Knuth-Morris algo readme

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Knuth_Morris_Pratt_Algorithm/Knuth-Morris_Pratt_Algorithm_README.md

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+# Knuth-Morris Pratt Algorithm
+
+1. It was invented by Donald Knuth and Vaughan Pratt.
+2. It was the first linear time complexity algorithm for string matching which is used to find a pattern in a text.
+3. This algorithm compares character by character from left to right.
+
+## Components of Knuth-Morris Pratt algorithm
+
+Prefix Table : In this algorithm whenever a mismatch occurs,it uses a preprocessed table known as Prefix Table to skip characters comparison while matching.
+
+LPS Table : It stands for Longest proper Prefix which is also suffix. Sometimes prefix table is also known as LPS Table.
+
+## Steps for Creating LPS Table
+
+1. Define a one dimensional array with the size equal to the length of the Pattern. (LPS[size])
+2. Define variables i & j. Set i = 0, j = 1 and LPS[0] = 0.
+3. Compare the characters at Pattern[i] and Pattern[j].
+4. If both are matched then set LPS[j] = i + 1 and increment both i & j values by one. Go to Step 3.
+5. If both are not matched then check the value of variable 'i'. If it is '0' then set LPS[j] = 0 and increment 'j' value by one, if it is not '0' then set i = LPS[i - 1].  Step 3.
+6. Repeat above steps until all the values of LPS[] are filled. 
+
+## ALGORITHM
+
+**Input** the main text, and the pattern, which will be searched.
+
+```
+Begin
+   n := size of text
+   m := size of pattern
+   
+   call findPrefix(pattern, m, prefArray)
+   while i < n, do
+      if text[i] = pattern[j], then
+         increase i and j by 1
+         
+      if j = m, then
+         print the location (i-j) as there is the pattern
+         j := prefArray[j-1]
+      else if i < n AND pattern[j] ≠ text[i] then
+         if j ≠ 0 then
+            j := prefArray[j - 1]
+         else
+            increase i by 1
+   done
+   End
+```
+
+**Output**: The location where patterns are found.
+
+##  How The Knuth-Morris Pratt Algorithm Work?
+
+Let us see an example
+
+Consider the following Text and Pattern
+
+Text : ABC ABCDAB ABCDABCDABDE
+
+Pattern : ABCDABD
+
+LPS[] table for the above pattern is as follows
+
+LPS[] is {0,1,2,3,4,5,6}
+
+**Step 1:** Start comparing first character of pattern with first character of Text from left to right
+
+Text: ABC ABCDAB ABCDABCDABDE
+
+Pattern: ABCDABD
+
+0123456
+
+Here mismatch occurred at Pattern[3],so we need to consider LPS[2] value. Since LPS[2] value is '0' we must compare first character in pattern with next character in Text.
+
+**Step 2:** Start comparing first character of pattern with next character of Text.
+
+Text : ABC ABCDAB ABCDABCDABDE
+
+Pattern : ABCDABD
+
+0123456
+
+Here mismatch occurred at Pattern[6], so we need to consider LPS[5] value. Since LPS[5] value is '2' we compare Pattern[2] character with mismatched character in Text.
+
+**Step 3:** Since LPS value is '2' no need to compare the Pattern[0] and Pattern[1] values
+
+Text : ABC ABCDAB ABCDABCDABDE
+
+Pattern : ABCDABD
+
+0123456
+
+Here mismatch occurred at pattern[2],so we need to consider LPS[1] value. Since LPS[1] value is  '0' we must compare first character in Pattern with next character in Text. 
+
+**Step 4** Compare Pattern[0] with next character in Text
+
+Text : ABC ABCDAB ABCDABCDABDE
+
+Pattern : ABCDABD
+
+0123456
+
+Here mismatch occurred at Pattern[6], so we need to consider LPS[5] value. Since LPS[5] value is '2' we compare Pattern[2] character with mismatched character in Text.
+
+**Step 5:** Compare Pattern[2] with mismatched character in Text.
+
+Text : ABC ABCDAB ABCDABCDABDE
+
+Pattern : ABCDABD
+
+0123456
+
+Here all the characters of Patterns matched with a substring in Text which is starting from index value 15.
+
+So, we conclude that given Pattern found at index 15 in Text.
+
+**TIME COMPLEXITY**
+
+The time complexity of Knuth-Morris Pratt Algorithm is O(n).
+
+**SPACE COMPLEXITY**
+
+It also has a space complexity of O (m) because there’s some pre-processing involved.
+
+**SEE ALSO**
+
+1. https://github.com/jainaman224/Algo_Ds_Notes/blob/master/Knuth_Morris_Pratt_Algorithm/KMP.cpp
+2. https://github.com/jainaman224/Algo_Ds_Notes/blob/master/Knuth_Morris_Pratt_Algorithm/KMP.java
+3. https://github.com/jainaman224/Algo_Ds_Notes/blob/master/Knuth_Morris_Pratt_Algorithm/KMP.py
+4. https://github.com/jainaman224/Algo_Ds_Notes/blob/master/Knuth_Morris_Pratt_Algorithm/KMP.cs
+
+**REFERENCES**
+
+1. https://www.geeksforgeeks.org/kmp-algorithm-for-pattern-searching/
+2. [https://en.wikipedia.org/wiki/Knuth%E2%80%93Morris%E2%80%93Pratt_algorithm](https://en.wikipedia.org/wiki/Knuth–Morris–Pratt_algorithm)