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

Recall & Review

beginner

What is the main goal of palindrome partitioning?

To split a string into parts where each part is a palindrome.

beginner

What does backtracking help with in palindrome partitioning?

It helps explore all possible ways to split the string and find all palindrome partitions.

beginner

How do you check if a substring is a palindrome?

Compare characters from start and end moving towards the center; if all match, it's a palindrome.

intermediate

Why do we remove the last added substring during backtracking?

To undo the last choice and try other possible partitions.

advanced

What is the time complexity of palindrome partitioning using backtracking?

It can be exponential in the worst case because it explores all partitions.

What is a palindrome?

A A string with only vowels

B A string with all unique characters

C A string that reads the same forwards and backwards

D A string with no repeating characters

A palindrome reads the same forwards and backwards.

In palindrome partitioning, what does backtracking do?

A Tries all possible partitions and removes invalid ones

B Sorts the string

C Counts the number of palindromes

D Reverses the string

Backtracking tries all partitions and removes those that don't form palindromes.

Which of these substrings is a palindrome?

A "aba"

B "ab"

C "abc"

D "ac"

"aba" reads the same forwards and backwards.

What is the first step in backtracking for palindrome partitioning?

A Check if the whole string is a palindrome

B Start from the first character and try all substrings

C Reverse the string

D Split the string into single characters

Backtracking starts from the first character and tries all possible substrings.

Why do we backtrack after adding a palindrome substring?

A To stop the process

B To count the palindromes

C To sort the substrings

D To explore other partitions by removing the last substring

Backtracking removes the last substring to try other possible partitions.

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

Think about choosing substrings and undoing choices to explore all options.

Describe how to check if a substring is a palindrome in the context of partitioning.

Imagine reading the substring from both ends at the same time.

Practice

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

easy

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

B. To find the longest palindrome substring in a string

C. To count the number of palindromes in a string

D. To split a string into all possible palindrome substrings

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 D

4. Quick Check:

   Palindrome partitioning = all palindrome splits [OK]

Hint: Backtracking explores all palindrome splits step-by-step [OK]

Common Mistakes:

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

2. Which of the following TypeScript function signatures correctly represents a backtracking function for palindrome partitioning?

easy

A. function backtrack(s: number[], start: string, path: string[], result: string[][]): string

B. function backtrack(s: string, start: number, path: string, result: string[]): boolean

C. function backtrack(s: string, start: number, path: string[], result: string[][]): void

D. function backtrack(s: string[], start: number, path: string[], result: string[][]): number

Solution

1. Step 1: Analyze parameter types

   The string to partition is 's: string', start index is 'number', path is an array of strings, and result is an array of string arrays.

2. Step 2: Check return type

   Backtracking functions usually return void because they build results by modifying the result array.

3. Final Answer:

   function backtrack(s: string, start: number, path: string[], result: string[][]): void -> Option C

4. Quick Check:

   Correct signature = function backtrack(s: string, start: number, path: string[], result: string[][]): void [OK]

Hint: Backtracking returns void and uses arrays for path and result [OK]

Common Mistakes:

• Using wrong parameter types like number[] instead of string
• Returning boolean or number instead of void
• Passing path as string instead of string[]

3. What will be the output of the following TypeScript code snippet for palindrome partitioning of string "aab"?

function isPalindrome(s: string): boolean {
  return s === s.split('').reverse().join('');
}

function backtrack(s: string, start: number, path: string[], result: string[][]): void {
  if (start === s.length) {
    result.push([...path]);
    return;
  }
  for (let end = start + 1; end <= s.length; end++) {
    const substr = s.substring(start, end);
    if (isPalindrome(substr)) {
      path.push(substr);
      backtrack(s, end, path, result);
      path.pop();
    }
  }
}

const result: string[][] = [];
backtrack("aab", 0, [], result);
console.log(result);

medium

A. [["aa", "ab"]]

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

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

D. [["aab"]]

Solution

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

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

2. Step 2: Trace backtracking calls

   Partitions found are ["a", "a", "b"] and ["aa", "b"] added to result.

3. Final Answer:

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

4. Quick Check:

   All palindrome splits of "aab" = [["a", "a", "b"], ["aa", "b"]] [OK]

Hint: Check all palindrome substrings and backtrack all splits [OK]

Common Mistakes:

• Including non-palindrome substrings like "ab"
• Missing the "aa" substring partition
• Returning only one partition instead of all

4. Identify the bug in the following backtracking code for palindrome partitioning and select the fix:

function isPalindrome(s: string): boolean {
  return s === s.split('').reverse().join('');
}

function backtrack(s: string, start: number, path: string[], result: string[][]): void {
  if (start > s.length) {
    result.push([...path]);
    return;
  }
  for (let end = start + 1; end <= s.length; end++) {
    const substr = s.substring(start, end);
    if (isPalindrome(substr)) {
      path.push(substr);
      backtrack(s, end, path, result);
      path.pop();
    }
  }
}

medium

A. Change condition to if (start === s.length) to stop recursion correctly

B. Change substring to slice for correct substring extraction

C. Remove path.pop() to keep all partitions

D. Change for loop to end < s.length to avoid out of bounds

Solution

1. Step 1: Analyze base case condition

   Condition 'start > s.length' allows start to be s.length + 1, which is invalid index.

2. Step 2: Correct base case for recursion end

   It should be 'start === s.length' to indicate full string processed and add path to result.

3. Final Answer:

   Change condition to if (start === s.length) to stop recursion correctly -> Option A

4. Quick Check:

   Base case must be start === s.length [OK]

Hint: Base case triggers when start equals string length [OK]

Common Mistakes:

• Using > instead of === in base case
• Removing path.pop() causing wrong partitions
• Changing substring method unnecessarily

5. Given the string "racecar", which of the following is NOT a valid palindrome partitioning produced by a backtracking algorithm?

hard

A. ["rac", "ecar"]

B. ["racecar"]

C. ["r", "a", "c", "e", "c", "a", "r"]

D. ["r", "aceca", "r"]

Solution

1. Step 1: Check palindrome validity of each substring

   "rac" and "ecar" are not palindromes; others are single letters or full palindrome.

2. Step 2: Confirm valid partitions

   Partitions with only palindrome substrings are valid; those with non-palindromes are invalid.

3. Final Answer:

   ["rac", "ecar"] -> Option A

4. Quick Check:

   Non-palindrome substrings invalidate partition [OK]

Hint: Check each substring is palindrome to validate partition [OK]

Common Mistakes:

• Assuming any split is valid without palindrome check
• Confusing full string palindrome with partial substrings
• Ignoring single character substrings as palindromes