[Swift] What I learned about Memoization

2021/5/27 20:16
Recently, I go to the college for studying programming again. At first, I imagined it is boring because I knew everything.
Although, The terminology of 'memoization' is very impressive and motivated me to learn new things. Today, I want to share a good effect and show an example. I learned by Javascript in the class so I will try use Swift.

What is Memoization

According to Wikipedia, memoization is an optimization technique used primarily to speed up computer programs by storing the results of expensive function calls and returning the cached result when the same inputs occur again. Memoization has also been used in other contexts (and for purposes other than speed gains), such as in simple mutually recursive descent parsing.
Sometimes, we use the recursive function to simplify the complicated algorithm.
However, it may become the reason to slow down. Then, you need to change the algorithm or use memoization.


For example, there is one of the famous algorithms 'fibonacci sequence'. You'll see the simple code below.
func fibonacci(_ n: Int) -> Int {
  n < 2 ? n : fibonacci(n-1) + fibonacci(n-2)
This is the most simple solution. If given number is more than 2, calculate the sum of the last two number.
If you are interested in more details about fibonacci, please search yourself.
On the other hand, let's code with memoization.
var cache = [Int: Int]()
func cachedFibonacci(_ n: Int) -> Int {
  if let v = cache[n] {
    return v

  let newValue = n < 2 ? n : cachedFibonacci(n-1) + cachedFibonacci(n-2)
  cache[n] = newValue
  return newValue
This example code is quiet manual but very useful.

Comparing methods

we can measure time since Jan, 1, 2001 to use CFAbsoluteTimeGetCurrent in Xcode playground.
At this time, it is enable to get the difference to call this function with calling fibonacci function before and after, and calculate the gap of them.
let start1 = CFAbsoluteTimeGetCurrent()
let diff1 = CFAbsoluteTimeGetCurrent() - start1

// 0.05279099941253662

let start2 = CFAbsoluteTimeGetCurrent()
let diff2 = CFAbsoluteTimeGetCurrent() - start2

// 0.00033092498779296875
Obviously, time with memoization is 100 times faster than the one without memoization.
This is the reason why we should implement the algorithm.


Today, I introduced about memoization with using fibonacci sequence.
Actually when measured the time gap, you can see the necessarily.
If you faced to the issue like slow functions, I hope you recall this article.
Thank you! Enjoy your coding.