Step by Step solution about How to resolve the algorithm Benford's law step by step in the Go programming language

This Go program generates and analyzes the first 1000 Fibonacci numbers. A detailed breakdown of the code:

1. Package and Imports:

   • The program starts with the package main declaration, indicating that it's the entry point of the executable.
   • It imports the fmt package for input and output and the math package for mathematical functions.

2. Fib1000 Function:

   • This function generates the first 1000 Fibonacci numbers and stores them in a slice r.
   • It uses the classic Fibonacci sequence calculation: starting with a and b as 0 and 1, it repeatedly calculates the next Fibonacci number as a + b and updates a and b accordingly.
   • The loop iterates 1000 times to fill the r slice.

3. main Function:

   • This function is the program's entry point.
   • It calls the Fib1000 function to generate the Fibonacci numbers.

4. show Function:

   • This function takes a slice of Fibonacci numbers c and a title title as input.
   • It initializes a slice f of length 9 to count the occurrences of each digit (1-9) in the Fibonacci numbers.
   • It iterates over the c slice, incrementing the corresponding element in f for each Fibonacci number.
   • It then prints the title and a table with three columns: "Digit" (representing the digits 1-9), "Observed" (percentage of observed occurrences of each digit), and "Predicted" (percentage of predicted occurrences of each digit).
   • The predicted occurrences are calculated using the formula math.Log10(1+1/float64(i+1)), where i is the digit index.

5. Program Execution:

   • The program executes the main function.
   • The Fib1000 function generates the first 1000 Fibonacci numbers and passes them to the show function.
   • The show function analyzes the digits of these numbers and prints the results.

This program demonstrates how to generate and analyze large sequences of numbers using loops, slices, and mathematical functions in Go. It also illustrates how to count and compare observed and predicted occurrences of digits in a dataset.

package main

import (
    "fmt"
    "math"
)

func Fib1000() []float64 {
    a, b, r := 0., 1., [1000]float64{}
    for i := range r {
        r[i], a, b = b, b, b+a
    }
    return r[:]
}

func main() {
    show(Fib1000(), "First 1000 Fibonacci numbers")
}

func show(c []float64, title string) {
    var f [9]int
    for _, v := range c {
        f[fmt.Sprintf("%g", v)[0]-'1']++
    }
    fmt.Println(title)
    fmt.Println("Digit  Observed  Predicted")
    for i, n := range f {
        fmt.Printf("  %d  %9.3f  %8.3f\n", i+1, float64(n)/float64(len(c)),
            math.Log10(1+1/float64(i+1)))
    }
}