Merge pull request #280 from Shivam20233/master

Added Manacher's Algo

Author: master-fury

Pattern_Matching/src/Manacher's Algo

@@ -0,0 +1,88 @@
+// Manacher's algorithm is used to find the longest palindromic substring in any string. It is 
+// required to solve sub-problems of some very hard problems.
+// Manacher's algorithm was invented by Manacher for listing all the palindromes that appear at 
+// the start of any given string, it was later observed that the same algorithm can be used to 
+// find the longest palindromic substring of any string in linear time.
+
+#include <iostream>
+#include <vector>
+#include <algorithm>
+using namespace std;
+
+// A function to print a substring.
+void printSubstring(string str, int left, int right){
+    for (int i = left; i <= right; i++)
+        cout << str[i];
+}
+
+// Implementation of Manacher's Algorithm
+void longestPalSubstring(string s){
+    /*
+        If length of given string is n then its length after
+        inserting n+1 "#", one "@", and one "$" will be
+        (n) + (n+1) + (1) + (1) = 2n+3
+    */
+    int strLen = 2 * s.length() + 3;
+    char* sChars = new char[strLen];
+
+    /*
+        Inserting special characters to ignore special cases
+        at the beginning and end of the array
+        "abc" -> @ # a # b # c # $
+        "" -> @#$
+        "a" -> @ # a # $
+    */
+    sChars[0] = '@';
+    sChars[strLen - 1] = '$';
+    int t = 1;
+
+    for (char c : s){
+        sChars[t++] = '#';
+        sChars[t++] = c;
+    }
+    sChars[t] = '#';
+
+    int maxLen = 0;
+    int start = 0;
+    int maxRight = 0;
+    int center = 0;
+    int* p = new int[strLen]; // i's radius, which doesn't include i
+
+    for(int i = 1; i < strLen - 1; i++){
+        if (i < maxRight){
+            p[i] = min(maxRight - i, p[2 * center - i]);
+        }
+
+        // Expanding along the center
+        while (sChars[i + p[i] + 1] == sChars[i - p[i] - 1]){
+            p[i]++;
+        }
+
+        // Updating center and its bound
+        if (i + p[i] > maxRight){
+            center = i;
+            maxRight = i + p[i];
+        }
+
+        // Updating ans
+        if (p[i] > maxLen){
+            start = (i - p[i] - 1) / 2;
+            maxLen = p[i];
+        }
+    }
+
+    // Printing the longest palindromic substring
+    cout << "The Longest Palindromic Substring is: ";
+    printSubstring(s, start, start + maxLen - 1);
+}
+
+// Driver Code
+int main(){
+    string str = "daabddfddbegtd";
+
+    longestPalSubstring(str);
+    return 0;
+}
+
+Time Complexity: O(N).
+Space Complexity: O(N).