Longest Palindromic Substring in DSA C# - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of expanding around center approach

What is the output of the following C# code that finds the longest palindromic substring by expanding around each center?

DSA C#

using System;

class Program {
    static string LongestPalindrome(string s) {
        if (string.IsNullOrEmpty(s)) return "";
        int start = 0, maxLen = 1;
        for (int i = 0; i < s.Length; i++) {
            int len1 = ExpandFromCenter(s, i, i);
            int len2 = ExpandFromCenter(s, i, i + 1);
            int len = Math.Max(len1, len2);
            if (len > maxLen) {
                maxLen = len;
                start = i - (len - 1) / 2;
            }
        }
        return s.Substring(start, maxLen);
    }

    static int ExpandFromCenter(string s, int left, int right) {
        while (left >= 0 && right < s.Length && s[left] == s[right]) {
            left--;
            right++;
        }
        return right - left - 1;
    }

    static void Main() {
        Console.WriteLine(LongestPalindrome("babad"));
    }
}

A "aba"

B "bab"

C "bad"

D "ba"

💡 Hint

Check how the center expansion chooses the palindrome when multiple have the same length.

The code expands around each character and between characters to find palindromes. For input "babad", both "bab" and "aba" are palindromes of length 3. The code returns the first longest palindrome found, which is "bab" starting at index 0.

🧠 Conceptual

intermediate

Understanding palindrome expansion indices

In the expand around center method for longest palindromic substring, what does the returned value represent?

A The length of the palindrome found by expanding from the given left and right indices

B The starting index of the palindrome in the string

C The ending index of the palindrome in the string

D The number of expansions performed before mismatch

💡 Hint

Look at how the while loop expands and what is returned after it stops.

The method expands while characters at left and right are equal, then returns the length of the palindrome found, calculated as right - left - 1.

🔧 Debug

advanced

Identify the error in this palindrome substring code

What error will occur when running this code snippet to find the longest palindromic substring?

DSA C#

string s = "cbbd";
int start = 0, maxLen = 1;
for (int i = 0; i < s.Length; i++) {
    int len1 = Expand(s, i, i);
    int len2 = Expand(s, i, i + 1);
    int len = Math.Max(len1, len2);
    if (len > maxLen) {
        maxLen = len;
        start = i - (len / 2);
    }
}
string result = s.Substring(start, maxLen);

int Expand(string str, int left, int right) {
    while (left >= 0 && right < str.Length && str[left] == str[right]) {
        left--;
        right++;
    }
    return right - left - 1;
}

A No error, code runs correctly and returns "bb"

B Compile-time error due to missing method declaration

C ArgumentOutOfRangeException due to incorrect start index calculation

D NullReferenceException because Expand method is called incorrectly

💡 Hint

Check how start index is calculated when length is even.

The start index calculation uses integer division len / 2 which causes incorrect start index for even length palindromes, possibly negative or out of range, causing ArgumentOutOfRangeException in Substring.

🚀 Application

advanced

Longest palindromic substring length for a given input

What is the length of the longest palindromic substring in the string "forgeeksskeegfor"?

A 10

B 8

C 12

D 14

💡 Hint

Look for the longest palindrome inside the string, it is "geeksskeeg".

The longest palindromic substring is "geeksskeeg" which has length 10.

🧠 Conceptual

expert

Time complexity of longest palindromic substring algorithms

Which of the following statements about the time complexity of longest palindromic substring algorithms is correct?

A Dynamic programming approach runs in O(n) time and O(n^2) space

B Manacher's algorithm runs in O(n^3) time but uses O(n) space

C Brute force checking all substrings runs in O(n) time

D The expand around center approach runs in O(n^2) time and uses O(1) extra space

💡 Hint

Consider how many centers are expanded and how much space is used.

Expand around center checks 2n-1 centers, each expansion takes O(n), total O(n^2) time with constant extra space. Manacher's algorithm runs in O(n) time. DP approach is O(n^2) time and space. Brute force is O(n^3).

Practice

1. What is the main goal of the Longest Palindromic Substring problem?

easy

A. Find the longest substring that reads the same forwards and backwards

B. Count all palindromic substrings in the string

C. Reverse the entire string

D. Find the longest substring without repeating characters

Solution

1. Step 1: Understand the problem definition

   The problem asks to find the longest substring within a given string that is a palindrome, meaning it reads the same forwards and backwards.

2. Step 2: Differentiate from similar problems

   Counting all palindromic substrings or reversing the string are different tasks. The focus here is on the longest palindromic substring only.

3. Final Answer:

   Find the longest substring that reads the same forwards and backwards -> Option A

4. Quick Check:

   Longest palindromic substring = Find the longest substring that reads the same forwards and backwards [OK]

Hint: Look for substring that mirrors itself exactly [OK]

Common Mistakes:

• Confusing substring with subsequence
• Counting all palindromes instead of longest
• Trying to reverse entire string

2. Which of the following C# code snippets correctly initializes a 2D boolean array dp for dynamic programming in the Longest Palindromic Substring problem?

easy

A. bool dp = new bool[s.Length, s.Length];

B. bool[][] dp = new bool[s.Length][];

C. bool[,] dp = new bool[s.Length, s.Length];

D. bool dp[][] = new bool[s.Length][s.Length];

Solution

1. Step 1: Understand C# array syntax

   In C#, a 2D array is declared as type[,] name = new type[size1, size2];. bool[,] dp = new bool[s.Length, s.Length]; uses this correct syntax.

2. Step 2: Identify incorrect syntax

   bool[][] dp = new bool[s.Length][]; declares jagged arrays but misses initializing inner arrays. bool dp[][] = new bool[s.Length][s.Length]; uses invalid syntax for C#. bool dp = new bool[s.Length, s.Length]; tries to declare a single boolean variable with array sizes, which is invalid.

3. Final Answer:

   bool[,] dp = new bool[s.Length, s.Length]; -> Option C

4. Quick Check:

   2D array in C# = bool[,] dp = new bool[s.Length, s.Length]; [OK]

Hint: Use comma inside brackets for 2D arrays in C# [OK]

Common Mistakes:

• Using jagged array syntax without initializing inner arrays
• Confusing C# array syntax with other languages
• Declaring arrays without proper dimensions

3. What will be the output of the following C# code snippet that finds the longest palindromic substring?

string s = "babad";
string result = LongestPalindrome(s);
Console.WriteLine(result);

string LongestPalindrome(string str) {
    int start = 0, maxLength = 1;
    int len = str.Length;
    bool[,] dp = new bool[len, len];
    for (int i = 0; i < len; i++) dp[i, i] = true;
    for (int length = 2; length <= len; length++) {
        for (int i = 0; i <= len - length; i++) {
            int j = i + length - 1;
            if (str[i] == str[j]) {
                if (length == 2 || dp[i + 1, j - 1]) {
                    dp[i, j] = true;
                    if (length > maxLength) {
                        start = i;
                        maxLength = length;
                    }
                }
            }
        }
    }
    return str.Substring(start, maxLength);
}

medium

A. "aba"

B. "bab"

C. "bad"

D. "babad"

Solution

1. Step 1: Understand the input and algorithm

   The input string is "babad". The code uses dynamic programming to find the longest palindromic substring by checking substrings of increasing length.

2. Step 2: Trace the longest palindrome found

   Both "bab" and "aba" are palindromes of length 3. The code updates start and maxLength when it finds a longer palindrome. It finds "bab" first and returns it.

3. Final Answer:

   "bab" -> Option B

4. Quick Check:

   Longest palindrome in "babad" = "bab" [OK]

Hint: DP finds first longest palindrome substring [OK]

Common Mistakes:

• Assuming "aba" is returned instead of "bab"
• Returning entire string instead of substring
• Ignoring substring length updates

4. Identify the bug in the following C# code snippet for finding the longest palindromic substring:

string LongestPalindrome(string s) {
    int n = s.Length;
    bool[,] dp = new bool[n, n];
    int maxLen = 1, start = 0;
    for (int i = 0; i < n; i++) dp[i, i] = true;
    for (int length = 2; length <= n; length++) {
        for (int i = 0; i < n - length; i++) {
            int j = i + length - 1;
            if (s[i] == s[j]) {
                if (length == 2 || dp[i + 1, j - 1]) {
                    dp[i, j] = true;
                    if (length > maxLen) {
                        start = i;
                        maxLen = length;
                    }
                }
            }
        }
    }
    return s.Substring(start, maxLen);
}

medium

A. The inner loop condition should be < i < n - length + 1

B. The substring method parameters are incorrect

C. The dp array is not initialized for single characters

D. The code does not check for palindrome substrings of length 1

Solution

1. Step 1: Analyze the inner loop boundary

   The inner loop runs with condition i < n - length. For substring length 'length', the last valid start index is n - length, but the loop only goes up to n - length - 1, missing it. The loop condition should be i <= n - length or equivalently i < n - length + 1 to include the last substring.

2. Step 2: Identify off-by-one error

   This is an off-by-one error in the inner loop condition. Other options are incorrect because the dp array is initialized for single characters, the substring parameters are correct, and length 1 substrings are handled.

3. Final Answer:

   The inner loop condition should be < i < n - length + 1 -> Option A

4. Quick Check:

   Loop boundary off-by-one = The inner loop condition should be < i < n - length + 1 [OK]

Hint: Check loop boundaries carefully for substring indices [OK]

Common Mistakes:

• Ignoring off-by-one errors in loops
• Misunderstanding substring parameters
• Assuming dp initialization is missing

5. Given the string "forgeeksskeegfor", which approach will correctly find the longest palindromic substring and what is the substring?

hard

A. Expand Around Center approach; substring is "forgeeksskeegfor"

B. Dynamic Programming approach; substring is "forgeeksskeegfor"

C. Brute Force approach; substring is "forgeeksskeegfor"

D. Expand Around Center approach; substring is "geeksskeeg"

Solution

1. Step 1: Understand the input string and palindrome

   The string "forgeeksskeegfor" contains the palindrome "geeksskeeg" in the middle, which is the longest palindromic substring.

2. Step 2: Identify correct approach and substring

   The Expand Around Center approach efficiently finds palindromes by expanding from each center. It will find "geeksskeeg" correctly. The entire string is not a palindrome, so options B, C, and D are incorrect.

3. Final Answer:

   Expand Around Center approach; substring is "geeksskeeg" -> Option D

4. Quick Check:

   Longest palindrome = "geeksskeeg" via center expansion [OK]

Hint: Expand from centers to find longest palindrome fast [OK]

Common Mistakes:

• Assuming entire string is palindrome
• Confusing brute force with efficient methods
• Missing the correct longest substring