Edit Distance using Dynamic Programming

In the previous post, I discussed a recursive method for finding the Edit Distance (once again, refer previous post for details) between two strings. Some of you might have noticed that the recursive function (in this case) could just as easily be utilized in a Dynamic Programming method.

However, we would be increasing the space complexity by using a 2D array (as is the case with many Dynamic Programming problems). The time complexity would reduce to O( length of String1 * length of String2 ). Since the whole logic has already been explained in the previous post, here is the algorithm.

int EditDistance( String1, String2 )

{

m = String1.length

n = String2.length

For i=0 , i<=m , i++

V[i][0] = i

For i=0 , i<=n , i++

V[0][i] = i

//cells in first row and column of temporary 2D array V set to corresponding number

For i=1 , i<=m , i++

{

For j=1 , j<=n , j++

{

If ( String1[i-1] == String2[j-1] )

V[i][j]=V[i-1][j-1]

Else

V[i][j] = 1 + min( min(V[i][j-1], V[i-1][j]), V[i-1][j-1])

}

}

RETURN V[m][n] //last element of 2D array (last row, last column)

}

So the logic remains the same. The only difference is that we avoid the use of system stack and instead store previous results in a 2D array. Neat! 🙂