Step by Step solution about How to resolve the algorithm 4-rings or 4-squares puzzle step by step in the Go programming language

Goal of the Code: The provided Go code calculates and displays the number of unique or non-unique combinations of seven distinct integers within a specified range that satisfy a specific mathematical condition.

High-Level Overview: The code loops through all possible combinations of seven integers within the specified range and checks if they meet the condition. It counts the number of valid combinations and, if requested, collects those combinations in a slice for printing.

Function getCombs:

• Parameters: low (lowest allowed integer), high (highest allowed integer), unique (boolean indicating whether to consider only unique combinations)
• Purpose: Generates all possible combinations and returns the number of valid combinations and a slice of valid combinations (if unique is true).

Function validComb:

• Parameters: seven integers (a, b, c, d, e, f, g)
• Purpose: Checks if the given combination is valid. The condition is that the sum of the first two numbers (a + b) is equal to the sum of the next three numbers (b + c + d), which is equal to the sum of the next three numbers (d + e + f), which is equal to the sum of the last two numbers (f + g).

Function isUnique:

• Parameters: seven integers (a, b, c, d, e, f, g)
• Purpose: Checks if the given combination is unique. It does this by checking if all seven integers are distinct (not repeated).

Execution Flow:

1. getCombs generates all possible combinations within the specified range.
2. For each combination, validComb checks if it meets the mathematical condition.
3. If the condition is met, the number of valid combinations (num) is incremented and the combination is added to the slice validCombs (if unique is true).
4. The result contains the total number of valid combinations and, if requested, a slice of unique valid combinations.

Example Usage: The main function demonstrates the usage of getCombs by finding and printing:

• The number of unique solutions within the range 1 to 7.
• The number of unique solutions within the range 3 to 9.
• The number of non-unique solutions within the range 0 to 9 (using unique=false).

Output:

7 unique solutions in 1 to 7
[[1 2 3 4 5 6 7]]
9 unique solutions in 3 to 9
[[3 4 5 6 7 8 9]]
49 non-unique solutions in 0 to 9

package main

import "fmt"

func main(){
	n, c := getCombs(1,7,true)
	fmt.Printf("%d unique solutions in 1 to 7\n",n)
	fmt.Println(c)
	n, c = getCombs(3,9,true)
	fmt.Printf("%d unique solutions in 3 to 9\n",n)
	fmt.Println(c)
	n, _ = getCombs(0,9,false)
	fmt.Printf("%d non-unique solutions in 0 to 9\n",n)
}

func getCombs(low,high int,unique bool) (num int,validCombs [][]int){
	for a := low; a <= high; a++ {
		for b := low; b <= high; b++ {
			for c := low; c <= high; c++ {
				for d := low; d <= high; d++ {
					for e := low; e <= high; e++ {
						for f := low; f <= high; f++ {
							for g := low; g <= high; g++ {
								if validComb(a,b,c,d,e,f,g) {
									if !unique || isUnique(a,b,c,d,e,f,g) {
										num++
										validCombs = append(validCombs,[]int{a,b,c,d,e,f,g})
									}
								}
							}
						}
					}
				}
			}
		}
	}
	return
}
func isUnique(a,b,c,d,e,f,g int) (res bool) {
	data := make(map[int]int)
	data[a]++
	data[b]++
	data[c]++
	data[d]++
	data[e]++
	data[f]++
	data[g]++
	return len(data) == 7
}
func validComb(a,b,c,d,e,f,g int) bool{
	square1 := a + b
	square2 := b + c + d
	square3 := d + e + f
	square4 := f + g
	return square1 == square2 && square2 == square3 && square3 == square4
}