Understanding Dynamic Programming: A Guide to Solving Complex Problems Efficiently

DP stands for "Dynamic Programming". It is a method for solving complex problems by breaking them down into smaller subproblems, solving each subproblem only once, and storing the solutions to subproblems to avoid redundant computation.

In other words, DP is a technique for solving problems recursively by breaking them down into smaller pieces, solving each piece independently, and then combining the solutions to the pieces to solve the original problem. By doing so, we can avoid redundant computations and solve the problem more efficiently.

DP is particularly useful for solving problems that have overlapping subproblems, where the same subproblem may be encountered multiple times with different inputs. By storing the solutions to these subproblems, we can avoid recomputing them multiple times and instead use the stored solutions to solve the original problem more quickly.

Some common characteristics of DP problems include:

* Optimal substructure: The problem can be broken down into smaller subproblems, and the optimal solution to the larger problem can be constructed from the optimal solutions of the subproblems.
* Overlapping subproblems: The same subproblem may be encountered multiple times with different inputs.
* Recursion: The problem can be solved recursively by breaking it down into smaller pieces and solving each piece independently.

Examples of DP problems include the Fibonacci sequence, the shortest path in a graph, and the longest common subsequence in two strings.