Sub Longest palindrome number find out using recursive

History of Palindrome String — Concept, Origins, and Use in Programming

What Is a Palindrome?

A palindrome is a word, phrase, number, or sequence that reads the same forwards and backwards, ignoring punctuation, spaces, and case.

✅ Examples:

Words: madam, level, radar
Phrases: "A man, a plan, a canal, Panama!"
Numbers: 121, 1221, 12321

Historical Origins

Ancient History

The concept of palindromes has existed for over 2000 years.
Earliest recorded palindrome:
The Latin palindrome “Sator Arepo Tenet Opera Rotas” (5-word square) dates back to 1st century CE (Pompeii, Italy).

Palindromes in World Cultures

Greek and Latin: Palindromes were used for poetry and religious texts.
Arabic and Persian: Complex palindromic poetry was a literary art form.

The concept of a palindrome is deeply significant in mathematics, computer science, and even in the physics of mirrors because it represents symmetry, reversibility, and pattern recognition.

Let’s break it down clearly:

What Is a Palindrome in Mirror Terms?

A palindrome is like a mirror image:

The left side reflects the right side.

Example:

"RADAR"

↑ ↑

R ↔ R

A ↔ A

D ← center

Why Palindromes Are Important

1. In Mathematics

✅ a. Symmetry & Patterns

Palindromic numbers (e.g., 121, 1331) reflect symmetry.
Mathematics loves symmetry because it reduces complexity in:

Geometry (mirror symmetry)
Number theory (palindromic primes)
Modular arithmetic

✅ b. Number Properties

Some mathematical problems are simplified by focusing on digit patterns.
Palindromic numbers often reveal base-specific properties, like in:

Binary (e.g., 101, 1001)
Decimal (e.g., 121, 12321)

2. In Computer Science

✅ a. String Reversal / Algorithm Practice

Palindromes are fundamental in:

Recursion
Two-pointer approach
Stack operations

✅ b. Data Validation / Symmetric Processing

Palindromes are used to check if a data structure or value is reversible.

Biology (DNA/RNA) matching (biotech):

Palindromic sequences are crucial in DNA replication and restriction enzymes.
e.g., GAATTC (complementary palindrome for EcoRI)

Reversible encryption (crypto)
Compiler parsers (mirror-based parsing rules)

✅ c. Palindrome in Machine Logic

Recognizing palindromes helps build finite automata and Turing machines.
Palindromes test the limits of computational power (e.g., stack memory needed to validate).

3. In Mirror and Optics (Physics)

In optics, a palindrome visually appears unchanged in a perfect mirror.
Mirror symmetry is used in:

Optical image processing
Symmetric 3D modeling
Fractal patterns in simulations

Why Is This Symmetry Valuable?

Field	Palindrome Value
Math	Detecting or Recognizing patterns, simplifying or streamlining problems
CS (Algorithms)	Validating or Verifying logic, building or constructing recursive solutions
CS (Theory)	Designing or Creating automata (palindromes need or necessitate a stack)
Physics	Modeling mirror and symmetry behaviors
Biology	DNA/RNA analysis, enzyme target sites

Bonus: Real-Life Palindrome Use Cases

Area	Palindrome Example	Why Useful
DNA Analysis	GAATTC ↔ CTTAAG	Enzymes target or aim palindromic sequences
Web Devloment	Palindrome sequence checker in JavaScript	UX demo, algorithm task or exercise
Networking	Palindromic packet configuration patterns	Debugging the packet symmetry process
The Cryptography	The Symmetric cipher keys featuring palindromes	Reversible encryption process

Popularity in Any Coding Interviews

Palindrome problems are notable for:

Reversing strings
Two-pointer techniques
Recursion
Dynamic Programming

Popular Variants:

Longest palindromic substring
Minimum cuts to partition string into palindromes
Palindrome pairs in a list of words

Table

Aspect	Description
Origin	Ancient Greece, Rome, and India
Meaning	Reads same forward and backward
Use in Programming	String problems, recursion, DP
Scientific Use	DNA sequencing, math (palindromic primes)
Common Example	racecar, madam,12321

🧑‍💻 Common Algorithm

package com.kcm.demo;

public class TestSubPalindrome {

/**

* @param s

* @param left

* @param right

* @return

static public String helper(String s, int left, int right) {

if (left > right) return null;

if(left >= 0 && right < s.length() && s.charAt(left) == s.charAt(right))

return helper(s,left-1,right+1);

else

return s.substring(left + 1, right);

}

/**

* @param s

* @return

public static String longestPalindrome(String s) {

if (s == null) return null;

String lngest = s.substring(0, 1);

for (int i = 0; i < s.length() - 1; i++) {

//odd cases like 121

String palindromeString = helper(s, i, i);

if (palindrome.length() > lngest.length()) {

lngest = palindromeString;

}

//even cases like 123321

palindromeString = helper(s, i, i + 1);

if (palindromeString.length() > lngest.length()) {

lngest = palindromeString ;

}

return lngest;

}

public static void main(String args[]) {

String str = "ABCCBAKARTIKMANDALOLADNAMKITRAKOJMALABCDCBA";

// String str = "MOMABCCBAKA";

System.out.println("Print longest palindrome from the word " + longestPalindrome (str));

}

java

Longest palindromic substring is: MALABCDCBA

The Java code you provided is meant to identify the longest palindromic substring within a particular string. Let's break down the code and how it works:

Explanation of the Code:

helper(String s, int left, int right):

This is a recursive helper method that expands around a potential center of a palindrome.
It checks characters on the left and right of a given center (or centers for even-length palindromes).
If the characters match, it continues expanding outward, and when they stop matching, it returns the palindromic substring.

longestPalindrome(String s):

This method iterates through each character in the string, treating each character (and each pair of adjacent characters) as the potential center of a palindrome.
It calls the helper method to expand around the center and find the longest palindrome for each potential center.
It keeps track of the longest palindrome found.