int editDistanceDynamicProg(string s1, string s2)
Let’s see how this is implemented using Dynamic Programming. We use the same above formula, but here we store the results into an array that needs an space.
This memorizing solution and using it whenever required is called as Dynamic Programming. To reduce the recursion overlaps we memorize the solution and uses it whenever there is an overlap in the recursion. Dynamic programming approachĪs the given problem has a recursive solution, this can also be solved by using Dynamic Programming. It seems very simple to code, but wait here the complexity of this problem is exponential which is. Return 1 + min(editDistanceRecursion(s1, s2, len1-1, len2 - 1),ĮditDistanceRecursion(s1, s2, len1, len2 - 1),ĮditDistanceRecursion(s1, s2, len1 - 1, len2)) Return editDistanceRecursion(s1, s2, len1 - 1, len2 - 1) int editDistanceRecursion(string s1, string s2, Using the above formula we can recursively find the minimum distance between any of the two given strings. (ED(str1, str2, length-1, length2)) // If insert. (ED(str1, str2, length, length2-1), // If remove. = ED(str1, str2, length1-1, length2-1) // if both the last characters same do nothing just reduce the size. So here we have a total of four possibilities of inputs.įull recursion formula ED(str1, str2, length1, length2) String length is at most one which means either 0 length or 1. Our example here is to take two strings, and lengths of them are at most “1”.
Now let’s take a few minimum possible examples to find the recursion formula. We can solve this problem using recursion. Character 'a' has to Remove from the first string to become as similar as the second string. 'N' has to replace with 'H' and need to insert the last character 'd'.Įdit distance here is 1. One 3rd character in the first string has to replace with 'a' to make as similar to the second string.Įdit distance is 2. For example, let's take below three below examples which contain all the three operations described above.Įdit distance here is 1. The operations can be Insert a character, Remove a character, or Replace a character with another. The minimum number of operations on a string (array of characters) to convert into another input string is called the edit distance between the two strings.
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