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Length of longest Palindromic Subsequence of even length with no two adjacent characters same

Given a string str, the task is to find the length of the longest palindromic subsequence of even length with no two adjacent characters same except the middle characters.

Examples: 

Input: str = “abscrcdba” 
Output:
Explanation: 
abccba is the required string which has no two consecutive characters same except the middle characters. Hence the length is 6

Input: str = “abcd” 
Output: 0

Approach: The idea is to form a recursive solution and store the values of the subproblems using Dynamic Programming. The following steps can be followed to compute the result: 

The following is the implementation of the above approach:




// C++ implementation of above approach
  
#include <bits/stdc++.h>
using namespace std;
  
#define lli long long int
  
// To store the values of subproblems
unordered_map<string, lli> dp;
  
// Function to find the
// Longest Palindromic subsequence of even
// length with no two adjacent characters same
lli solve(string s, char c)
{
    // Base cases
    // If the string length is 1 return 0
    if (s.length() == 1)
        return 0;
  
    // If the string length is 2
    if (s.length() == 2) {
  
        // Check if the characters match
        if (s[0] == s[1] && s[0] == c)
            return 1;
        else
            return 0;
    }
  
    // If the value with given parameters is
    // previously calculated
    if (dp[s + " " + c])
        return dp[s + " " + c];
  
    lli ans = 0;
  
    // If the first and last character of the
    // string matches with the given character
    if (s[0] == s[s.length() - 1] && s[0] == c) 
    {
        // Remove the first and last character
        // and call the function for all characters
        for (char c1 = 'a'; c1 <= 'z'; c1++)
            if (c1 != c)
                ans = max(
                    ans,
                    1 + solve(s.substr(1, 
                                       s.length() - 2),
                                       c1));
    }
  
    // If it does not match
    else {
  
        // Then find the first and last index of
        // given character in the given string
        for (lli i = 0; i < s.length(); i++) 
        {
            if (s[i] == c) 
            {
                for (lli j = s.length() - 1; j > i; j--)
                    if (s[j] == c) 
                    {
                        if (j == i)
                            break;
  
                        // Take the substring from i
                        // to j and call the function
                        // with substring
                        // and the given character
                        ans = solve(s.substr(i, j - i + 1),
                                    c);
                        break;
                    }
  
                break;
            }
        }
    }
  
    // Store the answer for future use
    dp[s + " " + c] = ans;
    return dp[s + " " + c];
}
  
// Driver code
int main()
{
    string s = "abscrcdba";
  
    lli ma = 0;
  
    // Check for all starting characters
    for (char c1 = 'a'; c1 <= 'z'; c1++)
        ma = max(ma, solve(s, c1) * 2);
    cout << ma << endl;
  
    return 0;
}




// Java implementation of above approach
import java.util.*;
  
class GFG {
  
    // To store the values of subproblems
    static Map<String, Integer> dp = new HashMap<>();
  
    // Function to find the
    // Longest Palindromic subsequence of even
    // length with no two adjacent characters same
    static Integer solve(char[] s, char c)
    {
  
        // Base cases
        // If the String length is 1 return 0
        if (s.length == 1)
            return 0;
  
        // If the String length is 2
        if (s.length == 2) {
  
            // Check if the characters match
            if (s[0] == s[1] && s[0] == c)
                return 1;
            else
                return 0;
        }
  
        // If the value with given parameters is
        // previously calculated
        if (dp.containsKey(String.valueOf(s) + " " + c))
            return dp.get(String.valueOf(s) + " " + c);
        Integer ans = 0;
  
        // If the first and last character of the
        // String matches with the given character
        if (s[0] == s[s.length - 1] && s[0] == c)
        {
            // Remove the first and last character
            // and call the function for all characters
            for (char c1 = 'a'; c1 <= 'z'; c1++)
  
                if (c1 != c)
                    ans = Math.max(
                        ans,
                        1 + solve(Arrays.copyOfRange(
                                        s, 1
                                        s.length - 1),
                                        c1));
        }
  
        // If it does not match
        else {
  
            // Then find the first and last index of
            // given character in the given String
            for (Integer i = 0; i < s.length; i++) 
            {
                if (s[i] == c) 
                {
                    for (Integer j = s.length - 1
                         j > i;
                         j--)
                        if (s[j] == c) 
                        {
                            if (j == i)
                                break;
  
                            // Take the subString from i
                            // to j and call the function
                            // with subString
                            // and the given character
                            ans = solve(Arrays.copyOfRange(
                                            s, i, 
                                            j + 1),
                                            c);
                            break;
                        }
  
                    break;
                }
            }
        }
  
        // Store the answer for future use
        dp.put(String.valueOf(s) + " " + c, ans);
        return dp.get(String.valueOf(s) + " " + c);
    }
  
    // Driver code
    public static void main(String[] args)
    {
        String s = "abscrcdba";
  
        Integer ma = 0;
  
        // Check for all starting characters
        for (char c1 = 'a'; c1 <= 'z'; c1++)
            ma = Math.max(ma,
                          solve(s.toCharArray(), c1) * 2);
        System.out.print(ma + "\n");
    }
}
  
// This code is contributed by 29AjayKumar




# Python3 implementation of above approach
  
# To store the values of subproblems
dp = {}
  
# Function to find the
# Longest Palindromic subsequence of even
# length with no two adjacent characters same
  
  
def solve(s, c):
  
    # Base cases
    # If the string length is 1 return 0
    if (len(s) == 1):
        return 0
  
    # If the string length is 2
    if (len(s) == 2):
  
        # Check if the characters match
        if (s[0] == s[1] and s[0] == c):
            return 1
        else:
            return 0
  
    # If the value with given parameters is
    # previously calculated
    if (s + " " + c) in dp:
        return dp[s + " " + c]
  
    ans = 0
  
    # If the first and last character of the
    # string matches with the given character
    if (s[0] == s[len(s) - 1] and s[0] == c):
  
        # Remove the first and last character
        # and call the function for all characters
        for c1 in range(97, 123):
  
            if (chr(c1) != c):
                ans = max(ans, 1 + solve(
                    s[1: len(s) - 1], chr(c1)))
  
    # If it does not match
    else:
  
        # Then find the first and last index of
        # given character in the given string
        for i in range(len(s)):
  
            if (s[i] == c):
                for j in range(len(s) - 1, i, -1):
                    if (s[j] == c):
                        if (j == i):
                            break
  
                        # Take the substring from i
                        # to j and call the function
                        # with substring
                        # and the given character
                        ans = solve(s[i: j - i + 2], c)
                        break
  
                break
  
    # Store the answer for future use
    dp[s + " " + c] = ans
  
    return dp[s + " " + c]
  
  
# Driver code
if __name__ == "__main__":
  
    s = "abscrcdba"
  
    ma = 0
  
    # Check for all starting characters
    for c1 in range(97, 123):
        ma = max(ma, solve(s, chr(c1)) * 2)
  
    print(ma)
  
# This code is contributed by AnkitRai01




// C# implementation of
// the above approach
using System;
using System.Collections;
using System.Collections.Generic;
  
class GFG {
  
    // To store the values of subproblems
    static Dictionary<string, int> dp
        = new Dictionary<string, int>();
  
    // Function to find the
    // Longest Palindromic subsequence of even
    // length with no two adjacent characters same
    static int solve(char[] s, char c)
    {
  
        // Base cases
        // If the String length is 1 return 0
        if (s.Length == 1)
            return 0;
  
        // If the String length is 2
        if (s.Length == 2) {
  
            // Check if the characters match
            if (s[0] == s[1] && s[0] == c)
                return 1;
            else
                return 0;
        }
  
        // If the value with given parameters is
        // previously calculated
        if (dp.ContainsKey(new string(s) + " " + c))
            return dp[new string(s) + " " + c];
  
        int ans = 0;
  
        // If the first and last character of the
        // String matches with the given character
        if (s[0] == s[s.Length - 1] && s[0] == c) 
        {
  
            // Remove the first and last character
            // and call the function for all characters
            for (char c1 = 'a'; c1 <= 'z'; c1++)
  
                if (c1 != c) {
                    int len = s.Length - 2;
                    char[] tmp = new char[len];
  
                    Array.Copy(s, 1, tmp, 0, len);
                    ans = Math.Max(ans, 1 + solve(tmp, c1));
                }
        }
  
        // If it does not match
        else {
  
            // Then find the first and last index of
            // given character in the given String
            for (int i = 0; i < s.Length; i++) 
            {
                if (s[i] == c) 
                {
                    for (int j = s.Length - 1; j > i; j--)
                        if (s[j] == c) 
                        {
                            if (j == i)
                                break;
  
                            // Take the subString from i
                            // to j and call the function
                            // with subString and the
                            // given character
                            int len = j + 1 - i;
                            char[] tmp = new char[len];
                            Array.Copy(s, i, tmp, 0, len);
                            ans = solve(tmp, c);
                            break;
                        }
                    break;
                }
            }
        }
  
        // Store the answer for future use
        dp[new string(s) + " " + c] = ans;
        return dp[new string(s) + " " + c];
    }
  
    // Driver Code
    public static void Main(string[] args)
    {
        string s = "abscrcdba";
  
        int ma = 0;
  
        // Check for all starting characters
        for (char c1 = 'a'; c1 <= 'z'; c1++)
            ma = Math.Max(ma,
                          solve(s.ToCharArray(), c1) * 2);
  
        Console.Write(ma + "\n");
    }
}
  
// This code is contributed by rutvik_56




<script>
  
// Javascript implementation of above approach
  
// To store the values of subproblems
var dp = new Map();
  
// Function to find the
// Longest Palindromic subsequence of even
// length with no two adjacent characters same
function solve(s, c)
{
    // Base cases
    // If the string length is 1 return 0
    if (s.length == 1)
        return 0;
  
    // If the string length is 2
    if (s.length == 2) {
  
        // Check if the characters match
        if (s[0] == s[1] && s[0] == c)
            return 1;
        else
            return 0;
    }
  
    // If the value with given parameters is
    // previously calculated
    if (dp.has(s + " " + c))
        return dp.get(s + " " + c);
  
    var ans = 0;
  
    // If the first and last character of the
    // string matches with the given character
    if (s[0] == s[s.length - 1] && s[0] == c) 
    {
        // Remove the first and last character
        // and call the function for all characters
        for (var c1 = 'a'.charCodeAt(0); c1 <= 'z'.charCodeAt(0); c1++)
            if (String.fromCharCode(c1) != c)
                ans = Math.max(
                    ans,
                    1 + solve(s.substring(1, 
                                       s.length - 1),
                                       String.fromCharCode(c1)));
    }
  
    // If it does not match
    else {
  
        // Then find the first and last index of
        // given character in the given string
        for (var i = 0; i < s.length; i++) 
        {
            if (s[i] == c) 
            {
                for (var j = s.length - 1; j > i; j--)
                    if (s[j] == c) 
                    {
                        if (j == i)
                            break;
  
                        // Take the substring from i
                        // to j and call the function
                        // with substring
                        // and the given character
                        ans = solve(s.substring(i, j + 1),
                                    c);
                        break;
                    }
  
                break;
            }
        }
    }
  
    // Store the answer for future use
    dp.set(s + " " + c, ans);
    return ans;
}
  
// Driver code
var s = "abscrcdba";
var ma = 0;
// Check for all starting characters
for (var c1 = 'a'.charCodeAt(0); c1 <= 'z'.charCodeAt(0); c1++)
    ma = Math.max(ma, solve(s, String.fromCharCode(c1)) * 2);
document.write(ma);
  
</script>

Output
6

Time Complexity: O(N2)
Auxiliary Space: O(N)

Related Article: Longest Palindromic Subsequence
 


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