Check whether Strings are k distance apart or not

Last Updated : 06 Apr, 2023

Given two strings, the task is to find if they are only less than or equal to k edit distance apart. It means that strings are only k edit distance apart when there are only k mismatches.
Print Yes if there are less than or equal to k mismatches, Else No.
Also, print yes if both strings are already the same.

Examples:

Input :  str1 = "geeksforgeeks"    
         str2 = "geeksforgeek" 
         k = 1
Output :  Yes
Explanation: Only one character is mismatched 
             or to be removed i.e. s at last 

Input :  str1 = "nishant"  
         str2 = "nisha"   
         k = 1
Output :  No     
Explanation: 2 characters need to be removed
             i.e. n and t 

Input :  str1 = "practice"    
         str2 = "prac" 
         k = 3
Output :  No
Explanation: 4 characters are mismatched or to
             be removed i.e. t, i, c, e at last i.e. > k

Input :  str1 = "Ping"  str2 = "Paging"   k = 2
Output :  Yes   
Explanation: 2 characters need to be removed or 
            mismatched i.e. a and g in paging

Algorithm:

Check if the difference in the length of both strings is greater than k. If so, return false.
Find the edit distance of two strings. If the edit distance is less than or equal to k, return true. Else return false.

Implementation:

C++

// A Dynamic Programming based C++ program to
// find minimum number operations is less than
// or equal to k or not to convert str1 to str2
#include <bits/stdc++.h>
using namespace std;
 
// Utility function to find minimum of three numbers
int min(int x, int y, int z)
{
    return min(min(x, y), z);
}
 
int editDistDP(string str1, string str2, int m, int n)
{
    // Create a table to store results of subproblems
    int dp[m + 1][n + 1];
 
    // Fill d[][] in bottom up manner
    for (int i = 0; i <= m; i++) {
        for (int j = 0; j <= n; j++) {
            // If first string is empty, only option is to
            // insert all characters of second string
            if (i == 0)
                dp[i][j] = j; // Min. operations = j
 
            // If second string is empty, only option is to
            // remove all characters of second string
            else if (j == 0)
                dp[i][j] = i; // Min. operations = i
 
            // If last characters are same, ignore last char
            // and recur for remaining string
            else if (str1[i - 1] == str2[j - 1])
                dp[i][j] = dp[i - 1][j - 1];
 
            // If last character are different, consider all
            // possibilities and find minimum
            else
                dp[i][j] = 1 + min(dp[i][j - 1], // Insert
                                   dp[i - 1][j], // Remove
                                   dp[i - 1][j - 1]); // Replace
        }
    }
 
    return dp[m][n];
}
 
// Returns true if str1 and str2 are k edit distance apart,
// else false.
bool areKDistant(string str1, string str2, int k)
{
    int m = str1.length();
    int n = str2.length();
 
    if (abs(m - n) > k)
        return false;
 
    return (editDistDP(str1, str2, m, n) <= k);
}
 
// Driver program
int main()
{
    // your code goes here
    string str1 = "geek";
    string str2 = "gks";
    int k = 3;
 
    areKDistant(str1, str2, k) ? cout << "Yes" : cout << "No";
 
    return 0;
}

Java

// A Dynamic Programming based Java program to
// find minimum number operations is less than
// or equal to k or not to convert str1 to str2
class GFG {
 
    // Utility function to find minimum
    // of three numbers
    static int min(int x, int y, int z)
    {
        return Math.min(Math.min(x, y), z);
    }
 
    static int editDistDP(String str1, String str2,
                          int m, int n)
    {
        // Create a table to store
        // results of subproblems
        int dp[][] = new int[m + 1][n + 1];
 
        // Fill d[][] in bottom up manner
        for (int i = 0; i <= m; i++) {
            for (int j = 0; j <= n; j++) {
                // If first string is empty,
                // only option is to insert
                // all characters of second string
                if (i == 0)
                    dp[i][j] = j; // Min. operations = j
 
                // If second string is empty,
                // only option is to remove
                // all characters of second string
                else if (j == 0)
                    dp[i][j] = i; // Min. operations = i
 
                // If last characters are same,
                // ignore last char and recur
                // for remaining string
                else if (str1.charAt(i - 1) == str2.charAt(j - 1))
                    dp[i][j] = dp[i - 1][j - 1];
 
                // If last character are different,
                // consider all possibilities
                // and find minimum
                else
                    dp[i][j] = 1 + min(dp[i][j - 1], // Insert
                                       dp[i - 1][j], // Remove
                                       dp[i - 1][j - 1]); // Replace
            }
        }
 
        return dp[m][n];
    }
 
    // Returns true if str1 and str2 are
    // k edit distance apart, else false.
    static boolean areKDistant(String str1, String str2,
                               int k)
    {
        int m = str1.length();
        int n = str2.length();
 
        if (Math.abs(m - n) > k)
            return false;
 
        return (editDistDP(str1, str2, m, n) <= k);
    }
 
    // driver code
    public static void main(String[] args)
    {
        String str1 = "geek";
        String str2 = "gks";
        int k = 3;
 
        if (areKDistant(str1, str2, k))
            System.out.print("Yes");
        else
            System.out.print("No");
    }
}
 
// This code is contributed by Anant Agarwal.

Python3

# A Dynamic Programming based Python3 program to 
# find minimum number operations is less than 
# or equal to k or not to convert str1 to str2 
 
# Utility function to find minimum 
# of three numbers 
def minn(x, y, z) :
 
    return min(min(x, y), z) 
 
def editDistDP(str1, str2, m, n) :
 
    # Create a table to store results 
    # of subproblems 
    dp = [[0 for i in range(n + 1)] 
             for j in range(m + 1)] 
 
    # Fill d[][] in bottom up manner 
    for i in range(m + 1): 
        for j in range(n + 1): 
             
            # If first is empty, only option is 
            # to insert all characters of second 
            if (i == 0) :
                dp[i][j] = j # Min. operations = j 
 
            # If second is empty, only option is 
            # to remove all characters of second 
            else if (j == 0): 
                dp[i][j] = i # Min. operations = i 
 
            # If last characters are same, 
            # ignore last char and recur
            # for remaining 
            else if (str1[i - 1] == str2[j - 1]):
                dp[i][j] = dp[i - 1][j - 1] 
 
            # If last character are different, 
            # consider all possibilities and 
            # find minimum 
            else:
                dp[i][j] = 1 + minn(dp[i][j - 1], # Insert 
                                    dp[i - 1][j], # Remove 
                                    dp[i - 1][j - 1]) # Replace 
         
    return dp[m][n] 
 
# Returns true if str1 and str2 are
# k edit distance apart, else false. 
def areKDistant(str1, str2, k):
 
    m = len(str1)
    n = len(str2)
 
    if (abs(m - n) > k) :
        return False
 
    return (editDistDP(str1, str2, 
                       m, n) <= k) 
 
# Driver Code 
if __name__ == '__main__':
 
    str1 = "geek"
    str2 = "gks"
    k = 3
    if areKDistant(str1, str2, k):
        print("Yes")  
    else:
        print("No")
 
# This code is contributed 
# by SHUBHAMSINGH10

C#

// A Dynamic Programming based C# 
// program to find minimum number
// operations is less than or equal
// to k or not to convert str1 to str2
using System;
 
class GFG 
{
     
// Utility function to find minimum
// of three numbers
static int min(int x, int y, int z)
{
    return Math.Min(Math.Min(x, y), z);
}
 
static int editDistDP(string str1, string str2, 
                      int m, int n)
{
     
    // Create a table to store 
    // results of subproblems
    int [,]dp = new int[m + 1, n + 1];
 
    // Fill d[][] in bottom up manner
    for (int i = 0; i <= m; i++)
    {
        for (int j = 0; j <= n; j++)
        {
             
            // If first string is empty, 
            // only option is to insert
            // all characters of second string
            if (i == 0)
             
                // Min. operations = j
                dp[i, j] = j; 
 
            // If second string is empty, 
            // only option is to remove 
            // all characters of second string
            else if (j == 0)
             
                 // Min. operations = i
                dp[i, j] = i;
 
            // If last characters are same,
            // ignore last char and recur
            // for remaining string
            else if (str1[i - 1] == str2[j - 1])
                dp[i, j] = dp[i - 1,j - 1];
 
            // If last character are different, 
            // consider all possibilities
            // and find minimum
            else
                dp[i, j] = 1 + min(dp[i, j - 1], // Insert
                                    dp[i - 1, j], // Remove
                                   dp[i - 1, j - 1]); // Replace
        }
    }
 
    return dp[m, n];
}
 
// Returns true if str1 and str2 are
// k edit distance apart, else false.
static bool areKDistant(string str1, string str2, 
                        int k)
{
    int m = str1.Length;
    int n = str2.Length;
 
    if (Math.Abs(m - n) > k)
        return false;
 
    return (editDistDP(str1, str2, m, n) <= k);
}
 
// Driver Code
public static void Main ()
{
    string str1 = "geek";
    string str2 = "gks";
    int k = 3;
 
    if(areKDistant(str1, str2, k))
    Console.WriteLine("Yes"); 
    else
    Console.WriteLine("No"); 
}
}
 
// This code is contributed by vt_m.

PHP

<?php
// A Dynamic Programming based 
// PHP program to find minimum
// number operations is less 
// than or equal to k or not 
// to convert str1 to str2
 
// Utility function to find
// minimum of three numbers
function minn($x, $y, $z)
{
    return min(minn($x, $y), $z);
}
 
function editDistDP($str1, $str2, $m, $n)
{
    // Create a table to store 
    // results of subproblems
    $dp[$m + 1][$n + 1] = 0;
 
    // Fill d[][] in bottom up manner
    for ($i = 0; $i <= $m; $i++)
    {
        for ($j = 0; $j <= $n; $j++) 
        {
            // If first string is empty, 
            // only option is to insert
            // all characters of second string
            if ($i == 0)
             
                // Min. operations = j
                $dp[$i][$j] = $j; 
 
            // If second string is empty, 
            // only option is to remove all
            // characters of second string
            else if ($j == 0)
             
                // Min. operations = i
                $dp[$i][$j] = $i; 
 
            // If last characters are same, 
            // ignore last char and recur 
            // for remaining string
            else if ($str1[$i - 1] == $str2[$j - 1])
                $dp[$i][$j] = $dp[$i - 1][$j - 1];
 
            // If last character are different, 
            // consider all possibilities and 
            // find minimum
            else
                                // Insert         
                $dp[$i][$j] = 1 + min($dp[$i][$j - 1], 
                                // Remove
                                $dp[$i - 1][$j], 
                                // Replace
                                $dp[$i - 1][$j - 1]); 
        }
    }
 
    return $dp[$m][$n];
}
 
// Returns true if str1 and 
// str2 are k edit distance 
// apart, else false.
function areKDistant($str1, $str2, $k)
{
    $m = strlen($str1);
    $n = strlen($str2);
 
    if (abs($m - $n) > $k)
        return false;
 
    return (editDistDP($str1, $str2,
                       $m, $n) <= $k);
}
 
// Driver Code
$str1 = "geek";
$str2 = "gks";
$k = 3;
 
if(areKDistant($str1, $str2, $k)) 
echo"Yes" ; 
else
echo "No";
 
// This code is contributed by nitin mittal. 
?>

Javascript

<script>
    // A Dynamic Programming based Javascript program to
    // find minimum number operations is less than
    // or equal to k or not to convert str1 to str2
     
    // Utility function to find minimum
    // of three numbers
    function min(x, y, z)
    {
        return Math.min(Math.min(x, y), z);
    }
   
    function editDistDP(str1, str2, m, n)
    {
        // Create a table to store
        // results of subproblems
        let dp = new Array(m + 1);
   
        // Fill d[][] in bottom up manner
        for (let i = 0; i <= m; i++) {
            dp[i] = new Array(n + 1);
            for (let j = 0; j <= n; j++) {
                // If first string is empty,
                // only option is to insert
                // all characters of second string
                if (i == 0)
                    dp[i][j] = j; // Min. operations = j
   
                // If second string is empty,
                // only option is to remove
                // all characters of second string
                else if (j == 0)
                    dp[i][j] = i; // Min. operations = i
   
                // If last characters are same,
                // ignore last char and recur
                // for remaining string
                else if (str1[i - 1] == str2[j - 1])
                    dp[i][j] = dp[i - 1][j - 1];
   
                // If last character are different,
                // consider all possibilities
                // and find minimum
                else
                    dp[i][j] = 1 + min(dp[i][j - 1], // Insert
                                       dp[i - 1][j], // Remove
                                       dp[i - 1][j - 1]); // Replace
            }
        }
   
        return dp[m][n];
    }
   
    // Returns true if str1 and str2 are
    // k edit distance apart, else false.
    function areKDistant(str1, str2, k)
    {
        let m = str1.length;
        let n = str2.length;
   
        if (Math.abs(m - n) > k)
            return false;
   
        return (editDistDP(str1, str2, m, n) <= k);
    }
     
    let str1 = "geek";
    let str2 = "gks";
    let k = 3;
 
    if (areKDistant(str1, str2, k))
      document.write("Yes");
    else
      document.write("No");
     
</script>