SN\RangeDifferencer\AbstractLCS

Complexity

Total Complexity

64

Size/Duplication

Total Lines	392
Duplicated Lines	0 %

Importance

Changes

0

5 Methods

Rating	Name	Duplication	Size	Complexity
C	findMostProgress()	0	80	14
B	lcsRec()	0	36	7
B	longestCommonSubsequence()	0	46	9
F	findMiddleSnake()	0	124	33
A	getLength()	0	3	1

<?php
/**
 * (c) Steve Nebes <snebes@gmail.com>
 *
 * For the full copyright and license information, please view the LICENSE
 * file that was distributed with this source code.
 */

declare(strict_types=1);

namespace SN\RangeDifferencer;

abstract class AbstractLCS
{
    /** @const float 10^8, the value of N*M when to start bindnig the run time. */
    private const TOO_LONG = 100000000.0;

    /** @const float Limit the time to D^POW_LIMIT */
    private const POW_LIMIT = 1.5;

    /** @var int */
    private $maxDifferences = 0;

    /** @var int */
    private $length = 0;

    /**
     * @return int
     */
    public function getLength(): int
    {
        return $this->length;
    }

    /**
     * Myers' algorithm for longest common subsequence. O((M + N)D) worst case time, O(M + N + D^2) expected time, O(M
     * + N) space (http://citeseer.ist.psu.edu/myers86ond.html)
     *
     * Note: Beyond implementing the algorithm as described in the paper I have added diagonal range compression which
     * helps when finding the LCS of a very long and a very short sequence, also bound the running time to (N + M)^1.5
     * when both sequences are very long.
     *
     * After this method is called, the longest common subsequence is available by calling getResult() where result[0]
     * is composed of entries from l1 and result[1] is composed of entries from l2
     */
    public function longestCommonSubsequence(): void
    {
        $length1 = $this->getLength1();
        $length2 = $this->getLength2();

        if (0 === $length1 || 0 === $length2) {
            $this->length = 0;

            return;
        }

        $this->maxDifferences = (int)(($length1 + $length2 + 1) / 2);

        if ($length1 * $length2 > self::TOO_LONG) {
            // Limit complexity to D^POW_LIMIT for long sequences.
            $this->maxDifferences = (int)\pow($this->maxDifferences, self::POW_LIMIT - 1.0);
        }

        $this->initializeLcs($length1);

        // The common prefixes and suffixes are always part of some LCS, include them now to reduce our search space.
        $max = \min($length1, $length2);

        for (
            $forwardBound = 0;
            $forwardBound < $max && $this->isRangeEqual($forwardBound, $forwardBound);
            $forwardBound++
        ) {
            $this->setLcs($forwardBound, $forwardBound);
        }

        $backBoundL1 = $length1 - 1;
        $backBoundL2 = $length2 - 1;

        while ($backBoundL1 >= $forwardBound && $backBoundL2 >= $forwardBound &&
            $this->isRangeEqual($backBoundL1, $backBoundL2)) {
            $this->setLcs($backBoundL1, $backBoundL2);
            $backBoundL1--;
            $backBoundL2--;
        }

        $V = \array_fill(0, 2, \array_fill(0, $length1 + $length2 + 1, 0));
        $snake = [0, 0, 0];
        $lcsRec = $this->lcsRec($forwardBound, $backBoundL1, $forwardBound, $backBoundL2, $V, $snake);

        $this->length = $forwardBound + $length1 - $backBoundL1 - 1 + $lcsRec;
    }

    /**
     * The recursive helper function for Myers' LCS. Computes the LCS of $l1[$bottomL1 .. $topL1] and $l2[$bottomL2 ..
     * $topL2] fills in the appropriate location in lcs and returns the length.
     *
     * @param int   $bottomL1 The first sequence
     * @param int   $topL1    Index in the first sequence to start from (inclusive)
     * @param int   $bottomL2 The second sequence
     * @param int   $topL2    Index in the second sequence to start from (inclusive)
     * @param array $V        Furthest reaching D-paths
     * @param array $snake    Beginning x, y coordinates and the length of the middle snake
     * @return int Length of the lcs
     */
    private function lcsRec(int $bottomL1, int $topL1, int $bottomL2, int $topL2, array &$V, array &$snake): int
    {
        // Check that both sequences are non-empty.
        if ($bottomL1 > $topL1 || $bottomL2 > $topL2) {
            return 0;
        }

        $d = $this->findMiddleSnake($bottomL1, $topL1, $bottomL2, $topL2, $V, $snake);

        // Need to restore these so we don't lose them when they're overwritten by the recursion.
        $len = $snake[2];
        $startX = $snake[0];
        $startY = $snake[1];

        // The middle snake is part of the LCS, store it.
        for ($i = 0; $i < $len; $i++) {
            $this->setLcs($startX + $i, $startY + $i);
        }

        if ($d > 1) {
            return $len +
                $this->lcsRec($bottomL1, $startX - 1, $bottomL2, $startY - 1, $V, $snake) +
                $this->lcsRec($startX + $len, $topL1, $startY + $len, $topL2, $V, $snake);
        } elseif ($d === 1) {
            // In this case the sequences differ by exactly 1 line. We have already saved all the lines after the
            // difference in the for loop above, now we need to save all the lines before the difference.
            $max = \min($startX - $bottomL1, $startY - $bottomL2);

            for ($i = 0; $i < $max; $i++) {
                $this->setLcs($bottomL1 + $i, $bottomL2 + $i);
            }

            return $max + $len;
        }

        return $len;
    }

    /**
     * Helper function for Myers' LCS algorithm to find the middle snake for $l1[$bottomL1 .. $topL1] and $l2[$bottomL2
     * .. $topL2] The x, y coordinates of the start of the middle snake are saved in $snake[0], $snake[1] respectively
     * and the length of the snake is saved in $snake[2].
     *
     * @param int     $bottomL1 Index in the first sequence to start from (inclusive)
     * @param int     $topL1    Index in the first sequence to end from (inclusive)
     * @param int     $bottomL2 Index in the second sequence to start from (inclusive)
     * @param int     $topL2    Index in the second sequence to end from (inclusive)
     * @param int[][] $V        Array storing the furthest reaching D-paths for the LCS computation
     * @param int[]   $snake    Beginning x, y coordinates and the length of the middle snake
     * @return int
     */
    private function findMiddleSnake(
        int $bottomL1,
        int $topL1,
        int $bottomL2,
        int $topL2,
        array &$V,
        array &$snake
    ): int {
        $N = $topL1 - $bottomL1 + 1;
        $M = $topL2 - $bottomL2 + 1;

        $delta = $N - $M;
        $isEven = ($delta & 1) === 1 ? false : true;

        $limit = \min($this->maxDifferences, (int)(($N + $M + 1) / 2));

        // Offset to make it odd/even.
        // a 0 or 1 that we add to the start offset to make it odd/even
        $valueToAddForward = ($M & 1) === 1 ? 1 : 0;
        $valueToAddBackward = ($N & 1) === 1 ? 1 : 0;

        $startForward = -$M;
        $endForward = $N;
        $startBackward = -$N;
        $endBackward = $M;

        $V[0][$limit + 1] = 0;
        $V[1][$limit - 1] = $N;

        for ($d = 0; $d <= $limit; $d++) {
            $startDiag = \max($valueToAddForward + $startForward, -$d);
            $endDiag = \min($endForward, $d);
            $valueToAddForward = 1 - $valueToAddForward;

            // Compute forward furthest reaching paths.
            for ($k = $startDiag; $k <= $endDiag; $k += 2) {
                if ($k === -$d || ($k < $d && $V[0][$limit + $k - 1] < $V[0][$limit + $k + 1])) {
                    $x = $V[0][$limit + $k + 1];
                } else {
                    $x = $V[0][$limit + $k - 1] + 1;
                }

                $y = $x - $k;

                $snake[0] = $x + $bottomL1;
                $snake[1] = $y + $bottomL2;
                $snake[2] = 0;

                while ($x < $N && $y < $M && $this->isRangeEqual($x + $bottomL1, $y + $bottomL2)) {
                    $x++;
                    $y++;
                    $snake[2]++;
                }

                $V[0][$limit + $k] = $x;

                if (!$isEven && $k >= $delta - $d + 1 && $k <= $delta + $d - 1 && $x >= $V[1][$limit + $k - $delta]) {
                    return 2 * $d - 1;
                }

                // Check to see if we can cut down the diagonal range.
                if ($x >= $N && $endForward > $k - 1) {
                    $endForward = $k - 1;
                } elseif ($y >= $M) {
                    $startForward = $k + 1;
                    $valueToAddForward = 0;
                }
            }

            $startDiag = \max($valueToAddBackward + $startBackward, -$d);
            $endDiag = \min($endBackward, $d);
            $valueToAddBackward = 1 - $valueToAddBackward;

            // Compute backward furthest reaching paths.
            for ($k = $startDiag; $k <= $endDiag; $k += 2) {
                if ($k === $d || ($k !== -$d && $V[1][$limit + $k - 1] < $V[1][$limit + $k + 1])) {
                    $x = $V[1][$limit + $k - 1];
                } else {
                    $x = $V[1][$limit + $k + 1] - 1;
                }

                $y = $x - $k - $delta;
                $snake[2] = 0;

                while ($x > 0 && $y > 0 && $this->isRangeEqual($x - 1 + $bottomL1, $y - 1 + $bottomL2)) {
                    $x--;
                    $y--;
                    $snake[2]++;
                }

                $V[1][$limit + $k] = $x;

                if ($isEven && $k >= -$delta - $d && $k <= $d - $delta && $x <= $V[0][$limit + $k + $delta]) {
                    $snake[0] = $bottomL1 + $x;
                    $snake[1] = $bottomL2 + $y;

                    return 2 * $d;
                }

                // Check to see if we can cut down our diagonal range.
                if ($x <= 0) {
                    $startBackward = $k + 1;
                    $valueToAddBackward = 0;
                } elseif ($y <= 0 && $endBackward > $k - 1) {
                    $endBackward = $k - 1;
                }
            }
        }

        // Computing the true LCS is too expensive, instead find the diagonal with the most progress and pretend a
        // middle snake of length 0 occurs there.
        $mostProgress = $this->findMostProgress($M, $N, $limit, $V);

        $snake[0] = $bottomL1 + $mostProgress[0];
        $snake[1] = $bottomL2 + $mostProgress[1];
        $snake[2] = 0;

        /*
         * HACK: Since we didn't really finish the LCS computation we don't really know the length of the SES. We don't
         * do anything with the result anyway, unless it's <=1. We know for a fact SES > 1 so 5 is as good a number as
         *  any to return here.
         */

        return 5;
    }

    /**
     * Takes the array with furthest reaching D-paths from an LCS computation and returns the x,y coordinates and
     * progress made in the middle diagonal among those with maximum progress, both from the front and from the back.
     *
     * @param int     $M     Length of the first sequence for which LCS is being computed
     * @param int     $N     Length of the second sequence for which LCS is being computed
     * @param int     $limit Number of steps made in an attempt to find the LCS from the front and back
     * @param int[][] $V     Array storing the furthest reaching D-paths for the LCS computation
     *
     * @return int[] Array of 3 integers where $result[0] is the x coordinate of the current location in the diagonal
     *               with the most progress, $result[1] is the y coordinate of the current location in the diagonal with
     *               the most progress and $result[2] is the amount of progress made in that diagonal.
     */
    private function findMostProgress(int $M, int $N, int $limit, array &$V): array
    {
        $delta = $N - $M;

        if (($M & 1) === ($limit & 1)) {
            $forwardStartDiag = \max(-$M, -$limit);
        } else {
            $forwardStartDiag = \max(1 - $M, -$limit);
        }

        $forwardEndDiag = \min($N, $limit);

        if (($N & 1) === ($limit & 1)) {
            $backwardStartDiag = \max(-$N, -$limit);
        } else {
            $backwardStartDiag = \max(1 - $N, -$limit);
        }

        $backwardEndDiag = \min($M, $limit);

        $maxProgress = array_fill(
            0,
            (int)(\max($forwardEndDiag - $forwardStartDiag, $backwardEndDiag - $backwardStartDiag) / 2 + 1),
            [0, 0, 0]);
        // The first entry is current, it is initialized with 0s.
        $numProgress = 0;

        // First search the forward diagonals.
        for ($k = $forwardStartDiag; $k <= $forwardEndDiag; $k += 2) {
            $x = $V[0][$limit + $k];
            $y = $x - $k;

            if ($x > $N || $y > $M) {
                continue;
            }

            $progress = $x + $y;

            if ($progress > $maxProgress[0][2]) {
                $numProgress = 0;
                $maxProgress[0][0] = $x;
                $maxProgress[0][1] = $y;
                $maxProgress[0][2] = $progress;
            } elseif ($progress === $maxProgress[0][2]) {
                $numProgress++;
                $maxProgress[$numProgress][0] = $x;
                $maxProgress[$numProgress][1] = $y;
                $maxProgress[$numProgress][2] = $progress;
            }
        }

        // Initially the maximum progress is in the forward direction.
        $maxProgressForward = true;

        // Now search the backward diagonals.
        for ($k = $backwardStartDiag; $k <= $backwardEndDiag; $k += 2) {
            $x = $V[1][$limit + $k];
            $y = $x - $k - $delta;

            if ($x < 0 || $y < 0) {
                continue;
            }

            $progress = $N - $x + $M - $y;

            if ($progress > $maxProgress[0][2]) {
                $numProgress = 0;
                $maxProgressForward = false;
                $maxProgress[0][0] = $x;
                $maxProgress[0][1] = $y;
                $maxProgress[0][2] = $progress;
            } elseif ($progress === $maxProgress[0][2] && !$maxProgressForward) {
                $numProgress++;
                $maxProgress[$numProgress][0] = $x;
                $maxProgress[$numProgress][1] = $y;
                $maxProgress[$numProgress][2] = $progress;
            }
        }

        return $maxProgress[(int)($numProgress / 2)];
    }

    /**
     * @return int
     */
    abstract protected function getLength1(): int;

    /**
     * @return int
     */
    abstract protected function getLength2(): int;

    /**
     * @param int $i1
     * @param int $i2
     * @return bool
     */
    abstract protected function isRangeEqual(int $i1, int $i2): bool;

    /**
     * @param int $lcsLength
     */
    abstract protected function initializeLcs(int $lcsLength): void;

    /**
     * @param int $sl1
     * @param int $sl2
     */
    abstract protected function setLcs(int $sl1, int $sl2): void;
}