diff --git a/Dynamic Programming/Edit_Distance.java b/Dynamic Programming/Edit_Distance.java new file mode 100644 index 00000000..87c50421 --- /dev/null +++ b/Dynamic Programming/Edit_Distance.java @@ -0,0 +1,89 @@ + /** + Author : SUBHAM SANGHAI + A Dynamic Programming based solution for Edit Distance problem In Java + **/ + + /**Description of Edit Distance with an Example: + + Edit distance is a way of quantifying how dissimilar two strings (e.g., words) are to one another, + by counting the minimum number of operations required to transform one string into the other. The + distance operations are the removal, insertion, or substitution of a character in the string. + + + The Distance between "kitten" and "sitting" is 3. A minimal edit script that transforms the former into the latter is: + + kitten → sitten (substitution of "s" for "k") + sitten → sittin (substitution of "i" for "e") + sittin → sitting (insertion of "g" at the end).**/ + + import java.util.Scanner; + public class Edit_Distance + { + + + + public static int minDistance(String word1, String word2) + { + int len1 = word1.length(); + int len2 = word2.length(); + // len1+1, len2+1, because finally return dp[len1][len2] + int[][] dp = new int[len1 + 1][len2 + 1]; + /* If second string is empty, the only option is to + insert all characters of first string into second*/ + for (int i = 0; i <= len1; i++) + { + dp[i][0] = i; + } + /* If first string is empty, the only option is to + insert all characters of second string into first*/ + for (int j = 0; j <= len2; j++) + { + dp[0][j] = j; + } + //iterate though, and check last char + for (int i = 0; i < len1; i++) + { + char c1 = word1.charAt(i); + for (int j = 0; j < len2; j++) + { + char c2 = word2.charAt(j); + //if last two chars equal + if (c1 == c2) + { + //update dp value for +1 length + dp[i + 1][j + 1] = dp[i][j]; + } + else + { + /* if two characters are different , + then take the minimum of the various operations(i.e insertion,removal,substitution)*/ + int replace = dp[i][j] + 1; + int insert = dp[i][j + 1] + 1; + int delete = dp[i + 1][j] + 1; + + int min = replace > insert ? insert : replace; + min = delete > min ? min : delete; + dp[i + 1][j + 1] = min; + } + } + } + /* return the final answer , after traversing through both the strings*/ + return dp[len1][len2]; + } + + + // Driver program to test above function + public static void main(String args[]) + { + Scanner input = new Scanner(System.in); + String s1,s2; + System.out.println("Enter the First String"); + s1 = input.nextLine(); + System.out.println("Enter the Second String"); + s2 = input.nextLine(); + //ans stores the final Edit Distance between the two strings + int ans=0; + ans=minDistance(s1,s2); + System.out.println("The minimum Edit Distance between \"" + s1 + "\" and \"" + s2 +"\" is "+ans); + } + }