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Dynamic programming 5-1

1. Matrix Chain Multiplication Matrix Chain Multiplication (MCM) is a classic DP problem focused on finding the optimal way to…

December 12, 2024

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Dynamic programming 4-2

Bottom-Up Approach (Tabulation): In the bottom-up approach:  Advantages: Example: Fibonacci Sequence (Tabulation): FUNCTION fibonacci(n)     IF n <= 1         RETURN n…

December 12, 2024

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Dynamic programming 4-1

Bottom-Up vs. Top-Down Approaches: In dynamic programming, two main approaches-Top-Down (Memoization) and Bottom-Up (Tabulation)—help efficiently solve problems with overlapping subproblems.…

December 12, 2024

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Dynamic programming 3-1

Problem 1: Fibonacci Sequence The Fibonacci sequence follows the relation: [ F(n) = F(n – 1) + F(n – 2)…

December 12, 2024

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Dynamic programming 2-4

1. When to Use Memoization Memoization is particularly useful when: 2. When to Use Tabulation Tabulation is ideal when: 3.…

December 12, 2024

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Dynamic programming 2-3

1. Tabulation Technique (Bottom-Up Approach) Tabulation is an iterative, bottom-up approach for solving problems by first solving smaller subproblems and…

December 12, 2024

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Dynamic programming 2-2

1. How Memoization Works Memoization is implemented using a top down approach. The algorithm starts by solving the main problem…

December 12, 2024

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Dynamic programming 2-1

1. What is Memoization? (Top-Down Approach) Memoization is a top down dynamic programming technique where you recursively solve a problem…

December 12, 2024

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Dynamic programming 1-2

1. Memoization(TopDown Approach) in Dynamic Programming Memoization is a technique to optimize recursive algorithms by storing results of expensive function…

December 12, 2024