Fibonacci: recursion to DP
one step at a time.
Plain recursion solves the same calls again and again; storing each answer once (memo or table) makes it linear.
Free to use. Step forward and back at your pace, and share a link to the exact step you are stuck on.
What you actually watch.
The part a dry run on paper loses: the state, at every step.
Plain recursion solves the same calls again and again; storing each answer once (memo or table) makes it linear. That sentence is easy to agree with and hard to hold in your head on step nine, which is where most people lose the thread.
So the visualiser keeps it in front of you: the call tree, and the table filling in as answers stop being recomputed. The line of code being executed is highlighted as the picture changes, so the drawing and the code never drift apart. Step forward, step back, or let it play.
Put your own input in. Fibonacci: recursion to DP on a clean example teaches you the shape; fibonacci: recursion to dp on an empty input, a single element, or one with duplicates teaches you the thing an interviewer asks about.
How it runs, step by step.
The same order the visualiser moves in, so the list and the picture match.
- 1Break the problem into a smaller copy of itself.
- 2Solve the smallest cases directly: those are the base cases.
- 3Store each answer the first time it is computed.
- 4Reuse the stored answer instead of solving the same call twice.
Where people get this one wrong.
These are not made up. Each one is a switch in the tool: turn it on, run the same input, and watch the state go wrong.
- Memoised recursionThe same recursion, but every answer is stored. A repeat becomes one lookup (green, "cached"), so the tree shrinks to 2n − 1 calls.
- Bottom-up tableNo recursion: fill dp[0..n] from the left, each cell from the two before it. n + 1 cells, nothing repeated, no call stack.
Inputs worth trying.
The cases that teach something. Each one is a preset in the tool, with the reason it is there.
- fib(6)25 calls for 7 different values.
- n = 0A base case: one call, no recursion.
- n = 1The other base case.
- n = 2The smallest call that recurses.
- n = 4The first time a whole subtree, f(2), is computed twice.
What it costs.
The two numbers an interviewer will ask for, and what they mean here.
- Time
- O(φⁿ) → O(n)counted as real operations while it runs, not quoted from a table
- Space
- O(n)what the algorithm holds besides the input itself
- Pattern
- Recursion & DPSolve smaller copies, then stop solving them twice.
Once you can see it, go and use it.
Watching is the first ten minutes. The pattern sticks when you solve with it.
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About fibonacci: recursion to dp.
Open it in the app and the answers are easier to see than to read.
Open the visualiserWhat does the fibonacci: recursion to dp visualiser show?
Every step of the algorithm on input you choose: the call tree, and the table filling in as answers stop being recomputed, with the line of code being executed highlighted beside it. You can step forward, step back, or let it play. Spelled visualizer or visualiser, it is the same tool.
What is the time complexity of fibonacci: recursion to dp?
O(φⁿ) → O(n) time and O(n) space. The visualiser counts the real operations as it runs, so you can watch the number grow instead of taking the formula on trust.
Can I use my own input?
Yes. Type your own array, string or graph and the algorithm runs on that, including the edge cases that break a solution in an interview.
Is it free?
Yes. The app is free to start, with 100 AI credits when you sign up and 100 every month, and watching an algorithm costs no credits.