natural/lib/natural/distance/levenshtein_distance.js

General natural language (tokenizing, stemming (English, Russian, Spanish), part-of-speech tagging, sentiment analysis, classification, inflection, phonetics, tfidf, WordNet, jaro-winkler, Levenshtein distance, Dice's Coefficient) facilities for node.

/*
Copyright (c) 2012, Sid Nallu, Chris Umbel

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
*/

'use strict'

/*
 * contribution by sidred123
 */

/*
 * Compute the Levenshtein distance between two strings.
 * Algorithm based from Speech and Language Processing - Daniel Jurafsky and James H. Martin.
 */

const _ = require('underscore')

// Walk the path back from the matchEnd to the beginning of the match.
// Do this by traversing the distanceMatrix as you would a linked list,
// following going from cell child to parent until reach row 0.
function _getMatchStart (distanceMatrix, matchEnd, sourceLength) {
  let row = sourceLength
  let column = matchEnd
  let tmpRow
  let tmpColumn

  // match will be empty string
  if (matchEnd === 0) { return 0 }

  while (row > 1 && column > 1) {
    tmpRow = row
    tmpColumn = column
    row = distanceMatrix[tmpRow][tmpColumn].parentCell.row
    column = distanceMatrix[tmpRow][tmpColumn].parentCell.column
  }

  return column - 1
}

function getMinCostSubstring (distanceMatrix, source, target) {
  const sourceLength = source.length
  const targetLength = target.length
  let minDistance = sourceLength + targetLength
  let matchEnd = targetLength

  // Find minimum value in last row of the cost matrix. This cell marks the
  // end of the match string.
  for (let column = 0; column <= targetLength; column++) {
    if (minDistance > distanceMatrix[sourceLength][column].cost) {
      minDistance = distanceMatrix[sourceLength][column].cost
      matchEnd = column
    }
  }

  const matchStart = _getMatchStart(distanceMatrix, matchEnd, sourceLength)
  return { substring: target.slice(matchStart, matchEnd), distance: minDistance, offset: matchStart }
}

/*
* Returns the Damerau-Levenshtein distance between strings. Counts the distance
* between two strings by returning the number of edit operations required to
* convert `source` into `target`.
*
* Valid edit operations are:
*  - transposition, insertion, deletion, and substitution
*
* Options:
*  insertion_cost: (default: 1)
*  deletion_cost: number (default: 1)
*  substitution_cost: number (default: 1)
*  transposition_cost: number (default: 1)
*  search: boolean (default: false)
*  restricted: boolean (default: false)
*  damerau: boolean (depends on the function called)
*/
function DamerauLevenshteinDistance (source, target, options) {
  const damLevOptions = _.extend(
    { transposition_cost: 1, restricted: false },
    options || {},
    { damerau: true, search: false }
  )
  return levenshteinDistance(source, target, damLevOptions)
}

function DamerauLevenshteinDistanceSearch (source, target, options) {
  const damLevOptions = _.extend(
    { transposition_cost: 1, restricted: false },
    options || {},
    { damerau: true, search: true }
  )
  return levenshteinDistance(source, target, damLevOptions)
}

function LevenshteinDistanceSearch (source, target, options) {
  const levOptions = _.extend({}, options || {}, { damerau: false, search: true })
  return levenshteinDistance(source, target, levOptions)
}

function LevenshteinDistance (source, target, options) {
  const levOptions = _.extend({}, options || {}, { damerau: false, search: false })
  return levenshteinDistance(source, target, levOptions)
}

function levenshteinDistance (source, target, options) {
  if (isNaN(options.insertion_cost)) options.insertion_cost = 1
  if (isNaN(options.deletion_cost)) options.deletion_cost = 1
  if (isNaN(options.substitution_cost)) options.substitution_cost = 1

  if (typeof options.search !== 'boolean') options.search = false

  const isUnrestrictedDamerau = options.damerau && !options.restricted
  const isRestrictedDamerau = options.damerau && options.restricted

  let lastRowMap = null
  if (isUnrestrictedDamerau) {
    lastRowMap = {}
  }

  const sourceLength = source.length
  const targetLength = target.length
  const distanceMatrix = [[{ cost: 0 }]] // the root, has no parent cell

  for (let row = 1; row <= sourceLength; row++) {
    distanceMatrix[row] = []
    distanceMatrix[row][0] = { cost: distanceMatrix[row - 1][0].cost + options.deletion_cost, parentCell: { row: row - 1, column: 0 } }
  }

  for (let column = 1; column <= targetLength; column++) {
    if (options.search) {
      distanceMatrix[0][column] = { cost: 0 }
    } else {
      distanceMatrix[0][column] = { cost: distanceMatrix[0][column - 1].cost + options.insertion_cost, parentCell: { row: 0, column: column - 1 } }
    }
  }

  let lastColMatch = null
  for (let row = 1; row <= sourceLength; row++) {
    if (isUnrestrictedDamerau) {
      lastColMatch = null
    }
    for (let column = 1; column <= targetLength; column++) {
      const costToInsert = distanceMatrix[row][column - 1].cost + options.insertion_cost
      const costToDelete = distanceMatrix[row - 1][column].cost + options.deletion_cost

      const sourceElement = source[row - 1]
      const targetElement = target[column - 1]
      let costToSubstitute = distanceMatrix[row - 1][column - 1].cost
      if (sourceElement !== targetElement) {
        costToSubstitute = costToSubstitute + options.substitution_cost
      }

      const possibleParents = [
        { cost: costToInsert, coordinates: { row: row, column: column - 1 } },
        { cost: costToDelete, coordinates: { row: row - 1, column: column } },
        { cost: costToSubstitute, coordinates: { row: row - 1, column: column - 1 } }
      ]

      // We can add damerau to the possibleParents if the current
      // target-letter has been encountered in our lastRowMap,
      // and if there exists a previous column in this row where the
      // row & column letters matched
      const canDamerau = isUnrestrictedDamerau &&
                row > 1 && column > 1 &&
                lastColMatch &&
                targetElement in lastRowMap

      let costBeforeTransposition = null
      if (canDamerau) {
        const lastRowMatch = lastRowMap[targetElement]
        costBeforeTransposition =
                    distanceMatrix[lastRowMatch - 1][lastColMatch - 1].cost
        const costToTranspose = costBeforeTransposition +
                    ((row - lastRowMatch - 1) * options.deletion_cost) +
                    ((column - lastColMatch - 1) * options.insertion_cost) +
                    options.transposition_cost
        possibleParents.push({
          cost: costToTranspose,
          coordinates: {
            row: lastRowMatch - 1,
            column: lastColMatch - 1
          }
        })
      }
      // Source and target chars are 1-indexed in the distanceMatrix so previous
      // source/target element is (col/row - 2)
      const canDoRestrictedDamerau = isRestrictedDamerau &&
                row > 1 && column > 1 &&
                sourceElement === target[column - 2] &&
                source[row - 2] === targetElement

      if (canDoRestrictedDamerau) {
        costBeforeTransposition = distanceMatrix[row - 2][column - 2].cost
        possibleParents.push({
          cost: costBeforeTransposition + options.transposition_cost,
          coordinates: { row: row - 2, column: column - 2 }
        })
      }

      const minCostParent = _.min(possibleParents, function (p) { return p.cost })

      distanceMatrix[row][column] = { cost: minCostParent.cost, parentCell: minCostParent.coordinates }

      if (isUnrestrictedDamerau) {
        lastRowMap[sourceElement] = row
        if (sourceElement === targetElement) {
          lastColMatch = column
        }
      }
    }
  }

  if (!options.search) {
    return distanceMatrix[sourceLength][targetLength].cost
  }

  return getMinCostSubstring(distanceMatrix, source, target)
}

module.exports = {
  LevenshteinDistance: LevenshteinDistance,
  LevenshteinDistanceSearch: LevenshteinDistanceSearch,
  DamerauLevenshteinDistance: DamerauLevenshteinDistance,
  DamerauLevenshteinDistanceSearch: DamerauLevenshteinDistanceSearch
}