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Fibonacci Sequence Dynamic Programming Visualizer

STEM Interactive Visual Learning Program at TEC-Bridge AI

Fibonacci Controls

Fibonacci Sequence Visualization

Colors: Yellow = Current, Green = Computed, Blue = Using previous values

Algorithm Steps

How to Use

  1. Input: Enter a number n (0-20) to compute the nth Fibonacci number
  2. Start: Click "Start" to begin the dynamic programming computation
  3. Step Through: Click "Next" to see each step of the algorithm
  4. Observe: Watch how each Fibonacci number is built from previous values
  5. Colors: Yellow shows current computation, Blue shows values being used
  6. Reset: Click "Reset" to start over with a new number

Dynamic Programming Concept

Dynamic Programming solves complex problems by breaking them into simpler subproblems and storing results to avoid redundant calculations.

Fibonacci with DP:

  • Base cases: F(0) = 0, F(1) = 1
  • For n ≥ 2: F(n) = F(n-1) + F(n-2)
  • Store computed values to avoid recalculation
  • Build solution bottom-up from F(0) to F(n)
  • Time: O(n), Space: O(n) vs naive O(2^n)

Sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55...

Fibonacci Dynamic Programming Code Implementation

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