In the dynamic programming table for Levenshtein distance, what does the cell at index (i, j) typically represent?
The number of deletions required to transform the first string into the second string.
The number of insertions required to transform the first string into the second string.
The edit distance between the first i characters of the first string and the first j characters of the second string.
Whether the first i characters of the first string are identical to the first j characters of the second string.
What is the time complexity of a tabulated (bottom-up) Dynamic Programming solution for the Fibonacci sequence?
O(n^2)
O(n)
O(2^n)
O(n log n)
What is the primary purpose of using dynamic programming to calculate the Levenshtein distance?
To reduce the time complexity by storing and reusing previously computed distances.
To sort a list of strings in lexicographical order.
To determine if two strings are anagrams of each other.
To find all possible edit operations between two strings.
In a Dynamic Programming solution for LCS, what does a cell in the DP table typically represent?
The length of the LCS of the prefixes of the input sequences up to those indices.
The maximum length of the LCS found so far.
Whether the characters at those indices in the input sequences are the same.
The cost of inserting, deleting, or replacing a character to make the prefixes of the input sequences equal.
In the context of edit distance, what does a diagonal transition in the dynamic programming table represent?
Deletion of a character
Insertion of a character
Substitution of a character
Matching of two characters
In the context of Matrix Chain Multiplication, what do the dimensions of a matrix determine?
The values stored within the matrix.
The number of rows and columns in the matrix, affecting multiplication compatibility and cost.
The order in which the matrix was created.
The type of data stored in the matrix (integer, float, etc.).
The Longest Common Subsequence problem exhibits which of the following properties that make it suitable for Dynamic Programming?
Backtracking
Optimal Substructure and Overlapping Subproblems
Greedy Choice Property
Divide and Conquer
How is the DP table filled in the tabulated (bottom-up) Dynamic Programming solution for the LCS problem?
Column-by-column, from top to bottom.
Diagonally, from top-left to bottom-right.
It depends on the specific implementation.
Row-by-row, from left to right.
In the memoized solution for the Fibonacci sequence, what data structure is typically used to store previously computed values?
Array
Stack
Queue
Graph
What is a key advantage of using dynamic programming (memoization or tabulation) over a purely recursive approach for the Coin Change problem?
Dynamic programming reduces the space complexity of the solution.
Dynamic programming always finds a solution, while recursion might not.
Dynamic programming makes the solution easier to understand.
Dynamic programming avoids redundant calculations, improving efficiency.