Sum of element whose prime factors are present in array

Given an array arr[] of non-negative integers where 2 ? arr[i] ? 10⁶. The task is to find the sum of all those elements from the array whose prime factors are present in the same array. Examples:

Input: arr[] = {2, 3, 10} Output: 5 Factor of 2 is 2 which is present in the array Factor of 3 is 3, also present in the array Factors of 10 are 2 and 5, out of which only 2 is present in the array. So, sum = 2 + 3 = 5 Input: arr[] = {5, 11, 55, 25, 100} Output: 96

Approach: The idea is to first calculate the least prime factor till maximum element of the array with Prime Factorization using Sieve.

1. Now, Iterate the array and for an element arr[i]
2. If arr[i] != 1:
   • If leastPrimeFactor(arr[i]) is present in the array then update arr[i] / leastPrimeFactor(arr[i]) and go to step 2.
   • Else go to step 1.
3. Else update sum = sum + originalVal(arr[i]).
4. Print the sum in the end.

Below is the implementation of the above approach: 

C++

// C++ program to find the sum of the elements of an array
// whose prime factors are present in the same array
#include <bits/stdc++.h>
using namespace std;

#define MAXN 1000001

// Stores smallest prime factor for every number
int spf[MAXN];

// Function to calculate SPF (Smallest Prime Factor)
// for every number till MAXN
void sieve()
{
    spf[1] = 1;
    for (int i = 2; i < MAXN; i++)

        // Marking smallest prime factor for every
        // number to be itself.
        spf[i] = i;

    // Separately marking spf for every even
    // number as 2
    for (int i = 4; i < MAXN; i += 2)
        spf[i] = 2;

    for (int i = 3; i * i < MAXN; i++) {

        // If i is prime
        if (spf[i] == i) {

            // Marking SPF for all numbers divisible by i
            for (int j = i * i; j < MAXN; j += i)

                // Marking spf[j] if it is not
                // previously marked
                if (spf[j] == j)
                    spf[j] = i;
        }
    }
}

// Function to return the sum of the elements of an array
// whose prime factors are present in the same array
int sumFactors(int arr[], int n)
{

    // Function call to calculate smallest prime factors of
    // all the numbers upto MAXN
    sieve();

    // Create map for each element
    std::map<int, int> map;

    for (int i = 0; i < n; ++i)
        map[arr[i]] = 1;

    int sum = 0;

    for (int i = 0; i < n; ++i) {
        int num = arr[i];

        // If smallest prime factor of num is present in array
        while (num != 1 && map[spf[num]] == 1) {
            num /= spf[num];
        }

        // Each factor of arr[i] is present in the array
        if (num == 1)
            sum += arr[i];
    }

    return sum;
}

// Driver program
int main()
{
    int arr[] = { 5, 11, 55, 25, 100 };
    int n = sizeof(arr) / sizeof(arr[0]);

    // Function call to print required answer
    cout << sumFactors(arr, n);
    return 0;
}

Java

// Java program to find the sum of the elements of an array
// whose prime factors are present in the same array

import java.util.*;

public class GFG{

final static int MAXN = 1000001 ;

// Stores smallest prime factor for every number
static int spf[] = new int [MAXN];

    // Function to calculate SPF (Smallest Prime Factor)
    // for every number till MAXN
    static void sieve()
    {
        spf[1] = 1;
        for (int i = 2; i < MAXN; i++)

            // Marking smallest prime factor for every
            // number to be itself.
            spf[i] = i;

        // Separately marking spf for every even
        // number as 2
        for (int i = 4; i < MAXN; i += 2)
            spf[i] = 2;

        for (int i = 3; i * i < MAXN; i++) {

            // If i is prime
            if (spf[i] == i) {

                // Marking SPF for all numbers divisible by i
                for (int j = i * i; j < MAXN; j += i)

                    // Marking spf[j] if it is not
                    // previously marked
                    if (spf[j] == j)
                        spf[j] = i;
            }
        }
    }

    // Function to return the sum of the elements of an array
    // whose prime factors are present in the same array
    static int sumFactors(int arr[], int n)
    {

        // Function call to calculate smallest prime factors of
        // all the numbers upto MAXN
        sieve();

        // Create map for each element
        Map map=new HashMap();

        for(int i = 0 ; i < MAXN ; ++i)
            map.put(i,0) ;

        for (int i = 0; i < n; ++i)
            map.put(arr[i],1);


        int sum = 0;

        for (int i = 0; i < n; ++i) {
            int num = arr[i];

            // If smallest prime factor of num is present in array
            while (num != 1 && (int)(map.get(spf[num])) == 1) {
                num /= spf[num];
            }

            // Each factor of arr[i] is present in the array
            if (num == 1)
                sum += arr[i];
        }

        return sum;
    }

    // Driver program
     public static void main(String []args)
    {
        int arr[] = { 5, 11, 55, 25, 100 };
        int n = arr.length ;

        // Function call to print required answer
         System.out.println(sumFactors(arr, n)) ;
    }
    // This code is contributed by Ryuga
}

Python3

# Python program to find the sum of the
# elements of an array whose prime factors
# are present in the same array
from collections import defaultdict

MAXN = 1000001
MAXN_sqrt = int(MAXN ** (0.5))

# Stores smallest prime factor
# for every number
spf = [None] * (MAXN)

# Function to calculate SPF (Smallest
# Prime Factor) for every number till MAXN
def sieve():

    spf[1] = 1
    for i in range(2, MAXN):

        # Marking smallest prime factor
        # for every number to be itself.
        spf[i] = i

    # Separately marking spf for every
    # even number as 2
    for i in range(4, MAXN, 2):
        spf[i] = 2

    for i in range(3, MAXN_sqrt):

        # If i is prime
        if spf[i] == i:

            # Marking SPF for all numbers
            # divisible by i
            for j in range(i * i, MAXN, i):

                # Marking spf[j] if it is
                # not previously marked
                if spf[j] == j:
                    spf[j] = i

# Function to return the sum of the elements
# of an array whose prime factors are present
# in the same array
def sumFactors(arr, n):

    # Function call to calculate smallest
    # prime factors of all the numbers upto MAXN
    sieve()

    # Create map for each element
    Map = defaultdict(lambda:0)

    for i in range(0, n):
        Map[arr[i]] = 1

    Sum = 0

    for i in range(0, n):
        num = arr[i]

        # If smallest prime factor of num
        # is present in array
        while num != 1 and Map[spf[num]] == 1:
            num = num // spf[num]

        # Each factor of arr[i] is present
        # in the array
        if num == 1:
            Sum += arr[i]

    return Sum

# Driver Code
if __name__ == "__main__":

    arr = [5, 11, 55, 25, 100]
    n = len(arr)

    # Function call to print
    # required answer
    print(sumFactors(arr, n))

# This code is contributed by Rituraj Jain

C#

// C# program to find the sum of the elements
// of an array whose prime factors are present
// in the same array
using System;
using System.Collections.Generic;

class GFG
{
    static int MAXN = 1000001;

    // Stores smallest prime factor for every number
    static int []spf = new int [MAXN];

    // Function to calculate SPF (Smallest Prime Factor)
    // for every number till MAXN
    static void sieve()
    {
        spf[1] = 1;
        for (int i = 2; i < MAXN; i++)

            // Marking smallest prime factor for
            // every number to be itself.
            spf[i] = i;

        // Separately marking spf for every even
        // number as 2
        for (int i = 4; i < MAXN; i += 2)
            spf[i] = 2;

        for (int i = 3; i * i < MAXN; i++)
        {

            // If i is prime
            if (spf[i] == i)
            {

                // Marking SPF for all numbers divisible by i
                for (int j = i * i; j < MAXN; j += i)

                    // Marking spf[j] if it is not
                    // previously marked
                    if (spf[j] == j)
                        spf[j] = i;
            }
        }
    }

    // Function to return the sum of the elements
    // of an array whose prime factors are present
    // in the same array
    static int sumFactors(int []arr, int n)
    {

        // Function call to calculate smallest
        // prime factors of all the numbers upto MAXN
        sieve();

        // Create map for each element
        Dictionary<int, int> map = new Dictionary<int, int>();

        for(int i = 0 ; i < MAXN ; ++i)
            map.Add(i, 0);

        for (int i = 0; i < n; ++i)
        {
            if(map.ContainsKey(arr[i]))
            {
                map[arr[i]] = 1;
            }
            else
            {
                map.Add(arr[i], 1);
            }
        }

        int sum = 0;

        for (int i = 0; i < n; ++i)
        {
            int num = arr[i];

            // If smallest prime factor of num
            // is present in array
            while (num != 1 &&
             (int)(map[spf[num]]) == 1)
            {
                num /= spf[num];
            }

            // Each factor of arr[i] is present
            // in the array
            if (num == 1)
                sum += arr[i];
        }
        return sum;
    }

    // Driver Code
    public static void Main(String []args)
    {
        int []arr = { 5, 11, 55, 25, 100 };
        int n = arr.Length;

        // Function call to print required answer
        Console.WriteLine(sumFactors(arr, n));
    }
}

// This code is contributed by PrinciRaj1992

Javascript

// JavaScript program to find the sum of the
// elements of an array whose prime factors
// are present in the same array
let MAXN = 1000001
let MAXN_sqrt = Math.floor(MAXN ** (0.5))

// Stores smallest prime factor
// for every number
let spf = new Array(MAXN)

// Function to calculate SPF (Smallest
// Prime Factor) for every number till MAXN
function sieve()
{
    spf[1] = 1
    for (var i = 2; i < MAXN; i++)
    {
        // Marking smallest prime factor
        // for every number to be itself.
        spf[i] = i
    }

    // Separately marking spf for every
    // even number as 2
    for (var i = 4; i <  MAXN; i += 2)
        spf[i] = 2

    for (var i = 3; i < MAXN_sqrt; i++)
    {
        // If i is prime
        if (spf[i] == i)
        {
            // Marking SPF for all numbers
            // divisible by i
            for (var j = i * i; j < MAXN; j += i)
            {
                // Marking spf[j] if it is
                // not previously marked
                if (spf[j] == j)
                    spf[j] = i
            }
        }
    }
}

// Function to return the sum of the elements
// of an array whose prime factors are present
// in the same array
function sumFactors(arr, n)
{
    // Function call to calculate smallest
    // prime factors of all the numbers upto MAXN
    sieve()

    // Create map for each element
    let Map = {}

    for (var i = 0; i < n; i++)
        Map[arr[i]] = 1

    let Sum = 0

    for (var i = 0; i < n; i++)
    {
        let num = arr[i]

        // If smallest prime factor of num
        // is present in array
        while (num != 1 && Map.hasOwnProperty(spf[num]))
            num = Math.floor(num / spf[num])

        // Each factor of arr[i] is present
        // in the array
        if (num == 1)
            Sum += arr[i]
    }

    return Sum
}


// Driver Code
let arr = [5, 11, 55, 25, 100]
let n = arr.length

// Function call to print
// required answer
console.log(sumFactors(arr, n))

// This code is contributed by phasing17

Output:

96

Time Complexity: O(MAXN*log(log(MAXN)))

Auxiliary Space: O(MAXN)