Dynamic ProgrammingBeginner

Fibonacci (Dynamic Programming)

Computes Fibonacci numbers efficiently using dynamic programming to avoid redundant calculations. Demonstrates the power of memoization in transforming an exponential-time recursive solution into a linear-time algorithm. A classic introduction to dynamic programming concepts.

#dynamic-programming#memoization#recursion#optimization

Complexity Analysis

Time (Average)

O(n)

Expected case performance

Space

O(n)

Memory requirements

Time (Best)

O(n)

Best case performance

Time (Worst)

O(n)

Worst case performance

📚 CLRS Reference

Introduction to Algorithms•Chapter 15•Section 15.1

Quick Presets

Compute F(n) - Enter n (0-15)

Note: Higher values may generate many visualization steps due to recursion

Step: 1 / 0

Animation Speed500ms

SlowFast

Keyboard Shortcuts

Space Play/Pause← → StepR Reset1-4 Speed

Real-time Statistics

Algorithm Performance Metrics

Progress0%

Comparisons

Swaps

Array Accesses

Steps

1/ 0

Algorithm Visualization

Step 1 of 0

Initialize array to begin

Default

Comparing

Swapped

Sorted

Code Execution

Currently executing

Previously executed

Implementation

Related Algorithms

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Matrix Chain Multiplication

Advanced

Finds the optimal way to parenthesize a chain of matrices to minimize the number of scalar multiplications. Classic dynamic programming problem from CLRS Chapter 15.

O(n³)

O(n²)

dynamic-programmingoptimization

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Longest Common Subsequence (LCS)

Intermediate

Finds the longest subsequence present in two sequences in the same order. Uses dynamic programming to build a solution table. Applications include DNA sequence alignment, file difference tools (diff), and plagiarism detection.

O(m × n)

dynamic-programmingstrings

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Edit Distance (Levenshtein)

Intermediate

Dynamic programming algorithm that calculates the minimum number of single-character edits (insertions, deletions, substitutions) required to transform one string into another. Fundamental in spell checking, DNA sequence alignment, and natural language processing.

O(m × n)

dynamic-programmingstrings

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