Dynamic Programming —
Watch memoization click.
DP is where recursion meets memory. The "aha moment" happens when you see memoization eliminate hundreds of redundant calls in real time — and when you watch a DP table fill up cell by cell. Run your own Python code and see exactly how overlapping subproblems collapse into a clean O(n) solution.
What is Dynamic Programming?
Dynamic programming solves complex problems by breaking them into overlapping subproblems and storing results so they're never computed twice. There are two approaches: top-down (memoization — recursion + cache) and bottom-up (tabulation — fill a table iteratively). Both approaches make the logic crystal clear when visualized.
Why visualization changes everything
Most DP learners memorize patterns without understanding why they work. When you watch a memoization cache hit eliminate a subtree of calls, or see a DP table fill row by row — the pattern becomes intuitive. LearnBug shows every cache lookup and table update in real time.
Classic DP problems, visualized step by step
Fibonacci — Memoization
From O(2ⁿ) naive recursion to O(n) with a cache. Watch which subtrees get pruned on a cache hit — the DP "aha moment" made visible.
Climbing Stairs
Take 1 or 2 steps — how many ways to reach the top? Watch the DP array build from the base up and see how Fibonacci appears naturally.
Coin Change
Minimum coins to make a target amount. Watch the DP table fill from 0 to the target — and see how each coin denomination contributes to each cell.
0/1 Knapsack
Include or skip each item — which combination maximizes value within the weight limit? Watch the 2D DP table fill and see each decision unfold.
DP vs Recursion
Same problem — very different execution. Watch naive recursion make exponential calls while memoized DP solves the same problem in linear time.
Run your DP code on LearnBug
Watch your memoization cache fill up and see every redundant call get eliminated in real time.