What are some examples of dynamic programming?

What are some examples of dynamic programming?

Dynamic programming is a method for solving complex problems by breaking them down into simpler subproblems. Some classic examples include the Fibonacci sequence, the Knapsack problem, and the Longest Common Subsequence.

Can you explain the Fibonacci sequence using dynamic programming?

Sure! The Fibonacci sequence can be computed using dynamic programming by storing previously computed values. Instead of recalculating Fibonacci(n) multiple times, you store Fibonacci(n-1) and Fibonacci(n-2) in an array and use them to compute Fibonacci(n). This reduces the time complexity from exponential to linear.

What about the Knapsack problem?

The Knapsack problem involves selecting items with given weights and values to maximize value without exceeding a weight limit. Using dynamic programming, you can create a table to store the maximum value that can be achieved with each weight limit, building up from smaller subproblems.

Are there any real-world applications of dynamic programming?

Yes, dynamic programming is used in various fields such as operations research, economics, bioinformatics for sequence alignment, and even in machine learning for optimization problems.