# Largest Coprime Set Between two integers

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 ``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 > 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 a = ``new` `ArrayList<>();``        ``List > b = ``new` `ArrayList<>();``        ``a.add(n);``        ``List 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 maxi = ``new` `ArrayList<>();``        ``for` `(List 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> b = ``new` `List>();``    ``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`

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