Palindrome Partitioning Using Backtracking in DSA C# - Build from Scratch

Palindrome Partitioning Using Backtracking

📖 Scenario: Imagine you have a word and want to split it into parts where each part reads the same forwards and backwards. This is called palindrome partitioning. For example, the word "aab" can be split as ["a", "a", "b"] or ["aa", "b"]. We will write a program to find all such splits using a method called backtracking.

🎯 Goal: Build a C# program that takes a string and finds all possible palindrome partitions using backtracking. You will create the data, set up helper variables, write the backtracking logic, and finally print all palindrome partitions.

📋 What You'll Learn

Create a string variable with the exact value "aab"

Create a list of lists of strings called result to store all palindrome partitions

Write a helper function IsPalindrome that checks if a substring is a palindrome

Write a backtracking function Backtrack that finds all palindrome partitions

Print all palindrome partitions in the format: [["a", "a", "b"], ["aa", "b"]]

💡 Why This Matters

🌍 Real World

Palindrome partitioning helps in text processing, DNA sequence analysis, and finding symmetrical patterns in data.

💼 Career

Understanding backtracking and palindrome checks is useful for coding interviews and solving complex string problems in software development.

1

Create the input string

Create a string variable called s and set it to the exact value "aab".

DSA C#

# Create a string variable called s and set it to "aab"
# Your code here

Hint

Use string s = "aab"; to create the string.

2

Create the result list to store partitions

Create a variable called result of type List> and initialize it as an empty list to store all palindrome partitions.

DSA C#

string s = "aab";
// Create a List> called result to store partitions
# Your code here

Hint

Use new List>() to create an empty list of lists.

3

Write the palindrome check and backtracking functions

Write a method IsPalindrome that takes a string str, a start index start, and an end index end, and returns true if the substring is a palindrome. Then write a method Backtrack that takes an integer start and a list of strings currentList. It should find all palindrome partitions starting from start and add them to result. Use backtracking to explore all partitions.

DSA C#

string s = "aab";
List> result = new List>();

// Write IsPalindrome method
// Write Backtrack method
# Your code here

Hint

Use a while loop in IsPalindrome to compare characters. In Backtrack, use a for loop from start to s.Length - 1 and recurse when a palindrome is found.

4

Run backtracking and print all palindrome partitions

Call the Backtrack method starting from index 0 with an empty list. Then print the result list showing all palindrome partitions in the format: [["a", "a", "b"], ["aa", "b"]].

DSA C#

Hint

Call Backtrack(0, new List()) and then print result with nested loops to format output as shown.

Practice

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

easy

A. To find the longest palindrome substring in a string

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

C. To split a string into all possible palindrome substrings

D. To count the number of palindromes in a string

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 = all palindrome splits [OK]

Hint: Backtracking explores all palindrome splits of the string [OK]

Common Mistakes:

• Confusing palindrome partitioning with finding longest palindrome
• Thinking palindrome partitioning only counts palindromes
• Assuming palindrome partitioning reverses the string

2. Which of the following C# method signatures is correct for a backtracking function that partitions a string into palindromes?

easy

A. string Backtrack(string s, int start, List<string> currentPartition, List result)

B. int Backtrack(string s, int start, List<string> currentPartition)

C. bool Backtrack(string s, int start, List<string> currentPartition, List result)

D. void Backtrack(string s, int start, List<string> currentPartition, List result)

Solution

1. Step 1: Understand backtracking method requirements

   The method should explore partitions and store results, so it returns void and uses parameters to track state.

2. Step 2: Check method signatures

   void Backtrack(string s, int start, List<string> currentPartition, List result) returns void and takes parameters for string, start index, current partition, and result list, matching backtracking needs.

3. Final Answer:

   void Backtrack(string s, int start, List<string> currentPartition, List result) -> Option D

4. Quick Check:

   Backtracking method returns void with state parameters [OK]

Hint: Backtracking methods usually return void and use parameters to track state [OK]

Common Mistakes:

• Using return types other than void for backtracking
• Missing the result list parameter to store partitions
• Confusing return type with boolean or string

3. What will be the output of the following C# code snippet?

var result = new List();
Backtrack("aab", 0, new List<string>(), result);
Console.WriteLine(result.Count);

Assuming Backtrack partitions the string into all palindrome substrings correctly.

medium

A. 2

B. 3

C. 1

D. 4

Solution

1. Step 1: Identify palindrome partitions of "aab"

   Possible palindrome partitions are ["a", "a", "b"] and ["aa", "b"].

2. Step 2: Count all palindrome partitions

   There are 2 partitions, so result.Count will be 2 after backtracking.

3. Final Answer:

   2 -> Option A

4. Quick Check:

   Palindrome partitions of "aab" = 2 [OK]

Hint: Count all palindrome partitions generated by backtracking [OK]

Common Mistakes:

• Counting substrings instead of partitions
• Forgetting "aa" is a palindrome
• Assuming single partition only

4. Identify the bug in this backtracking code snippet for palindrome partitioning:

void Backtrack(string s, int start, List<string> current, List result) {
  if (start == s.Length) {
    result.Add(new List<string>(current));
    return;
  }
  for (int end = start; end < s.Length; end++) {
    if (IsPalindrome(s, start, end)) {
      current.Add(s.Substring(start, end - start));
      Backtrack(s, end + 1, current, result);
      current.RemoveAt(current.Count - 1);
    }
  }
}

medium

A. Base case condition should be start > s.Length

B. Substring length calculation is incorrect

C. RemoveAt should remove from index 0

D. IsPalindrome method parameters are wrong

Solution

1. Step 1: Check substring length calculation

   Substring(start, length) needs length = end - start + 1, but code uses end - start, missing last character.

2. Step 2: Verify other parts

   IsPalindrome parameters and RemoveAt usage are correct; base case is correct as start == s.Length.

3. Final Answer:

   Substring length calculation is incorrect -> Option B

4. Quick Check:

   Substring length = end - start + 1 [OK]

Hint: Substring length must include end index +1 [OK]

Common Mistakes:

• Using substring length as end - start instead of end - start + 1
• Removing wrong index from current list
• Incorrect base case condition

5. Given the string "racecar", how many palindrome partitions will the backtracking algorithm find? Consider all possible partitions where each substring is a palindrome.

hard

A. 10

B. 6

C. 8

D. 4

Solution

1. Step 1: List all palindrome partitions of "racecar"

   Partitions include ["r", "a", "c", "e", "c", "a", "r"], ["r", "a", "cec", "a", "r"], ["r", "aceca", "r"], ["racecar"], and others.

2. Step 2: Count all valid palindrome partitions

   Counting carefully, there are 10 valid palindrome partitions in total.

3. Final Answer:

   10 -> Option A

4. Quick Check:

   Palindrome partitions of "racecar" = 10 [OK]

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

Common Mistakes:

• Counting only single character partitions
• Missing longer palindrome substrings like "cec" or "aceca"
• Assuming only 1 or 2 partitions