Implemented KMP in C++ (#332)

* Folder structure and Readme file.

* Readme documentation.

* Pseudocode for kmp in readme.

* KMP algorithm implementation and readme update.

* Readme pesudocode reference.

Author: Mysjkin

String Manipulation/Knuth-Morris-Pratt/C++/KMP.cpp

@@ -0,0 +1,62 @@
+#include <iostream>
+#include <vector>
+
+using namespace std;
+
+// Computes the prefix-suffix array.
+vector<int> ComputePrefixFunction(string pattern){
+    int m = pattern.length();
+    vector<int> prefixArr(m);
+    prefixArr[0] = 0;
+    int k = 0;
+
+    for(int i=1; i<m; ++i){
+        while(k > 0 && pattern[k] != pattern[i]){
+            k = prefixArr[k];
+        }
+        if(pattern[k] == pattern[i]){
+            k++;
+        }
+        prefixArr[i] = k;
+    }
+    
+    return prefixArr;
+}
+
+// Returns a vector of indicies where there is a pattern match.
+vector<int> KMP(string text, string pattern){
+    int n = text.length();
+    int m = pattern.length();
+    vector<int> prefixArr = ComputePrefixFunction(pattern);
+    int q = 0;
+
+    vector<int> results;
+
+    for (int i = 0; i < n; ++i){
+        while(q > 0 && pattern[q] != text[i]){
+            q = prefixArr[q];
+        }
+        if(pattern[q] == text[i]){
+            q++;
+        }
+        if(q == m){
+            results.push_back(i-m);
+            q = prefixArr[q];
+        }
+    }
+    
+    return results;
+}
+
+int main(){
+    string example1 = "bacbababaabacabababaabaca";
+    string pattern1 = "abaabaca";
+
+    vector<int> result = KMP(example1, pattern1);
+    vector<int>::iterator itt;
+    cout << "Matches at the following indicies..." << endl;
+    for(itt = result.begin(); itt != result.end(); ++itt){
+        cout << *itt << endl;
+    }
+    return 0;
+}

String Manipulation/Knuth-Morris-Pratt/README.md

@@ -0,0 +1,66 @@
+# Knuth-Morris-Pratt (KMP) Algorithm
+KMP is a linear time string matching algorithm. The problem involves finding
+all occurences where a string pattern matches a substring in a text.
+The naive approach to string matching involves
+looping over all indicies over a text string and finding the indicies
+where the pattern p matches the substring starting at the index.
+
+s.t. pattern[0 ... m - 1] = text[idx ... idx + m - 1], where idx is some offset.
+
+The worst case of this approach is O(m*(n-m+1)), where m is |p| and n is |text|.
+
+The main drawback of the naive appraoch is that it handles overlaps
+poorly. Since it will go deep into the second nested loop when checking
+whether the substring and the pattern matches. When it hits a mismatch
+it will start over from the next increment, thereby redoing some of its
+comparisons.
+
+The KMP algorithm solves this problem by relying on some clever preprocessing,
+thereby reaching a linear time performance. The clever preprocessing is simply
+creating an array that contains information calculated by a prefix function, and this information describes how the pattern matches against shifts of itself. 
+We use this array to avoid the worst case situation of the naive approach by reusing previously performed comparisons.
+
+The prefix-function(i) is the longest prefix of p that is also a suffix of p[1 ... i]. The whole idea of finding these substrings in the
+pattern which are both prefixes and suffixes, is that they determine from what index in the pattern and text we should start from next, hence
+avoiding having to start all the way at the start index of the pattern and only one index further in the text each time we hit a
+character miss match.
+
+KMP runs in O(n + m). Note, KMP is only necessary when there are many overlapping parts, since it is only in such
+situations where the prefix-suffix array helps. However, the worst case linear time efficiency is guaranteed, meaning
+the KMP algorithm is useful in general cases aswell. 
+
+## Pseudocode
+Where t is the text string and p is the pattern.
+
+    KMP-Matcher(t, p):
+        n = len(t)
+        m = len(p)
+        prefix-arr = Compute-Prefix-Function(p)
+        q = 0
+        for i = 0 to n:
+            while q > 0 and p[q] != t[i]:
+                q = prefix-arr[q]
+            if p[q] == t[i]:
+                q++
+            if q == m:
+                patterns occurs at index i - m
+                q = prefix-arr[q]
+
+    Compute-Prefix-Function(p)
+        m = len(p)
+        new arr[0 ... m-1]
+        arr[0] = 0
+        k = 0
+        for i = 1 to m:
+            while k > 0 and  p[k] != p[i]:
+                k = arr[k]
+            if p[k] == p[i]:
+                k++
+            arr[i] = k
+        
+        return arr
+
+CLRS[p. 1006].
+
+
+