Which of the following statements is true about dynamic programming in string processing?a)Dynamic programming cannot be applied to string processing problems.b)Dynamic programming requires the use of recursive functions.c)Dynamic programming can be used to solve problems with overlapping subproblems.d)Dynamic programming can only be applied to problems with fixed-length strings.Correct answer is option 'C'. Can you explain this answer?

Question

Answer

Dynamic programming in string processing

Introduction:
Dynamic programming is a technique used to solve optimization problems by breaking them down into smaller overlapping subproblems and storing their solutions for reuse. It is a powerful method that can be applied to various domains, including string processing.

The Correct Answer:
The correct answer is option 'C': Dynamic programming can be used to solve problems with overlapping subproblems.

Explanation:
Dynamic programming can be effectively used in string processing problems where there are overlapping subproblems. This means that the solution to a larger problem can be constructed by combining the solutions to smaller subproblems. By storing the solutions to these subproblems, we can avoid redundant computations and improve the overall efficiency of the algorithm.

Example:
Consider the problem of finding the longest common subsequence (LCS) between two strings. The LCS is the longest sequence of characters that appear in the same order in both strings. This problem can be efficiently solved using dynamic programming.

Steps to solve the LCS problem using dynamic programming:
1. Identify the subproblems: In this case, the subproblems can be defined as finding the LCS for substrings of the two input strings.
2. Define the recurrence relation: The solution to the larger problem can be constructed by combining the solutions to smaller subproblems. The recurrence relation for this problem can be defined as follows:
- If the last characters of the two strings are the same, then the LCS is the LCS of the two strings without their last characters, plus the last character.
- If the last characters are different, then the LCS is the maximum of the LCS of the first string without its last character and the second string, and the LCS of the second string without its last character and the first string.
3. Build the solution bottom-up: Starting from the smallest subproblems, we can use the recurrence relation to build the solution for larger subproblems. By storing the solutions to these subproblems in a table, we can avoid redundant computations.
4. Retrieve the final solution: Once the table is filled, the solution to the original problem can be found by looking up the entry corresponding to the full input strings in the table.

Conclusion:
Dynamic programming is a powerful technique that can be applied to various string processing problems. It allows for efficient computation by breaking down the problem into smaller overlapping subproblems and storing their solutions for reuse. Therefore, option 'C' is the correct statement about dynamic programming in string processing.

Answer

Dynamic programming is a technique used to solve optimization problems by breaking them into overlapping subproblems and storing the results of subproblems to avoid redundant computation.

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