Given a number 
. The task is to find all such numbers less than N and are a product of exactly two distinct prime numbers.
For Example, 33 is the product of two distinct primes i.e 11 * 3, whereas numbers like 60 which has three distinct prime factors i.e 2 * 2 * 3 * 5.
Note: These numbers cannot be a perfect square.
Examples:
Input : N = 30
Output : 6, 10, 14, 15, 21, 22, 26
Input : N = 50
Output : 6, 10, 14, 15, 21, 22, 26, 33, 34, 35, 38, 39, 46
Algorithm:
- Traverse till N and check whether each number has exactly two prime factors or not.
- Now to avoid the situation like 49 having 7 * 7 product of two prime numbers, check whether the number is a perfect square or not to ensure that it has two distinct prime.
- If Step 1 and Step 2 satisfies then add the number in the vector list.
- Traverse the vector and print all the elements in it.
Below is the implementation of the above approach:
C++
// C++ program to find numbers that are product// of exactly two distinct prime numbers#include <bits/stdc++.h>using namespace std;// Function to check whether a number// is a PerfectSquare or notbool isPerfectSquare(long double x){ long double sr = sqrt(x); return ((sr - floor(sr)) == 0);}// Function to check if a number is a// product of exactly two distinct primesbool isProduct(int num){ int cnt = 0; for (int i = 2; cnt < 2 && i * i <= num; ++i) { while (num % i == 0) { num /= i; ++cnt; } } if (num > 1) ++cnt; return cnt == 2;}// Function to find numbers that are product// of exactly two distinct prime numbers.void findNumbers(int N){ // Vector to store such numbers vector<int> vec; for (int i = 1; i <= N; i++) { if (isProduct(i) && !isPerfectSquare(i)) { // insert in the vector vec.push_back(i); } } // Print all numbers till n from the vector for (int i = 0; i < vec.size(); i++) { cout << vec[i] << " "; }}// Driver functionint main(){ int N = 30; findNumbers(N); return 0;} |
Java
// Java program to find numbers that are product// of exactly two distinct prime numbersimport java.util.*; class GFG{// Function to check whether a number// is a PerfectSquare or notstatic boolean isPerfectSquare(double x){ double sr = Math.sqrt(x); return ((sr - Math.floor(sr)) == 0);}// Function to check if a number is a// product of exactly two distinct primesstatic boolean isProduct(int num){ int cnt = 0; for (int i = 2; cnt < 2 && i * i <= num; ++i) { while (num % i == 0) { num /= i; ++cnt; } } if (num > 1) ++cnt; return cnt == 2;}// Function to find numbers that are product// of exactly two distinct prime numbers.static void findNumbers(int N){ // Vector to store such numbers Vector<Integer> vec = new Vector<Integer>(); for (int i = 1; i <= N; i++) { if (isProduct(i) && !isPerfectSquare(i)) { // insert in the vector vec.add(i); } } // Print all numbers till n from the vector Iterator<Integer> itr = vec.iterator(); while(itr.hasNext()){ System.out.print(itr.next()+" "); } }// Driver functionpublic static void main(String[] args){ int N = 30; findNumbers(N);}}// This Code is Contributed by mits |
Python 3
# Python 3 program to find numbers that are product# of exactly two distinct prime numbersimport math # Function to check whether a number# is a PerfectSquare or notdef isPerfectSquare(x): sr = math.sqrt(x) return ((sr - math.floor(sr)) == 0)# Function to check if a number is a# product of exactly two distinct primesdef isProduct( num): cnt = 0 i = 2 while cnt < 2 and i * i <= num: while (num % i == 0) : num //= i cnt += 1 i += 1 if (num > 1): cnt += 1 return cnt == 2 # Function to find numbers that are product# of exactly two distinct prime numbers.def findNumbers(N): # Vector to store such numbers vec = [] for i in range(1,N+1) : if (isProduct(i) and not isPerfectSquare(i)) : # insert in the vector vec.append(i) # Print all numbers till n from the vector for i in range(len( vec)): print(vec[i] ,end= " ") # Driver functionif __name__=="__main__": N = 30 findNumbers(N) |
C#
// C# program to find numbers that are product // of exactly two distinct prime numbers using System;using System.Collections.Generic;class GFG{ // Function to check whether a number // is a PerfectSquare or not static bool isPerfectSquare(double x) { double sr = Math.Sqrt(x); return ((sr - Math.Floor(sr)) == 0); } // Function to check if a number is a // product of exactly two distinct primes static bool isProduct(int num) { int cnt = 0; for (int i = 2; cnt < 2 && i * i <= num; ++i) { while (num % i == 0) { num /= i; ++cnt; } } if (num > 1) ++cnt; return cnt == 2; } // Function to find numbers that are product // of exactly two distinct prime numbers. static void findNumbers(int N) { // Vector to store such numbers List<int> vec = new List<int>(); for (int i = 1; i <= N; i++) { if (isProduct(i) && !isPerfectSquare(i)) { // insert in the vector vec.Add(i); } } // Print all numbers till n from the vector foreach(var a in vec) Console.Write(a + " "); } // Driver code public static void Main(String[] args) { int N = 30; findNumbers(N); } } // This code has been contributed by 29AjayKumar |
PHP
<?php// PHP program to find numbers that are product// of exactly two distinct prime numbers// Function to check whether a number// is a PerfectSquare or notfunction isPerfectSquare($x){ $sr = sqrt($x); return (($sr - floor($sr)) == 0);}// Function to check if a number is a// product of exactly two distinct primesfunction isProduct($num){ $cnt = 0; for ($i = 2; $cnt < 2 && $i * $i <= $num; ++$i) { while ($num % $i == 0) { $num /= $i; ++$cnt; } } if ($num > 1) ++$cnt; return $cnt == 2;}// Function to find numbers that are product// of exactly two distinct prime numbers.function findNumbers($N){ // Vector to store such numbers $vec = array(); for ($i = 1; $i <= $N; $i++) { if (isProduct($i) && !isPerfectSquare($i)) { // insert in the vector array_push($vec, $i); } } // Print all numbers till n from the vector for ($i = 0; $i < sizeof($vec); $i++) { echo $vec[$i] . " "; }}// Driver Code$N = 30;findNumbers($N);// This code is contributed by ita_c |
Javascript
<script>// Javascript program to find numbers that are product // of exactly two distinct prime numbers // Function to check whether a number // is a PerfectSquare or not function isPerfectSquare(x) { sr = Math.sqrt(x); return ((sr - Math.floor(sr)) == 0); } // Function to check if a number is a // product of exactly two distinct primes function isProduct(num) { var cnt = 0; for(var i = 2; cnt < 2 && (i * i) <= num; ++i) { while (num % i == 0) { num = parseInt(num / i); ++cnt; } } if (num > 1) ++cnt; return cnt == 2; } // Function to find numbers that are product // of exactly two distinct prime numbers. function findNumbers( N) { // Vector to store such numbers vec = []; for (var i = 1; i <= N; i++) { if (isProduct(i) && !isPerfectSquare(i)) { // insert in the vector vec.push(i); } } // Print all numbers till n from the vector for (var i = 0; i < vec.length; i++) { document.write(vec[i] + " "); } } // Driver function var N = 30; findNumbers(N);// This code is contributed by noob2000.</script> |
Output:
6 10 14 15 21 22 26
Time Complexity: O(*)
Auxiliary Space: O(n) , since n extra space has been taken.
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