Dynamic Programming Patterns: Unlocking the Magic of Anime and Manga

Dynamic programming is more than just a problem-solving technique - it's like a magical journey into your favorite anime or manga series. Just as anime and manga have recurring patterns and themes, dynamic programming has its own set of patterns and techniques that can be applied to solve various problems.

By mastering these patterns, you can unlock the true power of dynamic programming and solve complex problems with ease. Let's explore some common dynamic programming patterns:

1. The Fibonacci Sequence

The Fibonacci sequence is a classic example in dynamic programming. It consists of a series of numbers where each number is the sum of the two preceding ones. Using dynamic programming, we can solve the Fibonacci sequence efficiently by breaking it down into smaller subproblems and storing the results to avoid redundant computations.

Here's an example of calculating the 6th number in the Fibonacci sequence using the top-down approach:

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The fibonacci_top_down function uses memoization to store the intermediate results and avoid recomputing the same subproblems. The n parameter represents the position of the number in the Fibonacci sequence.

By leveraging the power of dynamic programming patterns like the Fibonacci sequence, you can tackle a wide range of optimization problems just like your favorite anime or manga characters facing challenges and overcoming obstacles!

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def fibonacci_top_down(n, memo = {}):

    if n in memo:

        return memo[n]

    if n <= 2:

        return 1

    memo[n] = fibonacci_top_down(n-1, memo) + fibonacci_top_down(n-2, memo)

    return memo[n]

​

n = 6

print('Fibonacci using the top-down approach:', fibonacci_top_down(n))