Levenshtein Distance Levenshtein 编辑距离——一种相似度的计算方法

/*********************************************
Levenshtein Distance Algorithm
*******************************/
/***************************************************************************************************************/
/*Author: TianLiang
*/
/*Time: 2011/10/14
*/
/*Function: Get the distance of the two given strings
Step Description
1 Set n to be the length of s.
Set m to be the length of t.
If n = 0, return m and exit.
If m = 0, return n and exit.
Construct a matrix containing 0..m rows and 0..n columns.
2 Initialize the first row to 0..n.
Initialize the first column to 0..m.
3 Examine each character of s (i from 1 to n).
4 Examine each character of t (j from 1 to m).
5 If s[i] equals t[j], the cost is 0.
If s[i] doesn't equal t[j], the cost is 1.
6 Set cell d[i,j] of the matrix equal to the minimum of:
a. The cell immediately above plus 1: d[i-1,j] + 1.
b. The cell immediately to the left plus 1: d[i,j-1] + 1.
c. The cell diagonally above and to the left plus the cost: d[i-1,j-1] + cost.
7 After the iteration steps (3, 4, 5, 6) are complete, the distance is found in cell d[n,m].
*/
int CCalculateSimilarity::LevenshteinDistance(CString source,CString target)
{
//step 1
int n=source.GetLength(); //Set n to be the length of s.
int m=target.GetLength(); //Set m to be the length of t
if (m==0) return n; //If n = 0, return m and exit.
if (n==0) return m; //If m = 0, return n and exit.
//Construct a matrix
typedef vector< vector<int> >
Tmatrix;
Tmatrix matrix(n+1);
for(int i=0; i<=n; i++)
{
matrix[i].resize(m+1);
}
//step 2 Initialize
for(int i=1;i<=n;i++)
{
matrix[i][0]=i; //Initialize the first row to 0..n.
}
for(int i=1;i<=m;i++)
{
matrix[0][i]=i; //Initialize the first column to 0..m.
}
//step 3 Examine each character of s (i from 1 to n).
for(int i=1;i<=n;i++)
{
const TCHAR si=source[i-1];
//step 4
for(int j=1;j<=m;j++)
{
const TCHAR dj=target[j-1];
//step 5
int cost;
if(si==dj)
{
cost=0;
}
else
{
cost=1;
}
//step 6
const int above=matrix[i-1][j]+1;
const int left=matrix[i][j-1]+1;
const int diag=matrix[i-1][j-1]+cost;
matrix[i][j]=min(above,min(left,diag));
}
}
//step7
return matrix[n][m];
}

   在编写词语对齐软件的时候，要用到一些相似度的计算，最简单的莫过于2s/（s1+s2）这种计算方法了，当然还有上面呈现的这段代码：编辑距离相似度的计算方法。简单的讲，Levenshtein距离，用于比较字符串的相似程度。

　　    LD(s1, s2)=把s1变成s2需要的最小单字符操作（插入、删除和替换）的次数。

  这个相似度倒是帮了我不少忙，哈哈。分享下 

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