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Dynamic Programming Tutorial

DP doesn't have to be scary. Learn step-by-step with our AI tutor. From Fibonacci to advanced patterns.

What is Dynamic Programming?

The Simple Explanation

Dynamic Programming is just smart recursion. Instead of solving the same subproblem multiple times, you solve it once and remember the answer.

Think of it like this: if someone asks you to calculate 5 + 3 multiple times, you don't recalculate each time - you remember it's 8.

Two Approaches

Memoization (Top-Down)

Start with the main problem, break it down, cache results

Tabulation (Bottom-Up)

Start with smallest subproblems, build up to the answer

The DP Learning Path

Follow this sequence to master dynamic programming

1

Understand Recursion

Master recursive thinking before DP

2

Learn Memoization

Add caching to recursive solutions

3

Master Tabulation

Convert to iterative bottom-up approach

4

Recognize Patterns

Identify which DP pattern to apply

5

Optimize Space

Reduce memory usage in solutions

6

Practice, Practice

Solve 30+ DP problems for mastery

8 Essential DP Patterns

Master these patterns to solve 90% of DP interview questions

Fibonacci Pattern
Easy
Foundation of DP - simple recursion with memoization

Example problems:

Climbing StairsHouse RobberFibonacci Number
0/1 Knapsack
Medium
Choose or skip items to maximize value within constraints

Example problems:

Partition Equal Subset SumTarget SumOnes and Zeroes
Unbounded Knapsack
Medium
Items can be used unlimited times

Example problems:

Coin ChangeCoin Change 2Perfect Squares
Longest Common Subsequence
Medium
Compare two sequences to find common elements

Example problems:

LCSEdit DistanceDistinct Subsequences
Longest Increasing Subsequence
Medium
Find longest sorted subsequence in array

Example problems:

LISRussian Doll EnvelopesLargest Divisible Subset
Matrix Chain Multiplication
Hard
Optimal way to split/merge intervals

Example problems:

Burst BalloonsMinimum Cost TreeBoolean Parenthesization
DP on Strings
Medium
String manipulation and comparison problems

Example problems:

Palindrome SubstringsLongest PalindromeWildcard Matching
DP on Trees
Hard
Apply DP concepts to tree structures

Example problems:

House Robber IIIBinary Tree CameraTree Diameter

Why Learn DP with DSA 100 Days?

AI tutor explains concepts step-by-step
Visual animations for each algorithm
Practice problems ordered by difficulty
Hints without spoilers when you're stuck
Track your progress across all DP patterns
Solutions in Python, JavaScript, Java, C++

12 DP Problems

Included in our 100-problem curriculum, carefully ordered from easy to hard

Ready to Master Dynamic Programming?

Start with our free problems and level up with AI tutoring