Palindrome Partitioning Using Backtracking in DSA Java - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main goal of palindrome partitioning using backtracking?

To split a given string into all possible lists of substrings where each substring is a palindrome.

intermediate

How does backtracking help in palindrome partitioning?

Backtracking tries all possible partitions and abandons those that do not lead to a valid palindrome partition, exploring only valid paths.

beginner

What is a palindrome?

A string that reads the same forwards and backwards, like 'madam' or 'racecar'.

intermediate

In palindrome partitioning, why do we check substrings before recursing?

To ensure only palindrome substrings are included in the current partition path, avoiding invalid partitions early.

advanced

What is the time complexity characteristic of palindrome partitioning using backtracking?

It can be exponential in the worst case because it explores all possible partitions, but pruning reduces unnecessary checks.

What does a palindrome partitioning algorithm return for the string 'aab'?

A [["a", "ab"]]

B [["aab"]]

C [["a", "a", "b"], ["aa", "b"]]

D [["aa", "ab"]]

The string 'aab' can be partitioned into palindromes as ['a','a','b'] and ['aa','b'].

Which technique is primarily used in palindrome partitioning to explore all partitions?

A Divide and Conquer

B Dynamic Programming

C Greedy

D Backtracking

Backtracking is used to explore all possible partitions and backtrack when a partition is invalid.

What is the first step before recursing in palindrome partitioning?

A Sort the string

B Check if the substring is a palindrome

C Reverse the string

D Count characters

We check if the current substring is a palindrome before including it in the partition.

If the input string is empty, what should the palindrome partitioning algorithm return?

A [[]]

B []

C [[""]]

D null

An empty string has one partition: an empty list of substrings.

Why is palindrome partitioning considered an exponential time problem?

A Because it explores all possible substring partitions

B Because it sorts the string multiple times

C Because it uses dynamic programming

D Because it only checks one partition

The number of possible partitions grows exponentially with string length.

Explain how backtracking is used to find all palindrome partitions of a string.

Think about exploring all options and undoing choices.

Describe the role of palindrome checking in the partitioning process.

Why do we check substrings before going deeper?

Practice

1. What is the main goal of palindrome partitioning using backtracking?

easy

A. To count the number of palindromes in a string

B. To find the longest palindrome substring in a string

C. To split a string into all possible palindrome substrings

D. To reverse the string and check if it is a palindrome

Solution

1. Step 1: Understand palindrome partitioning

   Palindrome partitioning means dividing a string into parts where each part is a palindrome.

2. Step 2: Role of backtracking

   Backtracking helps explore all possible ways to split the string into palindrome parts.

3. Final Answer:

   To split a string into all possible palindrome substrings -> Option C

4. Quick Check:

   Palindrome partitioning = splitting into palindrome substrings [OK]

Hint: Backtracking explores all palindrome splits [OK]

Common Mistakes:

• Confusing palindrome partitioning with longest palindrome substring
• Thinking it only counts palindromes instead of listing partitions
• Assuming it reverses the whole string

2. Which of the following is the correct Java method signature for a backtracking function that partitions a string into palindromes?

easy

A. boolean backtrack(String s, int start, List<String> current)

B. void backtrack(String s, int start, List result, List<String> current)

C. int backtrack(String s, int start, List<String> result)

D. String backtrack(String s, int start, List result)

Solution

1. Step 1: Analyze method parameters

   The method needs the string, current start index, a list to store all partitions, and the current partition path.

2. Step 2: Check return type

   Backtracking methods usually return void because they build results via parameters.

3. Final Answer:

   void backtrack(String s, int start, List result, List<String> current) -> Option B

4. Quick Check:

   Backtracking method returns void and uses lists [OK]

Hint: Backtracking returns void and uses lists for results [OK]

Common Mistakes:

• Using wrong return type like int or boolean
• Missing current partition list parameter
• Returning String instead of void

3. What will be the output partitions for the input string "aab" using palindrome partitioning?

medium

A. [["aab"]]

B. [["aa", "ab"]]

C. [["a", "ab"]]

D. [["a", "a", "b"], ["aa", "b"]]

Solution

1. Step 1: Identify palindrome substrings

   "a" and "aa" are palindromes; "b" is a palindrome; "ab" is not.

2. Step 2: List all palindrome partitions

   Partitions are ["a", "a", "b"] and ["aa", "b"].

3. Final Answer:

   [["a", "a", "b"], ["aa", "b"]] -> Option D

4. Quick Check:

   Only palindrome splits included [OK]

Hint: Check each substring palindrome before partitioning [OK]

Common Mistakes:

• Including non-palindrome substrings like "ab"
• Missing the partition with "aa"
• Returning only one partition

4. Identify the error in this Java backtracking snippet for palindrome partitioning:

void backtrack(String s, int start, List result, List<String> current) {
  if (start == s.length()) {
    result.add(current);
    return;
  }
  for (int end = start; end < s.length(); end++) {
    if (isPalindrome(s, start, end)) {
      current.add(s.substring(start, end + 1));
      backtrack(s, end + 1, result, current);
      current.remove(current.size());
    }
  }
}

medium

A. Incorrect removal index in current.remove()

B. Missing base case for empty string

C. Wrong substring indices in s.substring()

D. Backtracking call uses wrong start index

Solution

1. Step 1: Check removal from current list

   List indices start at 0, so removing at current.size() causes IndexOutOfBoundsException.

2. Step 2: Correct removal index

   Should remove last element with current.remove(current.size() - 1).

3. Final Answer:

   Incorrect removal index in current.remove() -> Option A

4. Quick Check:

   Remove last element with size()-1 [OK]

Hint: Remove last added element with size()-1 index [OK]

Common Mistakes:

• Removing element at size() instead of size()-1
• Confusing substring indices
• Incorrect recursive call start index

5. Given the string "racecar", how many palindrome partitions will the backtracking algorithm generate?

hard

A. 6

B. 8

C. 4

D. 10

Solution

1. Step 1: Identify palindrome substrings in "racecar"

   Palindromes include "r", "a", "c", "e", "cec", "aceca", "racecar" and their combinations.

2. Step 2: Count all palindrome partitions

   Partitions are:
   ["racecar"],
   ["r", "aceca", "r"],
   ["r", "a", "cec", "a", "r"],
   ["r", "a", "c", "e", "c", "a", "r"],
   and others including splits like ["r", "a", "c", "ec", "a", "r"] are invalid because "ec" is not palindrome.
   Counting all valid partitions, the total is 6.

3. Final Answer:

   6 -> Option A

4. Quick Check:

   Count all palindrome partitions = 6 [OK]

Hint: Count all palindrome splits including nested palindromes [OK]

Common Mistakes:

• Counting only single-character partitions
• Missing longer palindrome substrings
• Double counting partitions