将一个序列变成另一个序列的最少修改步数。
例如下图，将字符串A变成字符串B，所需要的步骤为6个步骤，match表示0步，其他操作表示1步：
设计算法如下：
public sealed class MinimumEditDistance
{
public int[,] CalculateDistance(string originalStr, String targetStr)
{
int LenA = originalStr.Length;
int LenB = targetStr.Length;
int[,] C = new int[LenA + 1, LenB + 1];
for (int i = 0; i <= LenA; C[i, 0] = i, i++) ;//targetStr为空串时的边界条件
for (int j = 0; j <= LenB; C[0, j] = j, j++) ;//originalStr为空串时的边界条件
for (int i = 1; i <= LenA; i++)
{
for (int j = 1; j <= LenB; j++)
{
//删除：考虑C[i-1，j]，即i-1时已经达到最好情况，新添加的第i个字符需要删除掉
int candidateDel = C[i - 1, j] + 1;
//插入：考虑C[i，j-1]，即已经在i的情况下能够达到j-1时的最好情况，此时如果考虑j的情况就是直接插入第j个字符
int candidateIns = C[i, j - 1] + 1;
//匹配：考虑C[i-1，j-1]，即在i-1,j-1的情况下已经得到最好值，并且新近考虑的i和j字符相同，则无需任何额外动作
// int candidate = C[i-1, j-1];
//替换：考虑C[i-1，j-1]，即在i-1,j-1的情况下已经得到最好值，并且新近考虑的i和j字符不相同，则需一次替换额外动作
//int candidate = C[i - 1, j - 1]+1;
int candidateMatRep;
if (char.Equals(originalStr[i - 1], targetStr[j - 1]))
{
candidateMatRep = C[i - 1, j - 1];
}
else
{
candidateMatRep = C[i - 1, j - 1] + 1;
}
//三者取最小代价
C[i, j] = Math.Min(Math.Min(candidateDel, candidateIns), candidateMatRep);
}
}
return C;
}
public List<OperationOnOriginalStr> GetPossibleDesicion(int[,] C, int row, int col)
{
List<OperationOnOriginalStr> lo = new List<OperationOnOriginalStr>();for (int i = row, j = col; i > 0 || j > 0; )
{
if (C[i, j] == C[i - 1, j] + 1)//删除
{
lo.Add(new OperationOnOriginalStr(Operation.Delete, i-1));
i--;
}
else if (C[i, j] == C[i, j - 1] + 1) //插入
{
lo.Add(new OperationOnOriginalStr(Operation.Insert, i-1, j-1));
j--;
}
else if (C[i, j] == C[i - 1, j - 1])//匹配
{
lo.Add(new OperationOnOriginalStr(Operation.Match, i-1,j-1));
i--;
j--;
}
else //替换
{
lo.Add(new OperationOnOriginalStr(Operation.Replace, i-1, j-1));
i--;
j--;
}
}return lo.Reverse<OperationOnOriginalStr>().ToList<OperationOnOriginalStr>();
}
}
public enum Operation
{
Delete,
Insert,
Replace,
Match
}
public class OperationOnOriginalStr
{
public OperationOnOriginalStr(Operation op, int aindex, int? bindex = null)
{
operation = op;
AIndex = aindex;
BIndex = bindex;
}
public Operation operation { get; set; }
public int AIndex { get; set; }
public int? BIndex { get; set; }
}
调用方法如下：
MinimumEditDistance med = new MinimumEditDistance();
var C = med.CalculateDistance(A, B);
var steps = med.GetPossibleDesicion(C, A.Length, B.Length);
steps.ForEach(s => Console.WriteLine("Operation:{0},A[{1}],B[{2}]", s.operation, s.AIndex, s.BIndex));
作者：Andy Zeng
欢迎任何形式的转载，但请务必注明出处。
http://www.cnblogs.com/andyzeng/p/3736012.html