Longest Palindromic Substring in DSA C# - Execution Trace

Concept Flow - Longest Palindromic Substring

Start at each index i in string

↓

Expand around center i (odd length)

↓

Expand around center i and i+1 (even length)

↓

Check palindrome length

↓

Update longest palindrome if longer

↓

Move to next index i+1

↓

Repeat until end of string

↓

Return longest palindrome substring

We check each character as a center and expand outwards to find palindromes, updating the longest found.

Execution Sample

DSA C#

string s = "babad";
string longest = "";
for (int i = 0; i < s.Length; i++) {
  string odd = Expand(s, i, i);
  string even = Expand(s, i, i + 1);
  longest = odd.Length > longest.Length ? odd : longest;
  longest = even.Length > longest.Length ? even : longest;
}
return longest;

This code finds the longest palindromic substring by expanding around each character and its neighbor.

Execution Table

Step	Operation	Center Indices	Palindrome Found	Longest Palindrome	Visual State
1	Expand odd around center 0	(0,0)	"b"	"b"	"b"
2	Expand even around center 0 and 1	(0,1)	""	"b"	"b"
3	Expand odd around center 1	(1,1)	"bab"	"bab"	"b" -> "a" -> "b"
4	Expand even around center 1 and 2	(1,2)	""	"bab"	"b" -> "a" -> "b"
5	Expand odd around center 2	(2,2)	"aba"	"bab"	"b" -> "a" -> "b"
6	Expand even around center 2 and 3	(2,3)	""	"bab"	"b" -> "a" -> "b"
7	Expand odd around center 3	(3,3)	"a"	"bab"	"b" -> "a" -> "b"
8	Expand even around center 3 and 4	(3,4)	""	"bab"	"b" -> "a" -> "b"
9	Expand odd around center 4	(4,4)	"d"	"bab"	"b" -> "a" -> "b"
10	Expand even around center 4 and 5	(4,5)	""	"bab"	"b" -> "a" -> "b"
11	End of string reached	-	-	"bab"	"b" -> "a" -> "b"

💡 All centers expanded; longest palindrome "bab" found.

Variable Tracker

Variable	Start	After Step 1	After Step 3	After Step 11
i	0	0	1	4
longest	""	"b"	"bab"	"bab"
odd palindrome	""	"b"	"bab"	"d"
even palindrome	""	""	""	""

Key Moments - 3 Insights

Why do we expand around two centers (i, i) and (i, i+1)?

Because palindromes can be odd length (centered at one character) or even length (centered between two characters). See execution_table rows 1 and 2.

Why does the longest palindrome update only when a longer palindrome is found?

To keep track of the maximum length palindrome found so far. This is shown in execution_table rows 3 and 5 where "bab" replaces "b".

What happens when expanding around a center finds no palindrome?

The expansion returns an empty string, so the longest palindrome remains unchanged. See execution_table rows 2 and 4.

Visual Quiz - 3 Questions

Look at the execution_table at step 3, what palindrome is found expanding around center (1,1)?

A "bab"

B "a"

C "b"

D ""

💡 Hint

Check the 'Palindrome Found' column at step 3 in execution_table.

At which step does the longest palindrome first update to "bab"?

A Step 1

B Step 3

C Step 5

D Step 9

💡 Hint

Look at the 'Longest Palindrome' column in execution_table to see when it changes to "bab".

If the input string was "aaaa", how would the longest palindrome change compared to the current execution?

A It would be "aa"

B It would remain "bab"

C It would be "aaaa" instead of "bab"

D It would be empty

💡 Hint

Consider how expanding around centers in a string of repeated characters finds longer palindromes.

Concept Snapshot

Longest Palindromic Substring:
- Check each index as palindrome center
- Expand around center for odd and even length
- Update longest palindrome if found longer
- Return longest substring found
- Time complexity O(n^2), space O(1)

Full Transcript

The Longest Palindromic Substring algorithm checks each character in the string as a center and expands outwards to find palindromes. It considers both odd length palindromes (centered at one character) and even length palindromes (centered between two characters). At each expansion, it compares the palindrome found with the longest palindrome so far and updates if longer. This process repeats for all indices until the entire string is checked. The final longest palindrome substring is returned. This approach runs in quadratic time and uses constant extra space.

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