Add README.md for Dynamic Programming Algorithms

[himanshulohote]

Description:

This pull request introduces a new README.md file to the dynamic_programming directory. The file provides comprehensive documentation for the dynamic programming algorithms implemented in this directory.

Changes Introduced:

• Added README.md to the dynamic_programming directory.
• The README includes:
  • An overview of dynamic programming and its purpose.
  • Descriptions of the various algorithms implemented, including their purpose and time complexity.
  • References to relevant literature and external resources for further reading.

Details:

• Coin Change Problem (coin_change.rs): Determines the minimum number of coins needed to make a given amount. Time Complexity: O(n * m), where n is the amount and m is the number of coin types.
• Edit Distance (edit_distance.rs): Calculates the minimum number of operations required to convert one string into another. Time Complexity: O(m * n), where m and n are the lengths of the two strings.
• Egg Dropping Problem (egg_dropping.rs): Determines the minimum number of attempts needed to find the highest floor from which an egg can be dropped without breaking. Time Complexity: O(k * n), where k is the number of eggs and n is the number of floors.
• Fibonacci Sequence (fibonacci.rs): Computes the nth Fibonacci number. Time Complexity: O(n)
• Knapsack Problem (knapsack.rs): Solves the problem of selecting items with given weights and values to maximize total value without exceeding the weight capacity. Time Complexity: O(n * W), where n is the number of items and W is the weight capacity.
• Longest Common Subsequence (longest_common_subsequence.rs): Finds the longest subsequence present in both of the given sequences. Time Complexity: O(m * n), where m and n are the lengths of the two sequences.
• Longest Increasing Subsequence (longest_increasing_subsequence.rs): Finds the length of the longest subsequence of a given sequence such that all elements of the subsequence are sorted in increasing order. Time Complexity: O(n^2) with dynamic programming approach.
• Maximum Subarray (maximum_subarray.rs): Finds the contiguous subarray within a one-dimensional array of numbers which has the largest sum. Time Complexity: O(n)
• Rod Cutting Problem (rod_cutting.rs): Determines the maximum revenue obtainable by cutting up a rod and selling the pieces. Time Complexity: O(n^2)

References:

• Introduction to Algorithms by Cormen et al. - A comprehensive reference on algorithms.
• Dynamic Programming - Wikipedia - Additional information on dynamic programming techniques.

Motivation:

Adding this README will provide users with a clear understanding of the dynamic programming algorithms included in this directory, their implementations, and their complexities. It will also offer direct links to resources for further study, improving the overall documentation quality of the repository.

Related Issue:

• See issue Add documentation #8 for more details on the documentation request.

[alexfertel]

LGTM! Thanks for your contribution!