给定一个整数N ，任务是找到直至给定整数N的所有不同的互素数集，以使一个元素出现的次数不超过一个集合。
A number a is said to be co-prime with b if GCD(a, b) = 1.
例子：
Input: N = 5
Output: (1, 2) (3, 4, 5)
Input: N = 6
Output: (1, 2) (3, 4) (5, 6)
方法：
- 为了解决上述问题，我们可以观察到，如果N小于4，则所有元素都已经互质素数直到N，因为它们的GCD始终为1。因此，对于N = [1，3]，可能互素集分别是(1)，(1、2)和(1、2、3)。
- 对于N> 3的所有值，有两种可能的情况：
- 如果N的值是偶数，则每个集合将包含2个相邻的元素，直到N个本身为止，因为相邻的数字始终互质为互素。
- 如果整数N的值是奇数，则每个集合将包含2个相邻元素，但最后一个集合将具有最后三个元素。
下面是上述方法的实现：
C++
// C++ implementation to print
// all distinct co-prime sets
// possible for numbers from 1 to N
#include
using namespace std;
// Function to print all coprime sets
void coPrimeSet(int n)
{
int firstadj, secadj;
// Check if n is less than 4
// then simply print all values till n
if (n < 4) {
cout << "( ";
for (int i = 1; i <= n; i++)
cout << i << ", ";
cout << ")\n";
}
// For all the values of n > 3
else {
// Check if n is even
// then every set will contain
// 2 adjacent elements up-to n
if (n % 2 == 0) {
for (int i = 0; i < n / 2; i++) {
firstadj = 2 * i + 1;
secadj = 2 * i + 2;
cout << "(" << firstadj
<< ", " << secadj << ")\n";
}
}
else {
// if n is odd then every set will
// contain 2 adjacent element
// except the last set which
// will have last three elements
for (int i = 0; i < n / 2 - 1; i++)
{
firstadj = 2 * i + 1;
secadj = 2 * i + 2;
cout << "(" << firstadj
<< ", " << secadj << ")\n";
}
// Last element for odd case
cout << "(" << n - 2 << ", " << n - 1
<< ", " << n << ")\n";
}
}
}
// Driver Code
int main()
{
int n = 5;
coPrimeSet(n);
return 0;
} Java
// Java implementation to print
// all distinct co-prime sets
// possible for numbers from 1 to N
import java.util.*;
class GFG{
// Function to print all co-prime sets
static void coPrimeSet(int n)
{
int firstadj, secadj;
// Check if n is less than 4 then
// simply print all values till n
if (n < 4)
{
System.out.print("( ");
for(int i = 1; i <= n; i++)
System.out.print(i + ", ");
System.out.print(")\n");
}
// For all the values of n > 3
else
{
// Check if n is even then
// every set will contain
// 2 adjacent elements up-to n
if (n % 2 == 0)
{
for(int i = 0; i < n / 2; i++)
{
firstadj = 2 * i + 1;
secadj = 2 * i + 2;
System.out.print("(" + firstadj +
", " + secadj + ")\n");
}
}
else
{
// If n is odd then every set will
// contain 2 adjacent element
// except the last set which
// will have last three elements
for(int i = 0; i < n / 2 - 1; i++)
{
firstadj = 2 * i + 1;
secadj = 2 * i + 2;
System.out.print("(" + firstadj +
", " + secadj + ")\n");
}
// Last element for odd case
System.out.print("(" + (n - 2) +
", " + ( n - 1) +
", " + n + ")\n");
}
}
}
// Driver code
public static void main(String[] args)
{
int n = 5;
coPrimeSet(n);
}
}
// This code is contributed by sapnasingh4991Python3
# Python3 implementation to print
# all distinct co-prime sets
# possible for numbers from 1 to N
# Function to prall co-prime sets
def coPrimeSet(n):
firstadj = 0;
secadj = 0;
# Check if n is less than 4 then
# simply prall values till n
if (n < 4):
print("( ");
for i in range(1, n + 1):
print(i + ", ");
print(")");
# For all the values of n > 3
else:
# Check if n is even then
# every set will contain
# 2 adjacent elements up-to n
if (n % 2 == 0):
for i in range(0, n /2 ):
firstadj = 2 * i + 1;
secadj = 2 * i + 2;
print("(", firstadj, ", ",
secadj, ")");
else:
# If n is odd then every set will
# contain 2 adjacent element
# except the last set which
# will have last three elements
for i in range(0, int(n / 2) - 1):
firstadj = 2 * i + 1;
secadj = 2 * i + 2;
print("(", firstadj, ", ",
secadj, ")");
# Last element for odd case
print("(", (n - 2), ", ",
(n - 1), ", ", n, ")");
# Driver code
if __name__ == '__main__':
n = 5;
coPrimeSet(n);
# This code is contributed by 29AjayKumarC#
// C# implementation to print
// all distinct co-prime sets
// possible for numbers from 1 to N
using System;
class GFG{
// Function to print all co-prime sets
static void coPrimeSet(int n)
{
int firstadj, secadj;
// Check if n is less than 4 then
// simply print all values till n
if (n < 4)
{
Console.Write("( ");
for(int i = 1; i <= n; i++)
Console.Write(i + ", ");
Console.Write(")\n");
}
// For all the values of n > 3
else
{
// Check if n is even then
// every set will contain
// 2 adjacent elements up-to n
if (n % 2 == 0)
{
for(int i = 0; i < n / 2; i++)
{
firstadj = 2 * i + 1;
secadj = 2 * i + 2;
Console.Write("(" + firstadj +
", " + secadj + ")\n");
}
}
else
{
// If n is odd then every set will
// contain 2 adjacent element
// except the last set which
// will have last three elements
for(int i = 0; i < n / 2 - 1; i++)
{
firstadj = 2 * i + 1;
secadj = 2 * i + 2;
Console.Write("(" + firstadj +
", " + secadj + ")\n");
}
// Last element for odd case
Console.Write("(" + (n - 2) +
", " + (n - 1) +
", " + n + ")\n");
}
}
}
// Driver code
public static void Main()
{
int n = 5;
coPrimeSet(n);
}
}
// This code is contributed by Code_Mech输出：
(1, 2)
(3, 4, 5)