Step by Step solution about How to resolve the algorithm Magnanimous numbers step by step in the Go programming language

The provided Go code is designed to identify and list "magnanimous" numbers within a specified range. Magnanimous numbers are defined as follows:

• Magnanimous numbers must be greater than or equal to 10.
• For a magnanimous number n, the sum of its digits (p) and the remainder when divided by 10 (q) must form a prime number.
• This condition must hold for all possible "p" and "q" values as you repeatedly divide n by 10.

The code addresses this task through the following key functions:

1. isPrime(n): Checks if a given number n is prime. It employs a simple optimization to handle common prime numbers less than 10. For larger numbers, it employs a loop to check for divisibility up to the square root of n.

2. ord(n): Converts a number n to its ordinal representation (e.g., 1st, 2nd, 3rd, etc.).

3. isMagnanimous(n): Determines if n is a magnanimous number by repeatedly dividing it by 10, checking if the sum of digits and the remainder form a prime number, and stopping when the quotient becomes less than 10.

4. listMags(from, thru, digs, perLine): Lists magnanimous numbers within a specified range. It iterates through numbers, checks for magnanimity, and prints them in a formatted manner, with options to customize the number of digits displayed and the number of values per line.

In the main function, the program showcases the functionality by listing magnanimous numbers in specific ranges:

• From 1 to 45, displayed with three digits and 15 numbers per line.
• From 241 to 250, displayed with one digit and 10 numbers per line.
• From 391 to 400, displayed with one digit and 10 numbers per line.

Overall, this code efficiently identifies and lists magnanimous numbers within specified ranges, demonstrating features such as prime number checking, ordinal number conversion, and customizable output formatting.

package main

import "fmt"

// OK for 'small' numbers.
func isPrime(n uint64) bool {
    switch {
    case n < 2:
        return false
    case n%2 == 0:
        return n == 2
    case n%3 == 0:
        return n == 3
    default:
        d := uint64(5)
        for d*d <= n {
            if n%d == 0 {
                return false
            }
            d += 2
            if n%d == 0 {
                return false
            }
            d += 4
        }
        return true
    }
}

func ord(n int) string {
    m := n % 100
    if m >= 4 && m <= 20 {
        return fmt.Sprintf("%dth", n)
    }
    m %= 10
    suffix := "th"
    if m < 4 {
        switch m {
        case 1:
            suffix = "st"
        case 2:
            suffix = "nd"
        case 3:
            suffix = "rd"
        }
    }
    return fmt.Sprintf("%d%s", n, suffix)
}

func isMagnanimous(n uint64) bool {
    if n < 10 {
        return true
    }
    for p := uint64(10); ; p *= 10 {
        q := n / p
        r := n % p
        if !isPrime(q + r) {
            return false
        }
        if q < 10 {
            break
        }
    }
    return true
}

func listMags(from, thru, digs, perLine int) {
    if from < 2 {
        fmt.Println("\nFirst", thru, "magnanimous numbers:")
    } else {
        fmt.Printf("\n%s through %s magnanimous numbers:\n", ord(from), ord(thru))
    }
    for i, c := uint64(0), 0; c < thru; i++ {
        if isMagnanimous(i) {
            c++
            if c >= from {
                fmt.Printf("%*d ", digs, i)
                if c%perLine == 0 {
                    fmt.Println()
                }
            }
        }
    }
}

func main() {
    listMags(1, 45, 3, 15)
    listMags(241, 250, 1, 10)
    listMags(391, 400, 1, 10)
}