Day 30: Introduction to Dynamic Programming
Day 30: Introduction to Dynamic Programming #
Welcome to Day 30 of our 60 Days of Coding Algorithm Challenge! Today, we’ll dive into Dynamic Programming (DP), a powerful algorithmic technique used to solve complex problems by breaking them down into simpler subproblems.
What is Dynamic Programming? #
Dynamic Programming is a method for solving complex problems by breaking them down into simpler subproblems. It is applicable when the subproblems are not independent, i.e., when subproblems share subsubproblems. A dynamic programming algorithm solves each subsubproblem only once and then saves its answer in a table, thereby avoiding the work of recomputing the answer every time the subsubproblem is encountered.
Key Characteristics of Dynamic Programming Problems #
- Optimal Substructure: An optimal solution to the problem contains optimal solutions to subproblems.
- Overlapping Subproblems: The problem can be broken down into subproblems which are reused several times.
Approaches to Dynamic Programming #
Top-down (Memoization): We solve the bigger problem by recursively finding the solution to smaller subproblems. Whenever we solve a subproblem, we …
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