昨天论坛看到的,简单写了一下 题目: 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
StepDescription
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 <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;
- }