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Dynamic Programming

Master optimization problems through interactive visualizations of memoization and tabulation techniques

5
Algorithms
5
Visualizations
100%
Complete
Ready
Status
🎒
Hard✅

0/1 Knapsack

Find the optimal way to fill a knapsack with maximum value

Time Complexity:O(n×W)
Space Complexity:O(n×W)
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📝
Medium✅

Longest Common Subsequence

Find the longest subsequence common to two sequences

Time Complexity:O(m×n)
Space Complexity:O(m×n)
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🌀
Easy✅

Fibonacci Sequence

Calculate Fibonacci numbers using memoization and tabulation

Time Complexity:O(n)
Space Complexity:O(n)
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🪙
Medium✅

Coin Change

Find minimum coins needed to make a given amount

Time Complexity:O(n×amount)
Space Complexity:O(amount)
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✏️
Medium✅

Edit Distance

Calculate minimum operations to transform one string to another

Time Complexity:O(m×n)
Space Complexity:O(m×n)
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What is Dynamic Programming?

Dynamic Programming is an algorithmic paradigm that solves complex problems by breaking them down into simpler subproblems and storing the results to avoid redundant calculations.

Key Principles:

  • • Overlapping Subproblems: Same subproblems solved multiple times
  • • Optimal Substructure: Optimal solution contains optimal solutions to subproblems
  • • Memoization: Top-down approach with caching
  • • Tabulation: Bottom-up approach building solutions

Learning Path

1
Start with Fibonacci - Learn basic memoization
2
Try Coin Change - Understand tabulation
3
Explore LCS - Work with 2D problems
4
Master Knapsack - Complex optimization