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• An adjacency matrix represents a graph using a 2D array (matrix).
• This type of storage uses sequential memory allocation — rows and columns are stored in contiguous memory.
• Hence, this method is called a Sequential Representation of a graph.

Solution

Answer: 4) B and C only

• Binary Search Tree (BST): Not necessarily balanced; height can degrade to O(n).
• AVL Tree: Height-balanced by definition (balance factor −1, 0, +1); height is O(log n).
• Red-Black Tree: Enforces black-height properties that keep height O(log n); treated as a height-balanced binary tree.
• B-Tree: Balanced (all leaves at the same level) but not a binary tree; the term “height-balanced tree” typically refers to binary trees. Hence excluded here.

Solution

Answer: (4) C, B, D, A

Explanation:
The standard steps for designing a dynamic programming algorithm are:

1. (C) Characterize the structure of an optimal solution.
2. (B) Recursively define the value of an optimal solution.
3. (D) Compute the value of an optimal solution (usually bottom-up).
4. (A) Construct the optimal solution from the computed information.

Hence, the correct order is C → B → D → A.

Solution

Solution

Why: The LCS length for the two sequences is $4$. $2,3,2,1$ is a subsequence of both: $\{1,\underline{2},3,\underline{2},4,1,\underline{2}\}$ and $\{\underline{2},4,\underline{3},1,\underline{2},\underline{1}\}$. Option (4) has length $5$ (too long), and (1), (2) are not subsequences of both.

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