Palindrome Partitioning

Given a string, partition it into a collection of substrings such that every substring in the collection is a palindrome. The goal is to find all possible ways to partition the string. This problem is a classic example of exploring combinatorial possibilities and often involves recursive or dynamic programming approaches.

Problem Description

You are tasked with writing a function that takes a string as input and returns a list of all possible palindrome partitions. A palindrome is a word, phrase, number, or other sequence of characters that reads the same backward as forward (e.g., "madam", "racecar").

Requirements:

The function should accept a single string s as input.
The function should return a list of lists, where each inner list represents a valid palindrome partition of the input string.
Each element within an inner list must be a substring of s.
Every substring in a partition must be a palindrome.
The concatenation of the substrings in any given partition must reconstruct the original string s.

Edge Cases to Consider:

An empty input string.
A string consisting of a single character.
A string that is itself a palindrome.
A string where no palindromic partitions are possible (except for individual characters).

Examples

Example 1:

Input: "aab"
Output: [["a","a","b"],["aa","b"]]
Explanation:
- ["a","a","b"]: "a", "a", and "b" are all palindromes. Concatenating them gives "aab".
- ["aa","b"]: "aa" and "b" are palindromes. Concatenating them gives "aab".

Example 2:

Input: "a"
Output: [["a"]]
Explanation: A single character string is always a palindrome.

Example 3:

Input: ""
Output: [[]]
Explanation: An empty string has one partition, which is an empty list of substrings.

Example 4:

Input: "aba"
Output: [["a","b","a"],["aba"]]
Explanation:
- ["a","b","a"]: "a", "b", and "a" are palindromes. Concatenating them gives "aba".
- ["aba"]: "aba" is a palindrome. Concatenating it gives "aba".

Constraints

1 <= s.length <= 16 (The length of the input string will be between 1 and 16, inclusive.)
s consists only of lowercase English letters.
The algorithm should be reasonably efficient for the given constraints.

Notes

You will likely need a helper function to efficiently check if a given substring is a palindrome.
Consider how to systematically explore all possible partitions. Backtracking or a similar recursive approach is often well-suited for this type of problem.
The order of partitions in the output list does not matter. The order of substrings within each partition does matter, as it must reconstruct the original string.

Palindrome Partitioning

Problem Description

Requirements:

The function should accept a single string s as input.

The function should return a list of lists, where each inner list represents a valid palindrome partition of the input string.

Each element within an inner list must be a substring of s.

Every substring in a partition must be a palindrome.

The concatenation of the substrings in any given partition must reconstruct the original string s.

Edge Cases to Consider:

An empty input string.

A string consisting of a single character.

A string that is itself a palindrome.

A string where no palindromic partitions are possible (except for individual characters).

Examples

Example 1:

Input: "aab" Output: [["a","a","b"],["aa","b"]] Explanation: - ["a","a","b"]: "a", "a", and "b" are all palindromes. Concatenating them gives "aab". - ["aa","b"]: "aa" and "b" are palindromes. Concatenating them gives "aab".

Example 2:

Input: "a" Output: [["a"]] Explanation: A single character string is always a palindrome.

Example 3:

Input: "" Output: [[]] Explanation: An empty string has one partition, which is an empty list of substrings.

Example 4:

Input: "aba" Output: [["a","b","a"],["aba"]] Explanation: - ["a","b","a"]: "a", "b", and "a" are palindromes. Concatenating them gives "aba". - ["aba"]: "aba" is a palindrome. Concatenating it gives "aba".

Notes

You will likely need a helper function to efficiently check if a given substring is a palindrome.

Consider how to systematically explore all possible partitions. Backtracking or a similar recursive approach is often well-suited for this type of problem.

The order of partitions in the output list does not matter. The order of substrings within each partition does matter, as it must reconstruct the original string.