Added README.md

Dynamic Programming/README.md

@@ -0,0 +1,28 @@
+## Longest Common Subsequence (LCS)
+
+Given two strings, S1 and S2, the task is to find the length of the Longest Common Subsequence. If there is no common subsequence, return 0. A subsequence is a string generated from the original string by deleting 0 or more characters and without changing the relative order of the remaining characters. For example , subsequences of “ABC” are “”, “A”, “B”, “C”, “AB”, “AC”, “BC” and “ABC”. In general a string of length n has 2n subsequences.
+
+LCS problem has great applications like diff utility (find the difference between two files) that we use in our day to day software development.
+
+**Examples:**
+
+```
+Input: S1 = “ABC”, S2 = “ACD”
+
+Output: 2
+
+Explanation: The longest subsequence which is present in both strings is “AC”.
+```
+
+Approach Used: Using Recursion – O(2^min(m,n)) Time and O(min(m, n)) Space
+
+```
+The idea is to compare the last two characters. While comparing the strings S1 and S2 two cases arise:
+
+
+1. Match : Make the recursion call  for the remaining strings (strings of lengths m-1 and n-1) and add 1 to result.
+
+2. Do not Match : Make two recursive calls. First for lengths m-1 and n, and second for m and n-1. Take the maximum of two results.
+ 
+Base case : If any of the strings become empty, we return 0.
+```