Given two positive integers L and R, the task is to find an integer X greater than 1 such that X is co-prime with all the integers from the range [L, R].
Examples:
Input: L = 16, R = 17
Output: 19
Explanation: Only number which is co-prime with all the integers from the range [16, 17] is 9.Input: L = 973360, R = 973432
Output: 973439
Approach: The simplest approach to solve the given problem is to find a prime number greater than R, because this integer does not divide any integer in the range of [L, R]. Therefore, the idea is to iterate from the value (R + 1) and if there exists any integer which is prime, then print that integer and break out of the loop.
Below is the implementation of the above approach:
C++
// C++ program for the above approach#include <bits/stdc++.h>using namespace std;// Function to check whether the// given number N is prime or notbool isPrime(int N){ // Base Case if (N == 1) return false; for (int i = 2; i * i <= N; i++) { // If N has more than one // factor, then return false if (N % i == 0) return false; } // Otherwise, return true return true;}// Function to find X which is co-prime// with the integers from the range [L, R]int findCoPrime(int L, int R){ // Store the resultant number int coPrime; // Check for prime integers // greater than R for (int i = R + 1;; i++) { // If the current number is // prime, then update coPrime // and break out of loop if (isPrime(i)) { coPrime = i; break; } } // Print the resultant number return coPrime;}// Driver Codeint main(){ int L = 16, R = 17; cout << findCoPrime(L, R); return 0;} |
Java
// Java program for the above approachimport java.io.*;import java.lang.*;import java.util.*;class GFG{// Function to check whether the// given number N is prime or notstatic boolean isPrime(int N){ // Base Case if (N == 1) return false; for(int i = 2; i * i <= N; i++) { // If N has more than one // factor, then return false if (N % i == 0) return false; } // Otherwise, return true return true;}// Function to find X which is co-prime// with the integers from the range [L, R]static int findCoPrime(int L, int R){ // Store the resultant number int coPrime; // Check for prime integers // greater than R for(int i = R + 1;; i++) { // If the current number is // prime, then update coPrime // and break out of loop if (isPrime(i)) { coPrime = i; break; } } // Print the resultant number return coPrime;}// Driver Codepublic static void main(String[] args){ int L = 16, R = 17; System.out.println(findCoPrime(L, R));}}// This code is contributed by Kingash |
Python3
# Python3 program for the above approach# Function to check whether the# given number N is prime or notdef isPrime(N): # Base Case if (N == 1): return False for i in range(2, N + 1): if i*i > N: break # If N has more than one # factor, then return false if (N % i == 0): return False # Otherwise, return true return True# Function to find X which is co-prime# with the integers from the range [L, R]def findCoPrime(L, R): # Store the resultant number coPrime, i = 0, R + 1 # Check for prime integers # greater than R while True: # If the current number is # prime, then update coPrime # and break out of loop if (isPrime(i)): coPrime = i break i += 1 # Print the resultant number return coPrime# Driver Codeif __name__ == '__main__': L,R = 16, 17 print (findCoPrime(L, R))# This code is contributed by mohit kumar 29. |
C#
// C# program for the above approachusing System;class GFG{// Function to check whether the// given number N is prime or notstatic bool isPrime(int N){ // Base Case if (N == 1) return false; for(int i = 2; i * i <= N; i++) { // If N has more than one // factor, then return false if (N % i == 0) return false; } // Otherwise, return true return true;}// Function to find X which is co-prime// with the integers from the range [L, R]static int findCoPrime(int L, int R){ // Store the resultant number int coPrime; // Check for prime integers // greater than R for(int i = R + 1;; i++) { // If the current number is // prime, then update coPrime // and break out of loop if (isPrime(i)) { coPrime = i; break; } } // Print the resultant number return coPrime;}// Driver Codepublic static void Main(string[] args){ int L = 16, R = 17; Console.WriteLine(findCoPrime(L, R));}}// This code is contributed by ukasp |
Javascript
<script>// javascript program for the above approach// Function to check whether the// given number N is prime or notfunction isPrime(N){ // Base Case if (N == 1) return false; for(var i = 2; i * i <= N; i++) { // If N has more than one // factor, then return false if (N % i == 0) return false; } // Otherwise, return true return true;}// Function to find X which is co-prime// with the integers from the range [L, R]function findCoPrime(L , R){ // Store the resultant number var coPrime; // Check for prime integers // greater than R for(var i = R + 1;; i++) { // If the current number is // prime, then update coPrime // and break out of loop if (isPrime(i)) { coPrime = i; break; } } // Print the resultant number return coPrime;}// Driver Codevar L = 16, R = 17;document.write(findCoPrime(L, R));// This code contributed by Princi Singh </script> |
Output:
19
Time Complexity: O(L * R1/2)
Auxiliary Space: O(1)
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