] + $this->replaceCost;
$rep_type = 'x';
}
$del_cost = $m[$xx - 1][$yy ] + $this->deleteCost;
$ins_cost = $m[$xx ][$yy - 1] + $this->insertCost;
if ($alt_cost) {
$del_char = $t[$xx - 1][$yy ];
$ins_char = $t[$xx ][$yy - 1];
$rep_char = $t[$xx - 1][$yy - 1];
if ($del_char !== 'd') {
$del_cost += $alt_cost;
}
if ($ins_char !== 'i') {
$ins_cost += $alt_cost;
}
if ($rep_char !== $rep_type) {
$rep_cost += $alt_cost;
}
}
if ($rep_cost <= $del_cost && $rep_cost <= $ins_cost) {
$cost = $rep_cost;
$type = $rep_type;
if ($rep_type === 's') {
$last_dy = $yy - 1;
}
} else if ($ins_cost <= $del_cost) {
$cost = $ins_cost;
$type = 'i';
} else {
$cost = $del_cost;
$type = 'd';
}
if ($use_damerau) {
$trn_count = (($xx - $dx - 2) + ($yy - $dy - 2) + 1);
$trn_cost = $m[$dx][$dy] + ($trn_count * $this->transposeCost);
if ($trn_cost < $cost) {
$cost = $trn_cost;
$type = array($dx + 1, $dy + 1, $type);
}
}
$m[$xx][$yy] = $cost;
if ($use_types) {
$t[$xx][$yy] = $type;
}
}
if ($use_damerau) {
$d[$x[$xx - 1]] = ($xx - 1);
}
}
$this->distanceMatrix = $m;
if ($use_types) {
$this->typeMatrix = $t;
}
}
private function getInfinity() {
return INF;
}
private function printMatrix(array $m) {
$x = $this->x;
$y = $this->y;
$p = '% 8s ';
printf($p, ' ');
foreach (head($m) as $yk => $yv) {
printf($p, idx($y, $yk - 1, '-'));
}
echo "\n";
foreach ($m as $xk => $xv) {
printf($p, idx($x, $xk - 1, '-'));
foreach ($xv as $yk => $yv) {
printf($p, ($yv == $this->getInfinity() ? 'inf' : $yv));
}
echo "\n";
}
}
private function printTypeMatrix(array $t) {
$x = $this->x;
$y = $this->y;
$p = '% 8s ';
printf($p, ' ');
foreach (head($t) as $yk => $yv) {
printf($p, idx($y, $yk - 1, '-'));
}
echo "\n";
foreach ($t as $xk => $xv) {
printf($p, idx($x, $xk - 1, '-'));
foreach ($xv as $yk => $yv) {
printf($p, ($yv == $this->getInfinity() ? 'inf' : $yv));
}
echo "\n";
}
}
private function applySmoothing($str, $full) {
if ($full) {
$prefix = '(^|[xdi])';
$suffix = '([xdi]|\z)';
} else {
$prefix = '([xdi])';
$suffix = '([xdi])';
}
// Smooth the string out, by replacing short runs of similar characters
// with 'x' operations. This makes the result more readable to humans,
// since there are fewer choppy runs of short added and removed substrings.
do {
$original = $str;
$str = preg_replace('/'.$prefix.'(s{3})'.$suffix.'/', '$1xxx$3', $str);
$str = preg_replace('/'.$prefix.'(s{2})'.$suffix.'/', '$1xx$3', $str);
$str = preg_replace('/'.$prefix.'(s{1})'.$suffix.'/', '$1x$3', $str);
} while ($str != $original);
return $str;
}
}