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Dynamic Programming is an algorithmic technique used to solve optimization problems by breaking them down into overlapping subproblems and efficiently storing and reusing the solutions to these subproblems. It provides an effective and elegant approach to solving problems that have an inherent recursive structure.
Dynamic Programming can be compared to watching _ or reading ____. Just like in ___ and ____, where a complex storyline is broken down into episodes or chapters, Dynamic Programming breaks down a complex problem into smaller subproblems. By solving these subproblems and storing their solutions, we can find the optimal solution to the original problem.
By using the principles of Dynamic Programming, we can solve a wide range of problems more efficiently and effectively than traditional approaches.
To illustrate the concept of Dynamic Programming, let's consider an example of finding the Fibonacci sequence.
1# Python code to find the nth Fibonacci number using Dynamic Programming
2
3def fibonacci(n):
4 if n <= 1:
5 return n
6 fib = [0] * (n + 1)
7 fib[1] = 1
8 for i in range(2, n + 1):
9 fib[i] = fib[i - 1] + fib[i - 2]
10 return fib[n]
11
12n = 6
13print(f'The {n}th Fibonacci number is', fibonacci(n))
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