Longest Common Substring in DSA C++ - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Longest Common Substring Length Calculation

What is the output of the following C++ code that calculates the length of the longest common substring between two strings?

DSA C++

int longestCommonSubstring(std::string s1, std::string s2) {
    int m = s1.size();
    int n = s2.size();
    int maxLen = 0;
    std::vector<std::vector<int>> dp(m + 1, std::vector<int>(n + 1, 0));
    for (int i = 1; i <= m; i++) {
        for (int j = 1; j <= n; j++) {
            if (s1[i - 1] == s2[j - 1]) {
                dp[i][j] = dp[i - 1][j - 1] + 1;
                maxLen = std::max(maxLen, dp[i][j]);
            }
        }
    }
    return maxLen;
}

int main() {
    std::string a = "abcde";
    std::string b = "abfce";
    std::cout << longestCommonSubstring(a, b);
    return 0;
}

A 2

B 3

C 4

D 1

💡 Hint

Check the longest sequence of matching characters in order between the two strings.

The longest common substring between "abcde" and "abfce" is "ab" which has length 2.

❓ Predict Output

intermediate

Longest Common Substring Length for Overlapping Strings

What will be the output of this C++ function call for longest common substring length?

DSA C++

std::cout << longestCommonSubstring("banana", "ananas");

A 4

B 5

C 2

D 3

💡 Hint

Look for the longest continuous matching substring.

The longest common substring is "anana" which has length 5.

🔧 Debug

advanced

Identify the Error in Longest Common Substring Implementation

What error will this code produce when trying to find the longest common substring length?

DSA C++

int longestCommonSubstring(std::string s1, std::string s2) {
    int m = s1.size();
    int n = s2.size();
    int maxLen = 0;
    std::vector<std::vector<int>> dp(m, std::vector<int>(n, 0));
    for (int i = 1; i <= m; i++) {
        for (int j = 1; j <= n; j++) {
            if (s1[i - 1] == s2[j - 1]) {
                dp[i][j] = dp[i - 1][j - 1] + 1;
                maxLen = std::max(maxLen, dp[i][j]);
            }
        }
    }
    return maxLen;
}

A Returns incorrect length 0

B Works correctly and returns the right length

C Compilation error due to missing header

D Runtime error: out_of_range exception

💡 Hint

Check the size of the dp vector and the indices used to access it.

The dp vector is sized m x n but the loops access dp[i][j] where i and j go up to m and n inclusive, causing out_of_range access.

🧠 Conceptual

advanced

Time Complexity of Longest Common Substring Algorithm

What is the time complexity of the dynamic programming approach to find the longest common substring of two strings of lengths m and n?

A O(m + n)

B O(m^2 * n^2)

C O(m * n)

D O(max(m, n))

💡 Hint

Consider the nested loops iterating over both strings.

The algorithm uses two nested loops each running up to m and n, resulting in O(m * n) time complexity.

🚀 Application

expert

Longest Common Substring Result After Multiple Updates

Given the following sequence of operations on two strings, what is the length of their longest common substring after all operations?

DSA C++

std::string s1 = "abcdefg";
std::string s2 = "xyzabcde";

// Operation 1: Remove last character from s1
s1.pop_back();
// Operation 2: Append 'f' to s2
s2.push_back('f');
// Operation 3: Replace first character of s1 with 'x'
s1[0] = 'x';

int result = longestCommonSubstring(s1, s2);
std::cout << result;

A 5

B 3

C 4

D 6

💡 Hint

Apply each operation step-by-step and then find the longest common substring.

After operations, s1 = "xbcdef" and s2 = "xyzabcdef". The longest common substring is "bcdef" with length 5.

Practice

1. What does the Longest Common Substring problem find between two strings s1 and s2?

easy

A. The longest sequence of characters that appear contiguously in both strings

B. The longest sequence of characters that appear in both strings but not necessarily contiguously

C. The total number of common characters between the two strings

D. The longest string formed by concatenating both strings

Solution

1. Step 1: Understand the problem definition

   The Longest Common Substring problem looks for the longest continuous sequence of characters that appears in both strings without any breaks.

2. Step 2: Differentiate from similar problems

   Unlike Longest Common Subsequence, which allows gaps, Longest Common Substring requires characters to be contiguous in both strings.

3. Final Answer:

   The longest sequence of characters that appear contiguously in both strings -> Option A

4. Quick Check:

   Longest Common Substring = contiguous matching characters [OK]

Hint: Look for continuous matching characters in both strings [OK]

Common Mistakes:

• Confusing substring with subsequence
• Thinking characters can be non-contiguous
• Counting total common characters instead of longest continuous

2. Which of the following C++ code snippets correctly initializes a 2D vector dp of size m+1 by n+1 with all zeros for Longest Common Substring?

easy

A. std::vector dp(m+1, std::vector<int>(n+1, 0));

B. std::vector<int> dp(m+1, std::vector<int>(n+1, 0));

C. std::vector dp(m, std::vector<int>(n));

D. std::vector dp(m+1, n+1, 0);

Solution

1. Step 1: Understand 2D vector initialization syntax

   To create a 2D vector with m+1 rows and n+1 columns filled with zeros, use nested vector initialization.

2. Step 2: Check each option

   std::vector dp(m+1, std::vector<int>(n+1, 0)); correctly creates a vector of vectors with m+1 rows, each row a vector of n+1 zeros. Others have syntax errors or wrong types.

3. Final Answer:

   std::vector dp(m+1, std::vector<int>(n+1, 0)); -> Option A

4. Quick Check:

   Correct 2D vector initialization = std::vector dp(m+1, std::vector<int>(n+1, 0)); [OK]

Hint: Use nested vector constructor for 2D zero initialization [OK]

Common Mistakes:

• Using wrong vector types in initialization
• Missing inner vector initialization
• Trying to pass three arguments to vector constructor

3. What is the output of the following C++ code snippet?

std::string s1 = "abcdxyz";
std::string s2 = "xyzabcd";
int m = s1.size(), n = s2.size();
std::vector dp(m+1, std::vector<int>(n+1, 0));
int maxLen = 0;
for (int i = 1; i <= m; i++) {
  for (int j = 1; j <= n; j++) {
    if (s1[i-1] == s2[j-1]) {
      dp[i][j] = dp[i-1][j-1] + 1;
      maxLen = std::max(maxLen, dp[i][j]);
    }
  }
}
std::cout << maxLen << std::endl;

medium

A. 3

B. 4

C. 1

D. 0

Solution

1. Step 1: Trace matching substrings

   The longest common substring is "abcd" (length 4), which appears contiguously at the start of s1 and end of s2. "xyz" is length 3.

2. Step 2: Check dp updates and maxLen

   dp updates length for matching characters. The longest continuous match found is length 4 for "abcd".

3. Final Answer:

   4 -> Option B

4. Quick Check:

   Longest common substring length = 4 [OK]

Hint: Check continuous matching segments, not total matches [OK]

Common Mistakes:

• Confusing substring with subsequence length
• Counting non-contiguous matches
• Off-by-one errors in indexing

4. Identify the bug in the following C++ code snippet for Longest Common Substring:

std::string s1 = "abcde";
std::string s2 = "abfde";
int m = s1.size(), n = s2.size();
std::vector dp(m+1, std::vector<int>(n+1, 0));
int maxLen = 0;
for (int i = 1; i <= m; i++) {
  for (int j = 1; j <= n; j++) {
    if (s1[i] == s2[j]) {
      dp[i][j] = dp[i-1][j-1] + 1;
      maxLen = std::max(maxLen, dp[i][j]);
    }
  }
}
std::cout << maxLen << std::endl;

medium

A. dp vector size should be (m+1) x (n+1) to avoid out-of-bound errors

B. maxLen should be initialized to -1 instead of 0

C. The loop indices should start from 0 instead of 1

D. The comparison should be s1[i-1] == s2[j-1] instead of s1[i] == s2[j]

Solution

1. Step 1: Check string indexing inside loops

   Loop variables i and j start from 1, so to access string characters correctly, indices should be i-1 and j-1.

2. Step 2: Identify the incorrect comparison

   The code compares s1[i] and s2[j], which causes out-of-bound access and wrong comparisons. It should be s1[i-1] == s2[j-1].

3. Final Answer:

   The comparison should be s1[i-1] == s2[j-1] instead of s1[i] == s2[j] -> Option D

4. Quick Check:

   Correct string indexing = i-1 and j-1 [OK]

Hint: Use i-1 and j-1 to index strings when loops start at 1 [OK]

Common Mistakes:

• Accessing string with i or j directly causing out-of-bounds
• Not initializing dp with correct size
• Starting loops at wrong indices

5. Given two strings s1 = "banana" and s2 = "ananas", write a C++ function to find the longest common substring and return it. What is the correct longest common substring?

hard

A. "anana"

B. "nana"

C. "ana"

D. "ban"

Solution

1. Step 1: Understand the longest common substring candidates

   Check substrings common to both strings. "ana" (length 3) appears multiple times in both strings. "anana" is not a substring of both strings contiguously.

2. Step 2: Verify other options

   "nana" length 4 is not a substring of s2; "ban" only in s1; "anana" is not a substring of s2.

3. Final Answer:

   "ana" -> Option C

4. Quick Check:

   Longest common substring between "banana" and "ananas" is "ana" [OK]

Hint: Check all continuous matches, pick longest common substring [OK]

Common Mistakes:

• Choosing longest common subsequence instead of substring
• Ignoring continuity requirement
• Assuming longer substrings without verifying presence