Dynamic Programming: Smarter, Not Harder Problem Solving

Dynamic Programming (DP) is a method for solving complex problems by breaking them down into smaller subproblems and solving them in a systematic way.

DP is useful for problems that can be broken down into smaller sub-problems that have overlapping substructures.

DP uses a technique called memoization, which is a way of storing the results of expensive function calls and returning the cached result when the same inputs occur again.

DP algorithms typically involve the use of a table or array to store the solutions to subproblems.

DP algorithms can be used to solve problems such as finding the shortest path in a graph, finding the longest common subsequence of two strings, and optimizing knapsack problems.

DP algorithms can be divided into two types: top-down and bottom-up.

Bottom-up DP involves starting with the smallest subproblems and working up to the original problem.

Top-down DP involves starting with the original problem and breaking it down into smaller subproblems.

DP algorithms require that the subproblems have the property of optimal substructure, which means that the optimal solution to a problem can be constructed from the optimal solutions to its subproblems.

DP algorithms also require that the subproblems have the property of overlapping subproblems, which means that the same subproblems are solved multiple times.

DP is widely used in various fields such as computer science, engineering, economics, and mathematics to solve various optimization and decision-making problems.