Update README.md

Author: Anushk2001

README.md

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 # Optimisation-of-Pattern-Matching
 
+Visit : [Documentation](https://drive.google.com/file/d/1AzBEZd2I72Sz0WjuPOL8ixdJeXt7eOcb/view?usp=sharing)
+
 I have chosen this theme to ensure the correctness of these algorithms and
 to learn deep mathematics behind these algorithms. I am desirous of
 learning how the text searching in text editors work, how spell errors are
 checked, etc. I will be analyzing the time and space complexities of the
 algorithms used in these practical cases and also implement them for my
 own satisfaction.
+
+
+# Knuth Morris Pratt (K.M.P.) String matching Algorithm:
+This algorithm is the most important algorithm for solving the problem of
+string matching. It solves this problem in linear time and space complexity.
+This algorithm improves the basic naive algorithm by not just going to the
+next window blindly and redoing the same work. It skips a few windows
+selectively and chooses the next window to check for the pattern by the
+concept of Longest Proper Prefixes and Suffixes (L.P.S.) This involves
+greedy and dynamic programming, programming paradigms. This
+algorithm cleverly uses the properties of the longest proper prefix of a
+string which is also a proper suffix for choosing the next window after a
+deviation is detected in
+the current processing window.
+
+# Z Algorithm :
+It is used to find the pattern as a substring in a string in O(n). KMP
+Algorithm also does the same task at the same time complexity but Z
+algorithm is quite more intuitive and easy to understand. It is commonly
+applied in many applications like finding a phrase in a pdf or a virtual
+dictionary. To accomplish this task a preprocessing stage occurs where we
+trade space for time. We create a Z Array where Z[i] represents the longest
+length of a substring starting at Z[i] which is also the prefix. To accomplish
+this is the main aim to understand this algorithm. Rest follows quite easily
+as we will see in this project. This approach also follows Dynamic
+Programming as we are reusing the previously calculated results.
+
+# Karp-Rabin Algorithm :
+This algorithm is entirely different from the ones discussed. This algorithm
+works on the concept of role hashing, which calculates the hash of one
+window from the previous window in the order of constant time. Ideally or
+theoretically, this hash function is collision-free as it works like a new
+number system having 256 digits and a number can be represented only
+in one way in a particular number system. But practically, a few collisions
+may occur by applying a modulus on the hash value for preventing
+arithmetic and space overflows. This method uses the hash of the
+windows as the primary filter for detecting patterns thus reducing the need
+of checking every window, unlike the naive algorithm.