Dynamic Programming

Master the art of solving complex problems by breaking them down into simpler subproblems. Watch how memoization and tabulation optimize recursive solutions.

Interactive Visualizations
State Transitions
Optimization Techniques
Multiple Approaches

Optimal Substructure

Solutions to larger problems depend on solutions to smaller subproblems

Overlapping Subproblems

Same subproblems are solved multiple times, making memoization valuable

Memoization

Store computed results to avoid redundant calculations and improve efficiency

Interactive DP Visualizations

Explore classic dynamic programming problems with step-by-step visualizations

Fibonacci Numbers

Classic example of memoization transforming exponential to linear time complexity

Time Complexity:O(n)
Space Complexity:O(n)
Difficulty:Beginner
Type:Top-down DP
Pattern:Memoization

Making Change

Find minimum coins needed to make change using bottom-up dynamic programming

Time Complexity:O(amount × coins)
Space Complexity:O(amount)
Difficulty:Intermediate
Type:Bottom-up DP
Pattern:Unbounded Knapsack

Longest Common Subsequence

2D DP table approach to find longest common subsequence between two strings

Time Complexity:O(m × n)
Space Complexity:O(m × n)
Difficulty:Intermediate
Type:2D DP Table
Pattern:String Matching

0/1 Knapsack

Classic optimization problem using 2D DP to maximize value within weight constraint

Time Complexity:O(n × W)
Space Complexity:O(n × W)
Difficulty:Intermediate
Type:2D DP Table
Pattern:Optimization
Coming Soon

Longest Increasing Subsequence

Find the length of longest strictly increasing subsequence in an array

Time Complexity:O(n²) / O(n log n)
Space Complexity:O(n)
Difficulty:Intermediate
Pattern:Subsequence
Coming Soon

Edit Distance

Minimum operations to transform one string to another using insertions, deletions, substitutions

Time Complexity:O(m × n)
Space Complexity:O(m × n)
Difficulty:Advanced
Pattern:String Transformation
Coming Soon

Maximum Subarray

Kadane's algorithm to find contiguous subarray with maximum sum

Time Complexity:O(n)
Space Complexity:O(1)
Difficulty:Beginner
Pattern:Subarray

House Robber

Maximum money that can be robbed without robbing adjacent houses

Time Complexity:O(n)
Space Complexity:O(1)
Difficulty:Beginner
Type:1D DP Array
Pattern:Decision Making

Dynamic Programming Approaches

Learn the two main paradigms of dynamic programming and when to use each approach

Top-down Approach

Memoization

How it works:

Start with the original problem and recursively break it down, storing results to avoid recomputation.

Best for:

  • • Natural recursive problems
  • • When you don't need all subproblems
  • • Tree-like recursion patterns

Examples:

Fibonacci, Tree DP, Some optimization problems

Bottom-up Approach

Tabulation

How it works:

Start with base cases and iteratively build up solutions to larger problems using a table.

Best for:

  • • When you need all subproblems
  • • Better space optimization
  • • Iterative problem patterns

Examples:

Coin Change, LCS, Knapsack, Edit Distance

Why Learn Dynamic Programming?

Dynamic programming is essential for solving optimization problems efficiently and is frequently tested in technical interviews.

Optimization

Transform exponential algorithms into polynomial time solutions through intelligent caching

Problem Solving

Develop systematic thinking for breaking complex problems into manageable subproblems

Interview Success

Master one of the most important topics in technical interviews at top companies