similarity 字符串编辑距离相似度匹配

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].

/// <summary>  
/// 编辑距离（Levenshtein Distance）  
/// </summary>  
/// <param name="source">源串</param>  
/// <param name="target">目标串</param>  
/// <param name="similarity">输出：相似度，值在0～１</param>  
/// <param name="isCaseSensitive">是否大小写敏感</param>  
/// <returns>源串和目标串之间的编辑距离</returns>  
public static Int32 LevenshteinDistance(String source, String target, out Double similarity, Boolean isCaseSensitive = false)  
{  
    if (String.IsNullOrEmpty(source))  
    {  
        if (String.IsNullOrEmpty(target))  
        {  
            similarity = 1;  
            return 0;  
        }  
        else  
        {  
            similarity = 0;  
            return target.Length;  
        }  
    }  
    else if (String.IsNullOrEmpty(target))  
    {  
        similarity = 0;  
        return source.Length;  
    }  
  
    String From, To;  
    if (isCaseSensitive)  
    {   // 大小写敏感  
        From = source;  
        To = target;  
    }  
    else  
    {   // 大小写无关  
        From = source.ToLower();  
        To = target.ToLower();  
    }  
  
    // 初始化  
    Int32 m = From.Length;  
    Int32 n = To.Length;  
    Int32[,] H = new Int32[m + 1, n + 1];  
    for (Int32 i = 0; i <= m; i++) H[i, 0] = i;  // 注意：初始化[0,0]  
    for (Int32 j = 1; j <= n; j++) H[0, j] = j;  
  
    // 迭代  
    for (Int32 i = 1; i <= m; i++)  
    {  
        Char SI = From[i - 1];  
        for (Int32 j = 1; j <= n; j++)  
        {   // 删除（deletion） 插入（insertion） 替换（substitution）  
            if (SI == To[j - 1])  
                H[i, j] = H[i-1, j-1];                      
            else  
                H[i, j] = Math.Min(H[i-1, j-1], Math.Min(H[i-1, j], H[i, j-1])) + 1;                      
        }  
    }  
  
    // 计算相似度  
    Int32 MaxLength = Math.Max(m, n);   // 两字符串的最大长度  
    similarity = ((Double)(MaxLength - H[m, n])) / MaxLength;  
  
    return H[m, n];    // 编辑距离  
}  
 

public static void CheckEditDistance()
{
    Int32 Distance;
    Double Similarity;

    while (true)
    {
        Console.WriteLine("------------------------------------");
        Console.Write("源串 = ");
        String Source = Console.ReadLine();
        if (Source == "q") break;

        Console.Write("目标串 = ");
        String Target = Console.ReadLine();

        Distance = LevenshteinDistance(Source, Target, out Similarity, true);
        Console.WriteLine("编辑距离 = " + Distance.ToString());
        Console.WriteLine("相似度 = " + Similarity.ToString("0.####"));
    }
}