Longest Common Substring in DSA Typescript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the Longest Common Substring problem?

It is the problem of finding the longest sequence of characters that appears in the same order and contiguously in two given strings.

beginner

Which data structure is commonly used to solve the Longest Common Substring problem efficiently?

A 2D array (dynamic programming table) is used to store lengths of common suffixes of substrings ending at different positions.

intermediate

In the dynamic programming approach, what does dp[i][j] represent?

dp[i][j] represents the length of the longest common substring ending at position i-1 in the first string and j-1 in the second string.

intermediate

What is the time complexity of the dynamic programming solution for Longest Common Substring?

The time complexity is O(m * n), where m and n are the lengths of the two input strings.

beginner

How do you update the dp table when characters at positions i-1 and j-1 do not match?

Set dp[i][j] to 0 because the substring must be contiguous, so no common substring ends at these positions.

What does the Longest Common Substring problem find?

A The longest sequence of characters appearing anywhere in both strings

B The longest sequence of characters appearing contiguously in both strings

C The longest sequence of characters appearing in only one string

D The shortest sequence of characters appearing in both strings

The problem finds the longest contiguous sequence common to both strings.

In the DP table, what does a zero value at dp[i][j] mean?

A No common substring ends at i-1 and j-1

B Characters at i-1 and j-1 match

C Longest substring length is 1

D Strings are identical up to i and j

Zero means no common substring ends at those positions because characters differ.

What is the main difference between Longest Common Substring and Longest Common Subsequence?

A Substring must be contiguous; subsequence can skip characters

B Subsequence must be contiguous; substring can skip characters

C Both require contiguous characters

D Both allow skipping characters

Substring requires characters to be next to each other; subsequence allows gaps.

What is the space complexity of the standard DP solution for Longest Common Substring?

A O(m + n)

B O(1)

C O(m * n)

D O(max(m, n))

The DP table uses space proportional to the product of the string lengths.

If two strings are 'abcde' and 'abfde', what is their longest common substring?

A 'abc'

B 'de'

C 'fde'

D 'ab'

'ab' is the longest contiguous sequence common to both strings.

Explain how the dynamic programming table is built for the Longest Common Substring problem.

Think about comparing characters and building up substring lengths step by step.

Describe the difference between Longest Common Substring and Longest Common Subsequence with examples.

Focus on continuity and skipping characters.