Implementing Dynamic Programming in Go: Fibonacci Sequence
In this post, we will explore how to implement dynamic programming by diving into the world of the Fibonacci sequence using the Go language. The Fibonacci sequence, a series of numbers where the next number is derived by adding up the two preceding ones, offers a neat playground for dynamic programming.
Update: here is part two of this post.
What is Dynamic Programming?
Before we deep dive into the implementation, it’s crucial to understand what exactly dynamic programming is. Dynamic programming is a method of solving problems that involve numerous overlapping sub-problems. It avoids computing the same sub-problem multiple times (overlapping sub-problems) by saving the computation in a table (memoization). For a more in-depth understanding, visit Wikipedia’s page on dynamic programming.
Meeting Go Language: A Brief Introduction
If you’re new to Go, here’s a short introduction: Go, also known as Golang, is an open-source programming language developed by Google. It is highly efficient and suitable for system-level programming, making it an excellent choice for implementing dynamic programming problems.
Implementing Fibonacci Sequence in Go using Dynamic Programming
Let’s look at the implementation of the Fibonacci sequence with the help of dynamic programming in Go.
func fib(n int) int {
fibSeq := [50]int{0, 1}
for i := 2; i <= n; i++ {
fibSeq[i] = fibSeq[i-1] + fibSeq[i-2]
}
return fibSeq[n]
}
The function `fib(n int)` takes an integer `n` as an argument, which represents the index of the Fibonacci sequence we’re interested in. The Fibonacci sequence array `fibSeq` is initialized with the known first two members, 0 and 1.
The `for loop` populates the rest of the array up to the requested member in the sequence by adding the two previous members together. Lastly, we return the required Fibonacci number.
Time Complexity Reduction
How many of you liked knowing the outcome of your exams before taking them? With dynamic programming, we effectively gain this “knowing the future” power by remembering our past computations. Consequently, instead of recalculating the same problems, we can look them up from our memory, significantly reducing the time complexity.
func fib(n int) int {
fibSeq := make(map[int]int)
if n <= 2 {
fibSeq[n] = 1
} else {
fibSeq[n] = fib(n-1) + fib(n-2)
}
return fibSeq[n]
}
By using a map instead of an array for `fibSeq`, we obtain a time complexity of O(n) instead of the O(2^n), which we would get with a naïve recursive approach.
Conclusion
As we’ve seen, dynamic programming offers an optimized solution to the Fibonacci sequence problem by storing intermediate results and avoiding repetitive calculations. Don’t you wish you could apply this to all areas of life—like cooking dinner once and then just re-heating it all week? Sadly, life demands more fresh cooking than that!
I hope you’ve enjoyed this walkthrough of implementing dynamic programming in Go for the Fibonacci sequence. Happy coding, and always remember—if your code doesn’t work, it’s a “feature,” not a bug!
Remember, the Fibonacci sequence is like a box of chocolates; even though you know what you’re going to get (a sum of the previous two), it’s always exciting to see the next number!
Signing off until next time, when we introduce another exciting topic!
