Added Solution to Palindrome_Partitioning

This pull request addresses issue #157 and provides a solution to the Palindrome Partitioning problem, implemented in C++. The problem requires partitioning a given string into substrings such that each substring in every partition is a palindrome. The objective is to return all possible palindrome partitions of the string.

The approach uses recursive backtracking to explore all potential partitions, leveraging the following steps to ensure efficiency and accuracy:

Recursive Backtracking for Partitioning: The function recursively explores each substring of the input string. For each substring, it checks if it forms a palindrome. If it does, it adds this substring to the current partition path and proceeds to partition the remaining string.

Palindrome Check Optimization: To ensure that only palindromic partitions are considered, a helper function is implemented to verify if each substring is a palindrome. This reduces unnecessary partition paths and enhances performance.

Dynamic Partition Storage: Using a path vector, each partition is dynamically built and stored only if it meets the palindrome criterion.

Summary of Changes Implements recursive backtracking to partition the string. Adds a helper function to efficiently check for palindromic substrings. Handles all edge cases, including single-character and completely palindromic strings.

Additional Information

Contributor: Khush Contribution as part of: Hacktoberfest This solution offers an efficient approach to the Palindrome Partitioning problem, leveraging backtracking for flexibility and a palindrome check for correctness. It provides clear logic and performance optimizations suitable for all input constraints.

abhisek247767 / LeetCode2024-6Companies30Days

Added Solution to Palindrome_Partitioning #158