# K-Primes (Numbers with k prime factors) in a range

• Difficulty Level : Hard
• Last Updated : 23 Jun, 2022

Given three integers A, B and K. We need to find no. of K-prime numbers in the range [A, B]. A number is called K-prime if it has exactly K distinct prime factors.

Examples:

```Input : A = 4, B = 10, K = 2.
Output : 6 10
Given range is [4, 5, 6, 7, 8, 9, 10].
From the above range 6 and 10 have 2 distinct
prime factors, 6 = 3*2; 10 = 5*2.

Input : A = 14, B = 18, K = 2.
Output : 14 15 18
Range = [14, 15].
Both 14, 15 and 18 have 2 distinct prime factors,
14 = 7*2, 15 = 3*5 and 18 = 2*3*3```

A simple solution is to traverse through given range. For every element of the range, find its prime factors. Finally print all those numbers whose prime factors are k.

An efficient solution is to use Sieve Of Eratosthenes Algorithm

```prime[n] = {true};
for (int p=2; p*p<=n; p++)
{
// If prime[p] is not changed, then
// it is a prime
if (prime[p] == true)
{
// Update all multiples of p
for (int i=p*2; i<=n; i += p)
prime[i] = false;
}
}
```

If we observe the above algorithm clearly it has a property of iterating through all the multiples of prime numbers less than N. So the number of times the algorithm marks a number not prime is equal to the number of prime factors of that number. To achieve this, maintain an array called marked and increase the count of a number every time when it is marked as not prime by the algorithm. And in the next step, we iterate through all the numbers in the range [A, B] and increase our count of k-prime numbers if marked[number] == K.

## C++

 `// CPP program to count all those numbers in``// given range whose count of prime factors``// is k``#include ``using` `namespace` `std;` `void` `printKPFNums(``int` `A, ``int` `B, ``int` `K)``{``    ``// Count prime factors of all numbers``    ``// till B.``    ``bool` `prime[B+1] = { ``true` `};``    ``int` `p_factors[B+1] = { 0 };``    ``for` `(``int` `p = 2; p <= B; p++)``        ``if` `(p_factors[p] == 0)``            ``for` `(``int` `i = p; i <= B; i += p)``                ``p_factors[i]++;` `    ``// Print all numbers with k prime factors``    ``for` `(``int` `i = A; i <= B; i++)``        ``if` `(p_factors[i] == K)``            ``cout << i << ``" "``;``}` `// Driver code``int` `main()``{``    ``int` `A = 14, B = 18, K = 2;``    ``printKPFNums(A, B, K);``    ``return` `0;``}`

## Java

 `// Java program to count``// all those numbers in``// given range whose count``// of prime factors``// is k` `import` `java.io.*;``import` `java.util.*;` `class` `GFG {``    ` `    ``static` `void` `printKPFNums(``int` `A, ``int` `B, ``int` `K)``    ``{``        ``// Count prime factors of all numbers``        ``// till B.``        ``int` `p_factors[] = ``new` `int``[B+``1``];``        ``Arrays.fill(p_factors,``0``);` `        ``for` `(``int` `p = ``2``; p <= B; p++)``            ``if` `(p_factors[p] == ``0``)``                ``for` `(``int` `i = p; i <= B; i += p)``                    ``p_factors[i]++;``     ` `        ``// Print all numbers with k prime factors``        ``for` `(``int` `i = A; i <= B; i++)``            ``if` `(p_factors[i] == K)``                ``System.out.print( i + ``" "``);``    ``}``     ` `    ``// Driver code``    ``public` `static` `void` `main(String args[])``    ``{``        ``int` `A = ``14``, B = ``18``, K = ``2``;``        ``printKPFNums(A, B, K);``    ``}``}`  `// This code is contributed``// by Nikita Tiwari.`

## Python3

 `# Python 3 program to count``# all those numbers in``# given range whose count``# of prime factors``# is k` `def` `printKPFNums(A, B, K) :` `    ``# Count prime factors``    ``# of all numbers``    ``# till B.``    ``prime ``=` `[ ``True``]``*``(B``+``1``)``    ``p_factors``=` `[ ``0` `]``*``(B``+``1``)``    ``for` `p ``in` `range``(``2``,B``+``1``) :``        ``if` `(p_factors[p] ``=``=` `0``)  :``            ``for` `i ``in` `range``(p,B``+``1``,p) :``                ``p_factors[i] ``=` `p_factors[i] ``+` `1`` ` `    ``# Print all numbers with``    ``# k prime factors``    ``for` `i ``in` `range``(A,B``+``1``) :``        ``if` `(p_factors[i] ``=``=` `K) :``            ``print``( i ,end``=``" "``)`  `# Driver code``A ``=` `14``B ``=` `18``K ``=` `2``printKPFNums(A, B, K)`  `# This code is contributed``# by Nikita Tiwari.`

## C#

 `// C# program to count all``// those numbers in given``// range whose count of``// prime factors is k``using` `System;` `class` `GFG {``    ` `    ``static` `void` `printKPFNums(``int` `A, ``int` `B,``                                    ``int` `K)``    ``{``        ``// Count prime factors of``        ``// all numbers till B.``        ``bool` `[]prime = ``new` `bool``[B + 1];``        ` `        ``for``(``int` `i = 0; i < B + 1; i++)``            ``prime[i] = ``true``;``            ` `        ``int` `[]p_factors = ``new` `int``[B + 1];``        ` `        ``for``(``int` `i = 0; i < B + 1; i++)``            ``p_factors[i] = 0;` `        ``for` `(``int` `p = 2; p <= B; p++)``            ``if` `(p_factors[p] == 0)``                ``for` `(``int` `i = p; i <= B; i += p)``                    ``p_factors[i]++;``    ` `        ``// Print all numbers with``        ``// k prime factors``        ``for` `(``int` `i = A; i <= B; i++)``            ``if` `(p_factors[i] == K)``                ``Console.Write( i + ``" "``);``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `Main()``    ``{``        ``int` `A = 14, B = 18, K = 2;``        ``printKPFNums(A, B, K);``    ``}``}` `// This code is contributed by nitin mittal.`

## PHP

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## Javascript

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Output:

`14 15 18`

Time Complexity: O(B2) , B is the range
Auxiliary Space: O(B), B is the range

Please suggest if someone has a better solution which is more efficient in terms of space and time.