Check if edit distance between two strings is one

An edit between two strings is one of the following changes.

2. Delete a character
3. Change a character

Given two string s1 and s2, find if s1 can be converted to s2 with exactly one edit. Expected time complexity is O(m+n) where m and n are lengths of two strings.

Examples:

```Input:  s1 = "geeks", s2 = "geek"
Output: yes
Number of edits is 1

Input:  s1 = "geeks", s2 = "geeks"
Output: no
Number of edits is 0

Input:  s1 = "geaks", s2 = "geeks"
Output: yes
Number of edits is 1

Input:  s1 = "peaks", s2 = "geeks"
Output: no
Number of edits is 2
```

We strongly recommend you to minimize your browser and try this yourself first.

A Simple Solution is to find Edit Distance using Dynamic programming. If distance is 1, then return true, else return false. Time complexity of this solution is O(n2)

An Efficient Solution is to simultaneously traverse both strings and keep track of count of different characters. Below is complete algorithm.

```Let the input strings be s1 and s2 and lengths of input
strings be m and n respectively.

1) If difference between m an n is more than 1,
return false.
2) Initialize count of edits as 0.
3) Start traversing both strings from first character.
a) If current characters don't match, then
(i)   Increment count of edits
(ii)  If count becomes more than 1, return false
(iii) If length of one string is more, then only
possible  edit is to remove a character.
Therefore, move ahead in larger string.
(iv)  If length is same, then only possible edit
is to  change a character. Therefore, move
b) Else, move ahead in both strings. ```

Below are C++ and Python implementations of above idea.

C++

```// C++ program to check if given two strings are
// at distance one.
#include <bits/stdc++.h>
using namespace std;

// Returns true if edit distance between s1 and
// s2 is one, else false
bool isEditDistanceOne(string s1, string s2)
{
// Find lengths of given strings
int m = s1.length(), n = s2.length();

// If difference between lengths is more than
// 1, then strings can't be at one distance
if (abs(m - n) > 1)
return false;

int count = 0; // Count of edits

int i = 0, j = 0;
while (i < m && j < n)
{
// If current characters don't match
if (s1[i] != s2[j])
{
if (count == 1)
return false;

// If length of one string is
// more, then only possible edit
// is to remove a character
if (m > n)
i++;
else if (m< n)
j++;
else //Iflengths of both strings is same
{
i++;
j++;
}

// Increment count of edits
count++;
}

else // If current characters match
{
i++;
j++;
}
}

// If last character is extra in any string
if (i < m || j < n)
count++;

return count == 1;
}

// Driver program
int main()
{
string s1 = "gfg";
string s2 = "gf";
isEditDistanceOne(s1, s2)?
cout << "Yes": cout << "No";
return 0;
}
```

Python

```# Python program to check if given two strings are
# at distance one

# Returns true if edit distance between s1 and s2 is
# one, else false
def isEditDistanceOne(s1, s2):

# Find lengths of given strings
m = len(s1)
n = len(s2)

# If difference between lengths is more than 1,
# then strings can't be at one distance
if abs(m - n) > 1:
return false

count = 0    # Count of isEditDistanceOne

i = 0
j = 0
while i < m and j < n:
# If current characters dont match
if s1[i] != s2[j]:
if count == 1:
return false

# If length of one string is
# more, then only possible edit
# is to remove a character
if m > n:
i+=1
elif m < n:
j+=1
else:    # If lengths of both strings is same
i+=1
j+=1

# Increment count of edits
count+=1

else:    # if current characters match
i+=1
j+=1

# if last character is extra in any string
if i < m or j < n:
count+=1

return count == 1

# Driver program
s1 = "gfg"
s2 = "gf"
if isEditDistanceOne(s1, s2):
print "Yes"
else:
print "No"

# This code is contributed by Bhavya Jain
```

Output:
`Yes`

Time complexity: O(n)
Auxiliary Space: O(1)

Thanks to Gaurav Ahirwar for suggesting above solution.

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