Added Longest Palindromic Substring solution to Daily-Coding-DS-ALGO-…

Leetcode/C++/Longest_Palindromic_Substring.cpp

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+/*
+Link to Leetcode problem : https://leetcode.com/problems/longest-palindromic-substring/
+
+Problem: Statement : Given a string s, return the longest palindromic substring in s.
+
+Example1
+Input:s = "babad"
+Output: "bab"
+Note: "aba" is also a valid answer.
+
+Example2
+Input: s = "cbbd"
+Output: "bb"
+*/
+
+/*--------------------------------------------------------------------------------------------------------
+                                               Approach
+                                      We can apply binary search
+ps == Palindromic Substring
+as we can always say that
+if we find ps of length x then what we are sure is than we can make ps of lengths x-2,x-4,x-6... so we
+will not check for lengths less than x but instead we will check for lengths x+2 , x+4 , x+6..
+
+and we can also say that
+
+if we can't find ps of length x then we will also not able to find ps with lengths x+2 ,x+4,x+6..
+but we may find ps of lengths x-2,x-4,x-6..
+so we will search for lengths less than x
+
+lets see this for both even and odd length with small sample
+
+odd
+length 5= "abcba"
+length 3= "bcb"
+length 1 ="c"
+even
+length 6 = "abccba"
+length 4 = "bccb"
+length 2 = "cc"
+So basically what we are doing is we are using the property of ps that if we remove first and last charater of ps then it will still be a ps.
+NOTE :The property always hold only if we remove even lengths from string
+and on basis of this we will apply binary seach seperatory for even lengths and odd lengths and return the ans which has greater length.
+
+----------------------------------------------------------------------------------------------------------------------------------------------------
+Time complexity analysis :
+As we applying binary search total no of operation will be log(N) and for each operation we need O(N^2) to check wheather we can make ps or not
+
+so final time complexity will be log(N)*(N^2)
+
+----------------------------------------------------------------------------------------------------------------------------------------------------
+
+Space complexity analysis :
+The main advantage of the using this approach is unlike general dp which uses O(N^2) space
+here space complexity of this approach will be O(N) that is becuase
+we are only using constant number of integers,bools and string to store , manipulate data inputs and our algorithm.
+Space complexity of integers , bool is O(1) and to store string it will be O(N).
+so overall it will be O(N).
+----------------------------------------------------------------------------------------------------------------------------------------------------
+*/
+
+class Solution {
+public:
+    string FindAnsForOdd(string s){
+    	int n = s.length();
+    	int lo=1;
+        int hi=n/2+(n%2)+1;
+        int mid,len;
+        string ans="";
+        string str;
+        string temp;
+        bool FoundString;
+        while(lo<hi){
+        	mid = (lo+hi)/2;
+        	len = 2*mid-1;  // making sure that I perform  binary search odd lengths
+        	FoundString = false;
+        	for(int i=0;i<n;i++){  // checking if we can form palindromic substring of length = len from string s
+        		if(i+len<=n){
+        			str="";
+        			for(int j=i;j<i+len;j++){
+        				str+=s[j];
+        			}
+        			temp = str;
+        			reverse(temp.begin(),temp.end());
+        			if(str==temp){   // checking if the substring is palindrome by reversing it and comparing it with its original form
+        				ans = str;
+        				FoundString = true;
+        				break;
+        			}
+        		}
+        		else{
+        			break;
+        		}
+        	}
+        	if(FoundString){
+        		lo = mid+1;
+        	}
+        	else{
+        		hi = mid;
+        	}
+        }
+        return ans;
+    }
+    string FindAnsForEven(string s){
+        int n = s.length();
+    	int lo=1;
+        int hi=n/2+1;
+        int mid,len;
+        string ans="";
+        string str;
+        string temp;
+        bool FoundString;
+        while(lo<hi){
+        	mid = (lo+hi)/2;
+        	len = 2*mid;   // making sure that I perform  binary search even lengths
+        	FoundString = false;
+        	for(int i=0;i<n;i++){  // checking if we can form palindromic substring of length = len from string s
+        		if(i+len<=n){
+        			str="";
+        			for(int j=i;j<i+len;j++){
+        				str+=s[j];
+        			}
+        			temp = str;
+        			reverse(temp.begin(),temp.end());
+                    if(str==temp){ // checking if the substring is palindrome by reversing it and comparing it with its original form
+        				ans = str;
+        				FoundString = true;
+        				break;
+        			}
+        		}
+        		else{
+        			break;
+        		}
+        	}
+        	if(FoundString){
+        		lo = mid+1;
+        	}
+        	else{
+        		hi = mid;
+        	}
+        }
+        return ans;
+    }
+    string longestPalindrome(string s) {
+        string ans1 = FindAnsForOdd(s);
+        string ans2 = FindAnsForEven(s);
+        return (ans1.length()>=ans2.length())?ans1:ans2;
+    }
+};
+