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Dynamic Programming 2
Question 1
If LCS("abcde", "ace") = 3, which subsequence represents the LCS?
- A
"abc"
- B
"ace"
- C
"acd"
- D
"ae"
Question 2
Minimum insertions required to make a string palindrome = ?
- A
length - LCS(s, reverse(s))
- B
length + LCS(s, reverse(s))
- C
LCS(s, reverse(s))
- D
2 * length
Question 3
What is the key idea behind the Burst Balloons problem?
- A
Greedy selection of largest balloon
- B
Divide and conquer DP by choosing the last balloon to burst
- C
Binary search on balloons
- D
Sorting balloons by value
Question 4
The LIS problem can be solved in O(N log N) using which technique?
- A
Dynamic programming only
- B
Segment tree
- C
Binary search on tails
- D
Greedy sorting
Question 5
Which pattern does Partition DP generally follow?
- A
Iterate over all possible partition points k and combine subproblems
- B
Use greedy approach to minimize cost
- C
Solve only using recursion without memoization
- D
Always use bitmasking
Question 6
Why do we compare arr[j] < arr[i] when updating dp[i] in LIS?
- A
To ensure the subsequence remains increasing
- B
To skip equal elements
- C
To find decreasing subsequences
- D
To avoid duplicate elements
Question 7
Why do Partition DP problems like MCM or Palindrome Partitioning use i and j as state variables?
- A
Because they operate on subranges, and optimal solutions depend on the range’s boundaries
- B
Because they require comparing two sequences
- C
Because each position is independent
- D
Because they don’t have overlapping subproblems
Question 8
In Matrix Chain Multiplication, why doesn’t the smallest local multiplication cost always lead to the global minimum?
- A
Because local minimal choices may prevent globally optimal parenthesization
- B
Because matrix multiplication is commutative
- C
Because we only minimize scalar operations, not structure
- D
Because each multiplication cost is constant
Question 9
Why can LCS or Edit Distance be optimized from O(N²) to O(N) space?
- A
Because each row depends only on the previous row
- B
Because all rows are independent
- C
Because we can skip half the table
- D
Because character comparison can be vectorized
Question 10
If a DP has n states and each state transition takes O(k) time, what’s the total time complexity?
- A
O(n × k)
- B
O(n + k)
- C
O(kⁿ)
- D
O(log n)
There are 10 questions to complete.