Edit Distance

There are two strings given. The first string is the source string and the second string is the target string. In this program, we have to find how many possible edits are needed to convert first string to the second string. 

The edit of strings can be either Insert some elements, delete something from the first string or modify something to convert into the second string.

Input and Output

Input:
Two strings to compare.
string 1: Programming
string 2: Programs
Output:
Enter the initial string: Programming
Enter the final string: Programs
The number of changes required to convert Programming to Programs is 4

Algorithm

editCount(initStr, finalStr, initLen, finalLen)

Input − The initial and final string and their lengths.
Output − Number of edits are required to make initStr to finalStr.

Begin
   if initLen = 0, then
      return finalLen
   if finalLen := 0, then
      return initLen

   if initStr[initLen - 1] = finalStr[finalLen - 1], then
      return editCount(initStr, finalStr, initLen – 1, finalLen - 1)
   answer := 1 + min of (editCount(initStr, finalStr, initLen , finalLen - 1)),
      (editCount(initStr, finalStr, initLen – 1, finalLen ),
      (editCount(initStr, finalStr, initLen – 1, finalLen - 1)
   return answer
End

Example

#include<iostream>
using namespace std;

int min(int x, int y, int z) {       //find smallest among three numbers
   if(x < y) {
      if(x < z)
         return x;
      else
         return z;
   }else {
      if(y < z)
         return y;
      else
         return z;
   }
}

int editCount(string initStr , string finalStr, int initLen, intfinalLen) {
   if (initLen == 0)       //when initial string is empty, add all characters of final string
      return finalLen;

   if (finalLen == 0)       //when final string is empty, delete all characters from initial string
      return initLen;

   //when last character matches, recursively check previous characters
   if (initStr[initLen-1] == finalStr[finalLen-1])
      return editCount(initStr, finalStr, initLen-1, finalLen-1);

   //if last character match is not found, check for insert, delete and update operations recursively
   return 1 + min ( editCount(initStr, finalStr, initLen, finalLen- 1),  // insert
 
      editCount(initStr, finalStr, initLen-1, finalLen), // delete
      editCount(initStr, finalStr, initLen-1, finalLen-1) // update
   );
}

int main() {
   string initStr;
   string finalStr;

   cout << "Enter the initial string: "; cin >> initStr;
   cout << "Enter the final string: "; cin >> finalStr;
   cout << "The number of changes required to convert " << initStr << " to " << finalStr;
   cout << " is " << editCount( initStr , finalStr, initStr.size(), finalStr.size()) << endl;
}

Output

Enter the initial string: Programming
Enter the final string: Programs
The number of changes required to convert Programming to Programs is 4