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Largest Coprime Set Between two integers

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Given two integers L and R which denotes a range, the task is to find the largest co-prime set of integers in range L to R. 
Examples: 
 

Input: L = 10, R = 25 
Output: 10 11 13 17 19 21 23
Input: L = 45, R = 57 
Output: 45 46 47 49 53 
 


 


Approach: The idea is to iterate from L to R and try to place the integer in a set such that the Greatest common divisor of the set remains 1. This can be done by storing the LCM of the set and each time before adding the element into the set check that the GCD of the number with LCM of the set remains 1. Finally, find the largest such set of the integers.
For Example: 
 

Let L = 10, R = 14

Element 10:
// Co-prime Sets 
S = {{10}},
LCM of Co-prime sets
A = {10}

Element 11:
// Element 11 can be added to
// the first set
S = {{10, 11}}
A = {110}

Element 12:
S = {{10, 11}, {12}}
A = {110, 12}

Element 13:
S = {{10, 11, 13}, {12}}
A = {1430, 12}

Element 14:
S = {{10, 11, 13}, {12}, {14}}
A = {1430, 12, 14}


 

C++

// C++ implementation to find
// the largest co-prime set in a
// given range
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the largest
// co-prime set of the integers
void findCoPrime(int n, int m)
{
    // Initialize sets
    // with starting integers
    vector<int> a = { n };
    vector<vector<int> > b = { a };
 
    // Iterate over all the possible
    // values of the integers
    for (int i = n + 1; i <= m; i++) {
 
        // lcm of each set in array
        // 'b' stored in set 'a'
        // so go through set 'a'
        for (int j = 0; j < a.size(); j++) {
            // if there gcd is 1 then
            // element add in that
            // array corresponding to b
            if (__gcd(i, a[j]) == 1) {
 
                // update the new lcm value
                int q = (i * a[j]) / __gcd(i, a[j]);
 
                b[j].push_back(i);
                a[j] = q;
            }
        }
        a.push_back(i);
        b.push_back({ i });
    }
    vector<int> maxi = {};
    for (int i = 0; i < b.size(); i++) {
        if (b[i].size() > maxi.size()) {
            maxi = b[i];
        }
    }
    for (auto i = maxi.begin(); i != maxi.end(); i++) {
        cout << *i << " ";
    }
    cout << endl;
}
 
// Driver Code
int main()
{
    int n = 10;
    int m = 14;
    findCoPrime(n, m);
    return 0;
}
 
// This code is contributed by rj13to.

                    

Java

import java.util.ArrayList;
import java.util.List;
 
public class Main {
    // Function to find the largest
    // co-prime set of the integers
    public static void findCoPrime(int n, int m)
    {
          // Initializing sets
        List<Integer> a = new ArrayList<>();
        List<List<Integer> > b = new ArrayList<>();
        a.add(n);
        List<Integer> innerList = new ArrayList<>();
        innerList.add(n);
        b.add(innerList);
        // Iterate over all the possible
        // values of the integers   
        for (int i = n + 1; i <= m; i++) {
          // lcm of each set in array
          // 'b' stored in set 'a'
          // so go through set 'a'
            for (int j = 0; j < a.size(); j++) {
                // if there gcd is 1 then
                // element add in that
                // array corresponding to b
                if (gcd(i, a.get(j)) == 1) {
                   // update the new lcm value
                    int q = (i * a.get(j)) / gcd(i, a.get(j));
                    b.get(j).add(i);
                    a.set(j, q);
                }
            }
            a.add(i);
            innerList = new ArrayList<>();
            innerList.add(i);
            b.add(innerList);
        }
 
        List<Integer> maxi = new ArrayList<>();
        for (List<Integer> list : b) {
            if (list.size() > maxi.size()) {
                maxi = list;
            }
        }
        for (Integer num : maxi) {
            System.out.print(num + " ");
        }
        System.out.println();
    }
    // Function to find the gcd of two numbers
    public static int gcd(int a, int b)
    {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }
 
    public static void main(String[] args)
    {
        int n = 10;
        int m = 14;
        findCoPrime(n, m);
    }
}

                    

Python

# Python implementation to find
# the largest co-prime set in a
# given range
 
import math
 
# Function to find the largest
# co-prime set of the integers
def findCoPrime(n, m):
    # Initialize sets
    # with starting integers
    a =[n]
    b =[[n]]
     
    # Iterate over all the possible
    # values of the integers
    for i in range(n + 1, m + 1):
     
        # lcm of each list in array
        # 'b' stored in list 'a'
        # so go through list 'a'
        for j in range(len(a)):
             
            # if there gcd is 1 then
            # element add in that
            # list corresponding to b
            if math.gcd(i, a[j])== 1:
                 
                # update the new lcm value
                q =(i * a[j])//math.gcd(i, a[j])
                r = b[j]
                r.append(i)
                b[j]= r
                a[j]= q
        else:
            a.append(i)
            b.append([i])
    maxi = []
    for i in b:
        if len(i) > len(maxi):
            maxi = i
    print(*maxi)
     
# Driver Code
if __name__ == "__main__":
    n = 10
    m = 14
    findCoPrime(n, m)

                    

C#

using System;
using System.Collections.Generic;
 
class MainClass {
   
  // Function to find the largest
  // co-prime set of the integers
  public static void findCoPrime(int n, int m) {
     
    // Initializing sets
    List<int> a = new List<int>();
    List<List<int>> b = new List<List<int>>();
    a.Add(n);
    List<int> innerList = new List<int>();
    innerList.Add(n);
    b.Add(innerList);
     
    // Iterate over all the possible
    // values of the integers   
    for (int i = n + 1; i <= m; i++) {
       
      // lcm of each set in array
      // 'b' stored in set 'a'
      // so go through set 'a'
      for (int j = 0; j < a.Count; j++) {
         
        // if there gcd is 1 then
        // element add in that
        // array corresponding to b
        if (gcd(i, a[j]) == 1) {
           
          // update the new lcm value
          int q = (i * a[j]) / gcd(i, a[j]);
          b[j].Add(i);
          a[j] = q;
        }
      }
      innerList = new List<int>();
      innerList.Add(i);
      b.Add(innerList);
      a.Add(i);
    }
 
    List<int> maxi = new List<int>();
    foreach (List<int> list in b) {
      if (list.Count > maxi.Count) {
        maxi = list;
      }
    }
    foreach (int num in maxi) {
      Console.Write(num + " ");
    }
    Console.WriteLine();
  }
 
  // Function to find the gcd of two numbers
  public static int gcd(int a, int b) {
    if (b == 0)
      return a;
    return gcd(b, a % b);
  }
 
  public static void Main(string[] args) {
    int n = 10;
    int m = 14;
    findCoPrime(n, m);
  }
}

                    

Javascript

// JavaScript implementation to find
// the largest co-prime set in a
// given range
 
// Function to find the largest
// co-prime set of the integers
function findCoPrime(n, m) {
// Initialize sets
// with starting integers
let a = [n];
let b = [[n]];
 
// Iterate over all the possible
// values of the integers
for (let i = n + 1; i <= m; i++) {
// lcm of each list in array
// 'b' stored in list 'a'
// so go through list 'a'
for (let j = 0; j < a.length; j++) {
 
  // if there gcd is 1 then
  // element add in that
  // list corresponding to b
  if (gcd(i, a[j]) === 1) {
 
    // update the new lcm value
    let q = (i * a[j]) / gcd(i, a[j]);
    let r = b[j];
    r.push(i);
    b[j] = r;
    a[j] = q;
  }
}
// if the current number is not co-prime with any
// existing number in a, then add it as a new set to a and b
if (!a.includes(i)) {
  a.push(i);
  b.push([i]);
}
}
 
let maxi = [];
for (let i = 0; i < b.length; i++) {
if (b[i].length > maxi.length) {
maxi = b[i];
}
}
console.log(...maxi);
}
 
// Utility function to find gcd of 2 numbers
function gcd(a, b) {
if (b === 0) return a;
return gcd(b, a % b);
}
 
// Driver Code
let n = 10;
let m = 14;
findCoPrime(n, m);

                    

Output: 
10 11 13

 


Last Updated : 09 Mar, 2023
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