Create KMP-algorithm.cpp

algorithms/CPlusPlus/Strings/KMP-algorithm.cpp

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+/*
+* the Knuth–Morris–Pratt string-searching algorithm (or KMP algorithm) searches for 
+* occurrences of a "word" W within a main "text string" S by employing the observation
+* that when a mismatch occurs, the word itself embodies sufficient information to 
+* determine where the next match could begin, thus bypassing re-examination of previously 
+* matched characters.(https://en.wikipedia.org/wiki/Knuth%E2%80%93Morris%E2%80%93Pratt_algorithm)
+* Complexity of KMP algorithm
+* Time complexity - O(n + m)
+*/
+
+#include <bits/stdc++.h>
+using namespace std;
+
+// Fills lps[] for given pattern pat[0..M-1]
+void computeLPSArray(string &pat, int M, vector<int> &lps)
+{
+	// length of the previous longest prefix suffix
+	int len = 0;
+
+	// lps[0] is always 0
+
+	// the loop calculates lps[i] for i = 1 to M-1
+	int i = 1;
+	while (i < M) {
+		if (pat[i] == pat[len]) {
+			len++;
+			lps[i] = len;
+			i++;
+		}
+		else // (pat[i] != pat[len])
+		{
+			if (len != 0) 
+				len = lps[len - 1];
+				// Note that we do not increment i here
+			
+			else { // if (len == 0)
+				lps[i] = 0;
+				i++;
+			}
+		}
+	}
+}
+
+
+// Prints occurrences of txt[] in pat[]
+void KMPSearch(string &pat, string &txt)
+{
+	int M = pat.length();
+	int N = txt.length();
+
+	// create lps[] that will hold the longest prefix suffix values for pattern
+	vector<int> lps(M, 0);
+
+	// Preprocess the pattern (calculate lps array)
+	computeLPSArray(pat, M, lps);
+
+	int i = 0; // index for txt
+	int j = 0; // index for pat
+	while (i < N) {
+		if (pat[j] == txt[i]) {
+			j++;
+			i++;
+		}
+
+		if (j == M) {
+			cout<<"Found pattern at index "<<i - j<<" ";
+			j = lps[j - 1];
+		}
+
+		// mismatch after j matches
+		else if (i < N && pat[j] != txt[i]) {
+			// Do not match lps[0..lps[j-1]] characters, they will match anyway
+			if (j != 0)
+				j = lps[j - 1];
+			else
+				i++;
+		}
+	}
+}
+
+int main() {
+	string txt = "ABABDABACDABABCABAB";
+	string pat = "ABABCABAB";
+
+	KMPSearch(pat, txt);
+	return 0;
+}