This video is a Part - 2 of Dynamic Programming Tutorial by Mahima Hans (Software Engineer at Adobe). You can also master the basics of dynamic programming and it's application. Check out our free masterclasses by industry-leading experts here: https://www.scaler.com/events?utm_sou...

Topics Covered
00:00 - Introduction
00:47 - Lead Codes Example
10:51 - Recursion Tree Example
19:23 - DP table Codes
22:32 - Min Costing Example
41:15 - Approach comparisons

Dynamic programming is a method for solving complex problems by breaking them down into simpler subproblems and solving each subproblem only once, storing the solutions to avoid redundant computations. It is particularly useful for optimisation problems, where the goal is to find the best solution among a set of possible solutions.

But what is problem solving?

Problem solving in dynamic programming involves applying the principles of dynamic programming to solve optimization problems efficiently. Here's a step-by-step overview of how dynamic programming is typically applied to solve a problem:

1. Identify Optimal Substructure: Determine if the problem can be broken down into smaller subproblems, and if the optimal solution to the original problem can be constructed from the optimal solutions of its subproblems.

2. Define Recurrence Relation: Formulate a recursive relation that expresses the solution to a larger problem in terms of solutions to its subproblems. This relation should capture the recurrence pattern of the problem.

3. Optimal Solution: Once the solutions to all subproblems are computed, retrieve the solution to the original problem from the table or cache.

4. Analysis: The time and space complexity of the solution to ensure it meets the requirements of the problem. Dynamic programming solutions are often optimized to reduce time and space complexity compared to naive recursive solutions.

There are two main approaches to dynamic programming:

Top-Down Approach (Memoization):
In this approach, the problem is solved recursively, breaking it down into smaller subproblems.
However, to avoid redundant computations, the solutions to subproblems are stored in a data structure like an array or a hash table. This process is called memoization. When a subproblem is encountered again, instead of recomputing its solution, the precomputed solution is retrieved from memory. Memoization ensures that each subproblem is solved only once, leading to improved efficiency.This approach is typically implemented using recursion with an added memoization mechanism.

Bottom-Up Approach (Tabulation):
In the bottom-up approach, the problem is solved iteratively, starting from the smallest subproblems and gradually building up to the larger ones.The solutions to subproblems are stored in a table or array. At each step, the solution to a larger problem is computed using the solutions to smaller subproblems, following a specific order to ensure that all necessary subproblems are already solved.
Since all subproblems are solved in a predefined order, there is no need for recursion or memoization. This approach is often more efficient in terms of both time and space complexity compared to the top-down approach. It's particularly useful when the recursive structure of the problem can be easily converted into an iterative process.

#scaler #dynamicprogramming #algorithm #problemsolving
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