CodeSignal Technical Assessment Dynamic Programming and Optimization 2

Question 1

What space optimization reduces the LCS DP table from O(m×n) to O(min(m,n))?

Accepted Answer

Using only two rows at a time (rolling array)

Answer

Since each row depends only on the previous row, storing just two rows reduces space from O(m×n) to O(n).

Question 2

In the coin change problem, what should be returned if no valid coin combination can make the target amount?

Accepted Answer

-1

Answer

Returning -1 is the conventional signal that no valid combination exists for the given amount.

Question 3

What does 'optimal substructure' mean in the context of dynamic programming?

Accepted Answer

The optimal solution to the problem contains optimal solutions to its subproblems

Answer

Optimal substructure means you can construct the global optimal answer by combining optimal answers to smaller subproblems.

Question 4

What is the time complexity of the standard matrix chain multiplication DP algorithm?

Accepted Answer

O(n³)

Answer

The matrix chain DP iterates over all chain lengths and all split points, resulting in O(n³) time complexity.

Question 5

Which DP approach builds the solution iteratively starting from the smallest subproblems?

Accepted Answer

Tabulation

Answer

Tabulation (bottom-up DP) fills a table from the base cases up, avoiding recursion entirely.

Codesignal Practice Test