SOLVE CODING CHALLENGE: LEARN DYNAMIC PROGRAMMING||Full tutorial|| For beginners
Course Title: Dynamic Programming: Mastering Optimization Techniques
Course Objective:
This course is designed to help learners understand Dynamic Programming (DP), a critical optimization technique used to solve complex problems by breaking them down into simpler subproblems. Whether you're preparing for coding interviews, competitive programming, or solving real-world optimization problems, this course will guide you through the foundations of dynamic programming, key concepts, and advanced techniques.
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Course Outline:
Module 1: Introduction to Dynamic Programming
What is Dynamic Programming?
Overview of dynamic programming as an optimization technique, comparing it with other approaches like brute force and greedy algorithms.
Characteristics of DP Problems
Understand how to identify a problem that can be solved using dynamic programming. Learn about overlapping subproblems and optimal substructure properties.
Top-Down vs. Bottom-Up Approaches
Explore the two primary techniques for implementing DP: memoization (top-down) and tabulation (bottom-up).
Module 2: Recursion and Memoization
Recursion Fundamentals
Review the basics of recursion and how it applies to dynamic programming.
Memoization Technique
Learn how to optimize recursive algorithms by storing results of subproblems to avoid redundant calculations.
Simple DP Problem: Fibonacci Sequence
Implement the Fibonacci sequence using both naive recursion and memoization to see the performance difference.
Module 3: Tabulation (Bottom-Up Dynamic Programming)
Introduction to Tabulation
Understand how tabulation builds a solution from the ground up by filling out a table or array.
Converting Recursive Solutions to Tabular Form
Learn how to transform a recursive solution into an iterative one using tabulation.
Example Problem: Coin Change Problem
Solve the coin change problem using tabulation and compare it to the memoization approach.
Module 4: Common DP Problems
1-Dimensional DP
Solve problems like the Climbing Stairs, House Robber, and Min Cost Path using 1D arrays.
2-Dimensional DP
Work on problems that require 2D arrays, such as the Longest Common Subsequence (LCS), Knapsack Problem, and Edit Distance.
Partitioning Problems
Learn how dynamic programming can solve partitioning problems like the Palindrome Partitioning and Subset Sum Problem.
Module 5: Advanced Dynamic Programming Techniques
State Transition and Problem Formulation
Learn how to define states and formulate the state transition equations for complex problems.
Space Optimization Techniques
Understand how to optimize the space complexity of DP algorithms, such as reducing a 2D array solution to 1D.
Bitmask Dynamic Programming
Discover the use of bitmasking in dynamic programming, which is helpful for problems involving subsets, like the Traveling Salesman Problem (TSP).
Matrix Exponentiation and DP
Learn how to apply matrix exponentiation to solve certain DP problems efficiently.
Module 6: Dynamic Programming on Trees and Graphs
DP on Trees
Understand how dynamic programming can be applied to tree structures for problems like finding the Longest Path in a Tree and Tree Diameter.
DP on Graphs
Explore the use of dynamic programming in graph-based problems such as the Shortest Path Algorithms (e.g., Bellman-Ford) and All-Pairs Shortest Path (Floyd-Warshall).
Bitmasking with Graphs
Solve advanced
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