added edit distance problem (#247)

Co-authored-by: Umang-IIT <73515380+Umang-IIT@users.noreply.github.com>

Author: umang-singla

Dynamic Programming/Edit Distance/Edit_Distance.cpp

@@ -0,0 +1,45 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+int minDistance(string A, string B) {
+    int n = A.size(),m=B.size();
+    
+    int dp[n][m];
+    
+    for(int i=0;i<n;i++){
+        bool exist = false;
+        for(int j=0;j<=i;j++) if(A[j]==B[0]) exist = true;
+        
+        if(exist) dp[i][0] = i;
+        else dp[i][0] = i+1;
+    }
+    
+    for(int i=0;i<m;i++){
+        bool exist = false;
+        for(int j=0;j<=i;j++) if(A[0]==B[j]) exist = true;
+        
+        if(exist) dp[0][i] = i;
+        else dp[0][i] = i+1;
+    }
+    
+    for(int i=1;i<n;i++){
+        for(int j=1;j<m;j++){
+            if(A[i]==B[j]) dp[i][j] = dp[i-1][j-1];
+            else{
+                dp[i][j] = 1+min(dp[i][j-1],min(dp[i-1][j],dp[i-1][j-1]));
+            }
+        }
+    }
+    
+    return dp[n-1][m-1];
+    
+}
+
+signed main()
+{
+    string A,B;
+    cin>>A>>B;
+    cout<<minDistance(A,B);
+
+    return 0;
+}

Dynamic Programming/Edit Distance/Readme.md

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+# Edit Distance
+
+The edit distance between two strings is the minimum number of operations required to transform one string into the other.
+
+The allowed operations are:
+<ul>
+    <li>Add one character to the string.</li>
+    <li>Remove one character from the string.</li>
+    <li>Replace one character in the string.</li>
+</ul>
+
+For example, the edit distance between LOVE and MOVIE is 2, because you can first replace L with M, and then add I.
+
+Your task is to calculate the edit distance between two strings.
+
+### Input:
+```
+The first argument of input contains a string, A.
+The second argument of input contains a string, B.
+```
+### Output:
+```
+Return an integer, representing the minimum number of steps required.
+```
+
+### Constraints:
+
+- 1 <= length(A), length(B) <= 450
+
+### Example:
+Input 1:<br>
+    A = "abad"<br>
+    B = "abac"
+
+Output 1:<br>
+    1
+
+Explanation 1:<br>
+    Operation 1: Replace d with c.