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dynamic programming
Fibonacci
The Fibonacci sequence is a classic dynamic programming problem where each number is the sum of the two preceding ones. A naive recursive approach has exponential time complexity, but by storing previously computed values in a DP table (memoization or bottom-up tabulation), we reduce it to linear time. This illustrates the core DP principle of trading space for time by eliminating redundant subproblem calculations.
Use Cases
- •Modeling growth patterns in nature (population growth, spiral structures)
- •Financial mathematics for option pricing and interest calculations
- •Teaching foundational dynamic programming and memoization techniques
Complexity Analysis
| Metric | Best | Average | Worst |
|---|---|---|---|
| Time | O(n) | O(n) | O(n) |
| Space | O(n) | ||
Visualization
| F(0) | F(1) | F(2) | F(3) | F(4) | F(5) | F(6) | F(7) | F(8) | F(9) | F(10) | |
|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Implementation
Output
Click "Run Code" to see output...