字符串相似/差异度算法(Levenshtein Distance)
Sep 9th,2011
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Levenshtein Distance算法(中文翻译：编辑距离算法) 由俄国科学家Levenshtein在1965年提出。
编辑距离，又称Levenshtein距离（也叫做Edit Distance），是指两个字串之间，由一个转成另一个所需的最少编辑操作次数。许可的编辑操作包括将一个字符替换成另一个字符，插入一个字符，删除一个字符。
例如将kitten一字转成sitting：
sitten （k→s）
sittin （e→i）
sitting （→g）
应用
DNA分析
拼字检查
语音辨识
抄袭侦测
其步骤:
| 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]. |
#include
#include
#include
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 > 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="<
#include
#include
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 > 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="<
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牛啊 😈