The Memoization Technique

Memoization is a technique that is used to speed up the execution of a function by storing the results of expensive function calls and returning the cached result when the same input occurs again. This can be particularly useful for algorithms that have a large number of recursive calls or for functions that are called multiple times with the same input.

In Go, it is easy to implement memoization using a simple map. For example, consider the following function that calculates the nth number in the Fibonacci sequence:

func fib(n int) int {
  if n == 0 || n == 1 {
    return n
  }
  return fib(n-1) + fib(n-2)
}

This function has a time complexity of O(2^n), which can be very slow for large values of n. We can use memoization to speed up the function by storing the results of each recursive call in a map:

var cache = make(map[int]int)

func fib(n int) int {
  if n == 0 || n == 1 {
    return n
  }
  if v, ok := cache[n]; ok {
    return v
  }
  result := fib(n-1) + fib(n-2)
  cache[n] = result
  return result
}

Now, the time complexity of the function is O(n), which is much faster for large values of n.

One thing to note is that the map used for memoization should be declared as a global variable, since it needs to be accessible from all recursive calls. It is also a good idea to clear the map after each function call, to avoid using up too much memory.

Overall, memoization is a simple but powerful technique for optimizing the performance of recursive functions in Go. It is especially useful for functions that are called multiple times with the same input, and can significantly improve the speed of your program.