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Find elements in given Array that are a factor of sum of remaining elements

  • Difficulty Level : Hard
  • Last Updated : 10 Feb, 2022

Given an array A[] of size N, the task is to find the elements in the array which are factors of the sum of the remaining element. So just select an element from an array and take the sum of the remaining elements and check whether the sum is perfectly divisible by the selected element or not. If it is divisible then return the element.

Examples:

Input: A[] = {2, 4, 6, 8, 10, 12, 14}
Output: [2, 4, 8, 14]
Explanation: 
1. Take sum for remaining element except selected one.
2. For element 2, sum of remaining element is 4+6+8+10+12+14=54 
3. Similarly for complete array: [54, 52, 50, 48, 46, 44, 42]
3. 54/2, 52/4, 48/8, 42/14 are perfectly divisible so resultant elements are [2, 4, 8, 14]

Input: A[]= {3, 6, 8, 10, 7, 15}
Output: [7]

 

Naive Approach: Take the sum of all elements from the array. Now subtract each element one by one from sum and append it to new array p[]. Divide each sum by the corresponding index element from a given array and append it to new array q[ ]. Multiply the corresponding element from array A[] and array q[] and compare it with similar indexed elements from array p[]. If they are equal then append it to a new array z[ ]. If no such element is found return -1.

Below is the implementation of the above approach.

C++




// c++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to find element
vector<int> Factor(vector<int> A)
{
 
  // Sum of all element
  int s = 0;
 
  for (int i = 0; i < A.size(); i++)
  {
    s += A[i];
  }
 
  // Subtract each element from sum
  vector<int> p;
  for (int i : A)
    p.push_back(s - i);
 
  // Divide corresponding element
  // from array p and l
  vector<int> q;
  for (int i = 0; i < A.size(); i++)
    q.push_back(p[i] / A[i]);
 
  // Check sum is divisible by
  // corresponding element or not
  vector<int> z;
  for (int i = 0; i < q.size(); i++)
  {
 
    // First we divided element now multiple
    // to check perfect divisibility of element
    if (q[i] * A[i] == p[i])
      z.push_back(A[i]);
  }
 
  return z;
}
 
// Driver code
int main()
{
  vector<int> A = {2, 4, 6, 8, 10, 12, 14};
 
  // Calling function
  vector<int> b = Factor(A);
 
  // Print required array
  for (auto i : b)
  {
    cout << i << " ";
  }
}
 
// This code is contributed by amreshkumar3.

Java




// Java program for the above approach
import java.util.ArrayList;
 
class GFG{
 
// Function to find element
static ArrayList<Integer> Factor(int[] A)
{
     
    // Sum of all element
    int s = 0;
 
    for(int i = 0; i < A.length; i++)
    {
        s += A[i];
    }
 
    // Subtract each element from sum
    ArrayList<Integer> p = new ArrayList<>();
    for(int i : A)
        p.add(s - i);
 
    // Divide corresponding element
    // from array p and l
    ArrayList<Integer> q = new ArrayList<Integer>();
    for(int i = 0; i < A.length; i++)
        q.add((int) Math.floor(p.get(i) / A[i]));
 
    // Check sum is divisible by
    // corresponding element or not
    ArrayList<Integer> z = new ArrayList<Integer>();
    for(int i = 0; i < q.size(); i++)
    {
         
        // First we divided element now multiple
        // to check perfect divisibility of element
        if (q.get(i) * A[i] == p.get(i))
            z.add(A[i]);
    }
     
    // If no such element found return -1
    if (z.size() == 0)
        return new ArrayList<Integer>();
         
    return z;
}
 
// Driver code
public static void main(String args[])
{
    int[] A = { 2, 4, 6, 8, 10, 12, 14 };
 
    // Calling function
    ArrayList<Integer> b = Factor(A);
 
    // Print required array
    System.out.println(b);
}
}
 
// This code is contributed by gfgking

Python3




# Python program for the above approach
 
# Function to find element
def Factor(A):
   
    # Sum of all element
    s = sum(A)
     
    # Subtract each element from sum
    p =[]
    for i in A:
        p.append(s-i)
 
    # Divide corresponding element
    # from array p and l
    q =[]
    for i in range(len(A)):
        q.append(p[i]//A[i])
 
    # Check sum is divisible by
    # corresponding element or not
    z =[]
    for i in range(len(q)):
       
          # First we divided element now multiple
        # to check perfect divisibility of element
        if q[i]*A[i]== p[i]:
            z.append(A[i])
             
    # If no such element found return -1
    if len(z)== 0:
      return -1
    return z
 
A = [2, 4, 6, 8, 10, 12, 14]
 
# Calling function
b = Factor(A)
 
# Print required array
print(b)

C#




// C# program for the above approach
using System;
using System.Collections.Generic;
 
public class GFG{
 
  // Function to find element
  static List<int> Factor(int[] A)
  {
 
    // Sum of all element
    int s = 0;
 
    for(int i = 0; i < A.Length; i++)
    {
      s += A[i];
    }
 
    // Subtract each element from sum
    List<int> p = new List<int>();
    foreach(int i in A)
      p.Add(s - i);
 
    // Divide corresponding element
    // from array p and l
    List<int> q = new List<int>();
    for(int i = 0; i < A.Length; i++)
      q.Add((int) Math.Floor((double)p[i] / A[i]));
 
    // Check sum is divisible by
    // corresponding element or not
    List<int> z = new List<int>();
    for(int i = 0; i < q.Count; i++)
    {
 
      // First we divided element now multiple
      // to check perfect divisibility of element
      if (q[i] * A[i] == p[i])
        z.Add(A[i]);
    }
 
    // If no such element found return -1
    if (z.Count == 0)
      return new List<int>();
 
    return z;
  }
 
  // Driver code
  public static void Main(String []args)
  {
    int[] A = { 2, 4, 6, 8, 10, 12, 14 };
 
    // Calling function
    List<int> b = Factor(A);
 
    // Print required array
    foreach(int i in b)
      Console.Write(i+", ");
  }
}
 
 
// This code is contributed by 29AjayKumar

Javascript




  <script>
      // JavaScript code for the above approach
 
      // Function to find element
      function Factor(A) {
 
          // Sum of all element
          let s = 0;
 
          for (let i = 0; i < A.length; i++) {
              s += A[i]
          }
 
          // Subtract each element from sum
          p = []
          for (i of A)
              p.push(s - i)
 
          // Divide corresponding element
          // from array p and l
          q = []
          for (i = 0; i < A.length; i++)
              q.push(Math.floor(p[i] / A[i]))
 
          // Check sum is divisible by
          // corresponding element or not
          z = []
          for (let i = 0; i < q.length; i++) {
 
              // First we divided element now multiple
              // to check perfect divisibility of element
              if (q[i] * A[i] == p[i])
                  z.push(A[i])
          }
          // If no such element found return -1
          if (z.length == 0)
              return -1
          return z
      }
      A = [2, 4, 6, 8, 10, 12, 14]
 
      // Calling function
      b = Factor(A)
 
      // Print required array
      document.write(b)
 
// This code is contributed by Potta Lokesh
  </script>
Output
[2, 4, 8, 14]

Time Complexity: O(N)
Auxiliary Space: O(N)

Efficient Approach: In this approach, there is no need to use multiple loops and multiple arrays. so space complexity and time complexity will be decreased. In this, all the subtraction, division, multiplication operation are performed in a single loop. Follow the steps below to solve the problem:

  • Initialize the variable s as the sum of the array A[].
  • Initialize the array z[] to store the result.
  • Iterate over the range [0, len(A)) using the variables i and perform the following tasks:
    • Initialize the variable a as s-l[i], b as a/A[i].
    • If b*A[i] equals a then append A[i] into z[].
  • After performing the above steps, print -1 if the resultant array is empty, else print the elements of the array z[] as the answer.

Below is the implementation of the above approach.

C++




// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to find sum of all elements of an array
int sum(vector<int>& A)
{
  int res = 0;
  for (auto it : A)
    res += it;
  return res;
}
 
// Function to find element
vector<int> Factor(vector<int>& A)
{
 
  // Sum of all element
  int s = sum(A);
  vector<int> z;
 
  // Loop to find the factors of sum.
  for (int i = 0; i < A.size(); ++i) {
 
    // a is sum of remaining elements.
    int a = s - A[i];
 
    // b is integer value or factor of b.
    int b = a / A[i];
 
    // Check the divisibility
    if (b * A[i] == a)
      z.push_back(A[i]);
  }
 
  // If no element found return -1
  if (z.size() == 0)
    return { -1 };
 
  return z;
}
 
// Drive Code
 
int main()
{
  vector<int> A = { 2, 4, 6, 8, 10, 12, 14 };
 
  // Calling function
  vector<int> b = Factor(A);
 
  // Print resultant element
  for (auto it : b)
    cout << it << " ";
 
  return 0;
}
 
// This code is contributed by rakeshsahni

Java




// Java program for the above approach
import java.util.*;
class GFG
{
 
  // Function to find sum of all elements of an array
  static int sum(int[] A)
  {
    int res = 0;
    for (int i = 0; i < A.length; i++) {
      res += A[i];
    }
    return res;
  }
 
  // Function to find element
  static ArrayList<Integer> Factor(int[] A)
  {
 
    // Sum of all element
    int s = sum(A);
    ArrayList<Integer> z = new ArrayList<Integer>();
 
    // Loop to find the factors of sum.
    for (int i = 0; i < A.length; ++i) {
 
      // a is sum of remaining elements.
      int a = s - A[i];
 
      // b is integer value or factor of b.
      int b = a / A[i];
 
      // Check the divisibility
      if (b * A[i] == a){
        z.add(A[i]);
      }
    }
 
    // If no element found return -1
    if (z.size() == 0){
      ArrayList<Integer> l1 = new ArrayList<Integer>();
      l1.add(-1);
      return l1;
    }
 
    return z;
  }
 
  // Drive Code
  public static void main (String[] args)
  {
    int A[] = new int[] { 2, 4, 6, 8, 10, 12, 14 };
 
    // Calling function
    ArrayList<Integer> b = Factor(A);
 
    // Print resultant element
    System.out.println(b);
  }
}
 
// This code is contributed by Shubham Singh

Python3




# Python program for the above approach
 
# Function to find element
def Factor(A):
 
    # Sum of all element
    s = sum(A)
    z = []
 
    # Loop to find the factors of sum.
    for i in range(len(A)):
 
        # a is sum of remaining elements.
        a = s-A[i]
 
        # b is integer value or factor of b.
        b = a//A[i]
 
        # Check the divisibility
        if b * A[i] == a:
            z.append(A[i])
 
    # If no element found return -1
    if len(z) == 0:
        return -1
 
    return z
 
 
A = [2, 4, 6, 8, 10, 12, 14]
 
# Calling function
b = Factor(A)
 
# Print resultant element
print(b)

C#




// C# program for the above approach
using System;
using System.Collections.Generic;
class GFG {
 
  // Function to find sum of all elements of an array
  static int sum(List<int> A)
  {
    int res = 0;
    foreach(int it in A) res += it;
    return res;
  }
 
  // Function to find element
  static List<int> Factor(List<int> A)
  {
 
    // Sum of all element
    int s = sum(A);
    List<int> z = new List<int>();
 
    // Loop to find the factors of sum.
    for (int i = 0; i < A.Count; ++i) {
 
      // a is sum of remaining elements.
      int a = s - A[i];
 
      // b is integer value or factor of b.
      int b = a / A[i];
 
      // Check the divisibility
      if (b * A[i] == a)
        z.Add(A[i]);
    }
 
    // If no element found return -1
    if (z.Count == 0)
      return new List<int>() { -1 };
 
    return z;
  }
 
  // Drive Code
 
  public static void Main()
  {
    List<int> A
      = new List<int>() { 2, 4, 6, 8, 10, 12, 14 };
 
    // Calling function
    List<int> b = Factor(A);
 
    // Print resultant element
    Console.Write("[ ");
    int it;
    for (it = 0; it < b.Count - 1; it++) {
      Console.Write(b[it] + ", ");
    }
    Console.Write(b[it] + " ]");
  }
}
 
// This code is contributed by ukasp.

Javascript




<script>
// JavaScript program for the above approach
 
// Function to find sum of all elements of an array
function sum(A)
{
  var res = 0;
  for (var it of A){
    res += parseInt(it);}
  return res;
}
 
// Function to find element
function Factor(A)
{
 
  // Sum of all element
  var s = sum(A);
   
  var z =[];
 
  // Loop to find the factors of sum.
  for (var i = 0; i < A.length; ++i) {
 
    // a is sum of remaining elements.
    var a = s - A[i];
 
    // b is integer value or factor of b.
    var b = parseInt(a / A[i]);
 
    // Check the divisibility
    if (b * A[i] == a)
      z.push(A[i]);
  }
 
  // If no element found return -1
  if (z.length == 0)
    return [ -1 ];
 
  return z;
}
 
// Drive Code
A = [ 2, 4, 6, 8, 10, 12, 14 ];
 
// Calling function
b = Factor(A);
 
// Print resultant element
for (var it of b)
document.write(it + " ");
 
//This code is contributed by Shubham Singh
</script>
Output
[2, 4, 8, 14]

Time Complexity: O(N)
Auxiliary Space: O(1)


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