[Essay] a preliminary understanding of Levenshtein Distance (Edit Distance) Editing Distance and character similarity Algorithms

Source: Internet
Author: User

A few days ago, I saw a post on the CSDN forum that needed to determine the number of characters in the difference between two strings. I have learned some algorithms to calculate the difference, but I am not familiar with it. let's take a moment to understand the Levenshtein Distance (Edit Distance) Editing Distance and character similarity algorithm.


For details about this algorithm, refer to wiki:


From Wikipedia:

"Edit distance, Also knownLevenshtein distanceThe minimum number of edits required to convert a string from one to another. Licensed editing operations include replacing one character with another, inserting one character, and deleting one character.


For example, convert kitten to sitting:

  1. Sitten (k → s)
  2. Sittin (e → I)
  3. Sitting (→ g)


Russian scientist Vladimir Levenshtein proposed this concept in 1965. "


English: http://zh.wikipedia.org/wiki/%E7%B7%A8%E8%BC%AF%E8%B7%9D%E9%9B%A2



Then I wrote a Demo to learn more.


Here is the pseudocode provided by Wikipedia:



Dynamic Planning is often used as a solution to this problem.

Levenshtein is an integer away from bytes (character str1 [1 .. lenStr1], character str2 [1 .. lenStr2])

Declare int d [0... lenstr1, 0... lenstr2]

Declare int I, j, cost


I equals from 0 to lenstr1

D [I, 0]: = I

J equals from 0 to lenstr2

D [0, J]: = J

I equals from 1 to lenstr1

J is equal to 1 to lenstr2.

If str1 [I] = str2 [J], cost: = 0

Otherwise, cost: = 1

D [I, j]: = Minimum value (

D [I-1, J] + 1, // distinct

D [I, J-1] + 1, // insert

D [I-1, J-1] + cost // replace counter



Returns d [lenStr1, lenStr2].



The Demo is as follows:


Using System; <br/> using System. collections. generic; <br/> using System. componentModel; <br/> using System. data; <br/> using System. drawing; <br/> using System. linq; <br/> using System. text; <br/> using System. windows. forms; <br/> namespace WindowsFormsApplication1 <br/>{< br/> public partial class Form1: Form <br/>{< br/> public Form1 () <br/>{< br/> InitializeComponent (); <br/>}< br/> private void button#click (object sender, EventArgs e) <br/>{</p> <p> char [] c1 = richTextBox1.Text. trim (). toCharArray (); <br/> char [] c2 = richTextBox2.Text. trim (). toCharArray (); <br/> int [,] result = Calculate (c1, c2); </p> <p> DataTable dt = new DataTable (); <br/> for (int I = 0; I <c1.Length + 2; I ++) <br/> {<br/> dt. columns. add (I. toString (); <br/>}< br/> for (int I = 0; I <c2.Length + 2; I ++) <br/> {<br/> DataRow row = dt. newRow (); <br/> dt. rows. add (row); <br/>}< br/> for (int I = 0; I <c2.Length + 2; I ++) <br/>{< br/> if (I <2) <br/>{< br/> dt. rows [I] [0] = string. empty; <br/>}< br/> else <br/> {<br/> dt. rows [I] [0] = c2 [I-2]; <br/>}< br/> for (int I = 0; I <c1.Length + 2; I ++) <br/>{< br/> if (I <2) <br/>{< br/> dt. rows [0] [I] = string. empty; <br/>}< br/> else <br/> {<br/> dt. rows [0] [I] = c1 [I-2]; <br/>}< br/> for (int I = 0; I <result. getLength (0); I ++) <br/>{< br/> for (int j = 0; j <result. getLength (1); j ++) <br/>{< br/> dt. rows [j + 1] [I + 1] = result [I, j]; <br/>}< br/> if (checkBox1.Checked = true) <br/>{< br/> maid = dt; <br/> maid = false; <br/> maid = autosizecolumnsmode. allCells; <br/>}< br/> label1.Text = string. format ("character similarity: {0}" <br/>, dt. rows [result. getLength (1)] [result. getLength (0)]. toString (); <br/>}< br/> public static int [,] Calculate (char [] First, char [] Second) <br/>{< br/> int lenFirst = First. length + 1; <br/> int lenSecond = Second. length + 1; <br/> int [,] matrixResult = new int [lenFirst, lenSecond]; <br/> for (int I = 0; I <lenFirst; I ++) matrixResult [I, 0] = I; <br/> for (int j = 0; j <lenSecond; j ++) matrixResult [0, j] = j; <br/> for (int I = 1; I <lenFirst; I ++) <br/>{< br/> for (int j = 1; j <lenSecond; j ++) <br/>{< br/> if (First [I-1] = Second [j-1]) <br/>{< br/> matrixResult [I, j] = matrixResult [I-1, j-1]; <br/>}< br/> else <br/> {<br/> matrixResult [I, j] = new int [] {matrixResult [I-1, j] + 1 <br/>, matrixResult [I, J-1] + 1 <br/>, matrixResult [I-1, J-1] + 1 <br/> }. min (); <br/>}< br/> return matrixResult; <br/>}< br/>

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