Recursive performance test

Let's start with a familiar piece of code

package main
import (
    "fmt"
    "time"
)
func main() {
    
    result := 0
    start := time.Now()
    for i := 1; i <= 40; i++ {
    
        result = fibonacci(i)
        fmt.Printf(" Sequence number  %d  position : %d\n", i, result)
    }
    end := time.Now()
    delta := end.Sub(start)
    fmt.Printf(" The execution time of the program is : %s\n", delta)
}
func fibonacci(n int) (res int) {
    
    if n <= 2 {
    
        res = 1
    } else {
    
        res = fibonacci(n-1) + fibonacci(n-2)
    }
    return
}

I feel that the implementation should be fast
But the implementation results are slow , as follows ：
``shell
Sequence number 1 position : 1
Sequence number 2 position : 1
Sequence number 3 position : 2
Sequence number 4 position : 3
Sequence number 5 position : 5
Sequence number 6 position : 8
Sequence number 7 position : 13
Sequence number 8 position : 21
Sequence number 9 position : 34
Sequence number 10 position : 55
Sequence number 11 position : 89
Sequence number 12 position : 144
Sequence number 13 position : 233
Sequence number 14 position : 377
Sequence number 15 position : 610
Sequence number 16 position : 987
Sequence number 17 position : 1597
Sequence number 18 position : 2584
Sequence number 19 position : 4181
Sequence number 20 position : 6765
Sequence number 21 position : 10946
Sequence number 22 position : 17711
Sequence number 23 position : 28657
Sequence number 24 position : 46368
Sequence number 25 position : 75025
Sequence number 26 position : 121393
Sequence number 27 position : 196418
Sequence number 28 position : 317811
Sequence number 29 position : 514229
Sequence number 30 position : 832040
Sequence number 31 position : 1346269
Sequence number 32 position : 2178309
Sequence number 33 position : 3524578
Sequence number 34 position : 5702887
Sequence number 35 position : 9227465
Sequence number 36 position : 14930352
Sequence number 37 position : 24157817
Sequence number 38 position : 39088169
Sequence number 39 position : 63245986
Sequence number 40 position : 102334155
Sequence number 41 position : 165580141
Sequence number 42 position : 267914296
Sequence number 43 position : 433494437
Sequence number 44 position : 701408733
The execution time of the program is : 6.36509246s

 When 40 Change it to 50 When , It's almost impossible to wait for the result 
 The improved code is as follows ：
```go
package main
import (
    "fmt"
    "time"
)
const LIM = 41
var fibs [LIM]uint64
func main() {
    var result uint64 = 0
    start := time.Now()
    for i := 1; i < LIM; i++ {
        result = fibonacci(i)
        fmt.Printf(" Sequence number  %d  position : %d\n", i, result)
    }
    end := time.Now()
    delta := end.Sub(start)
    fmt.Printf(" The execution time of the program is : %s\n", delta)
}
func fibonacci(n int) (res uint64) {
    //  Memorize ： Check whether Fibonacci is known in the array （n）
    if fibs[n] != 0 {
        res = fibs[n]
        return
    }
    if n <= 2 {
        res = 1
    } else {
        res = fibonacci(n-1) + fibonacci(n-2)
    }
    fibs[n] = res
    return
}