CodeSignal Technical Assessment Dynamic Programming and Optimization 1

Question 1

What is the time complexity of solving the 0/1 knapsack problem with n items and capacity W using dynamic programming?

Accepted Answer

O(nW)

Answer

The 0/1 knapsack DP fills a table of size n × W, giving O(nW) time complexity.

Question 2

Which dynamic programming strategy works top-down by caching results of already-solved subproblems?

Accepted Answer

Memoization

Answer

Memoization is a top-down technique that stores previously computed results to avoid redundant calculations.

Question 3

What two properties must a problem have to be solvable with dynamic programming?

Accepted Answer

Optimal substructure and overlapping subproblems

Answer

DP requires optimal substructure (optimal solution uses optimal sub-solutions) and overlapping subproblems (same subproblems recur).

Question 4

In the Longest Common Subsequence problem, what does dp[i][j] represent?

Accepted Answer

Length of LCS of the first i chars of s1 and first j chars of s2

Answer

dp[i][j] stores the length of the LCS considering only the first i characters of s1 and the first j characters of s2.

Question 5

What are the base case values for dp[0][j] and dp[i][0] in the edit distance problem?

Accepted Answer

dp[0][j] = j and dp[i][0] = i

Answer

Converting an empty string to a length-j string requires j insertions, and converting length-i to empty requires i deletions.

Codesignal Practice Test