字符串相似度算法（ Levenshtein Distance算法）

一个字符串可以通过增加一个字符，删除一个字符，替换一个字符得到另外一个字符串，假设，我们把从字符串A转换成字符串B，前面3种操作所执行的最少次数称为AB相似度
如  abc adc  度为 1
      ababababa babababab 度为 2
      abcd acdb 度为2

字符串相似度算法可以使用 Levenshtein Distance算法(中文翻译：编辑距离算法) 这算法是由俄国科学家Levenshtein提出的。其步骤

StepDescription1Set 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.2Initialize the first row to 0..n.
Initialize the first column to 0..m.
3Examine each character of s (i from 1 to n).4Examine each character of t (j from 1 to m).5If s[i] equals t[j], the cost is 0.
If s[i] doesn't equal t[j], the cost is 1.6Set 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.
7After the iteration steps (3, 4, 5, 6) are complete, the distance is found in cell d[n,m].

 

 

c++ 实现代码：

#include <iostream>#include <vector>#include <string>using namespace std;//算法int ldistance(const string source,const string target){ //step 1 int n=source.length(); int m=target.length(); if (m==0) return n; if (n==0) return m; //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; for(int i=1;i<=m;i++) matrix[0][i]=i; //step 3 for(int i=1;i<=n;i++) { const char si=source[i-1]; //step 4 for(int j=1;j<=m;j++) { const char 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];}int main(){ string s; string d; cout<<"source="; cin>>s; cout<<"diag="; cin>>d; int dist=ldistance(s,d); cout<<"dist="<<dist<<endl;}#include <iostream>#include <vector>#include <string>using namespace std;//算法int ldistance(const string source,const string target){ //step 1 int n=source.length(); int m=target.length(); if (m==0) return n; if (n==0) return m; //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; for(int i=1;i<=m;i++) matrix[0][i]=i; //step 3 for(int i=1;i<=n;i++) { const char si=source[i-1]; //step 4 for(int j=1;j<=m;j++) { const char 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];}int main(){ string s; string d; cout<<"source="; cin>>s; cout<<"diag="; cin>>d; int dist=ldistance(s,d); cout<<"dist="<<dist<<endl;}