Fibonacci Numbers Visualizer
Watch how memoization transforms the exponential Fibonacci algorithm into a linear time solution by storing computed values.
Time: O(n) with memo
Space: O(n)
Without memo: O(2^n)
Top-down DP
F(3)F(12)
Fast (300ms)Slow (2000ms)
Progress: Step 1 of 0Phase: start
Fibonacci Sequence
F(0)
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F(1)
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F(2)
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F(3)
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F(4)
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F(5)
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F(6)
?
Call Stack
Call stack is empty
Memoization Table
memo[0]
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memo[1]
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memo[2]
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memo[3]
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memo[4]
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memo[5]
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memo[6]
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Current Step:
Click Start to begin the Fibonacci visualization
Algorithm Details
With Memoization:
O(n)Without Memoization:
O(2^n)Space:
O(n)Type:Top-down DP
Real-world Applications
- •Financial modeling and compound interest
- •Population growth in biology
- •Computer graphics and spiral patterns
- •Algorithm optimization techniques
- •Nature patterns (flowers, pinecones, shells)
Memoization Benefits
- ✓Eliminates redundant calculations
- ✓Transforms exponential to linear time
- ✓Preserves natural recursive structure
- ✓Easy to implement and understand
- ℹTrade-off: Uses O(n) extra space