Dynamic Programming (DP) is a technique used to optimize recursive algorithms by storing intermediate results, avoiding redundant calculations, and thus significantly improving computational efficiency. It is particularly useful for problems that exhibit overlapping subproblems and optimal substructure.
The Fibonacci series is a sequence of numbers where each number is the sum of the two preceding ones, usually starting with 0 and 1. Mathematically, it is defined as:
The Knapsack Problem is a classic optimization problem that can be efficiently solved using dynamic programming. The goal is to choose a subset of items with maximum total value, subject to a weight constraint on the total weight of the chosen items.
The Longest Common Subsequence (LCS) problem is a classic computer science problem used to find the longest subsequence common to all sequences in a set of sequences (often just two sequences). A subsequence is a sequence derived from another sequence where some elements might be deleted without changing the order of the remaining elements.
Shortest path problems are key in optimizing routes in various applications like network design, transportation, and telecommunications. They focus on finding the shortest route from a start to a destination in a graph, which consists of nodes (vertices) and edges (connections between nodes).