Dynamic Programming

Dynamic Programming is nothing just memorized or cached response.

Dynamic Programming (DP) is an algorithm design technique used for optimization. It is mainly used to optimize recursive algorithms that have repeated calls for the same inputs. The idea is to store the results of subproblems, so we do not have to re-compute them when needed later. This simple optimization reduces time complexities from exponential to polynomial. DP is used in various fields, including computer science, mathematics, economics, and aerospace engineering¹. It is particularly useful in solving optimization problems.

Common Applications:

• Fibonacci Sequence: Calculating the nth Fibonacci number efficiently.

• Longest Common Subsequence (LCS): Finding the longest common subsequence between two strings or sequences.

• Knapsack Problem: Optimizing the value of items that can be fit into a knapsack with a given capacity.

• Bellman-Ford Algorithm: Finding shortest paths in graphs with negative edge weights.

• Edit Distance: Calculating the minimum number of edits required to transform one string into another.

• Matrix Chain Multiplication: Optimizing the order of matrix multiplications to minimize the number of scalar multiplications.