Find distinct integers for a triplet with given product

Given an integer X, the task is to find the three distinct integers greater than 1 i.e. A, B and C such that (A * B * C) = X. If no such triplet exists then print -1.

Examples:

Input: X = 64
Output: 2 4 8
(2 * 4 * 8) = 64

Input: X = 32
Output: -1
No such triplet exists.

Approach: Suppose we have a triplet (A, B, C). Notice that, for their product to be equal to X, each of the integer has to be a factor of X. So, store all the factors of X in O(sqrt(X)) time using the approach discussed in this article.
There will be at most sqrt(X) factors now. Next, iterate on each factor by running two loops, one picking A and another picking B. Now if this triplet is valid i.e. C = X / (A * B) where C is also a factor of X. To check that, store all the factors in an unordered_set. If a valid triplet is found then print the triplet else print -1.



Below is the implementation of the above approach:

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// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to find the required triplets
void findTriplets(int x)
{
    // To store the factors
    vector<int> fact;
    unordered_set<int> factors;
  
    // Find factors in sqrt(x) time
    for (int i = 2; i <= sqrt(x); i++) {
        if (x % i == 0) {
            fact.push_back(i);
            if (x / i != i)
                fact.push_back(x / i);
            factors.insert(i);
            factors.insert(x / i);
        }
    }
  
    bool found = false;
    int k = fact.size();
    for (int i = 0; i < k; i++) {
  
        // Choose a factor
        int a = fact[i];
        for (int j = 0; j < k; j++) {
  
            // Choose another factor
            int b = fact[j];
  
            // These conditions need to be
            // met for a valid triplet
            if ((a != b) && (x % (a * b) == 0)
                && (x / (a * b) != a)
                && (x / (a * b) != b)
                && (x / (a * b) != 1)) {
  
                // Print the valid triplet
                cout << a << " " << b << " "
                     << (x / (a * b));
                found = true;
                break;
            }
        }
  
        // Triplet found
        if (found)
            break;
    }
  
    // Triplet not found
    if (!found)
        cout << "-1";
}
  
// Driver code
int main()
{
    int x = 105;
  
    findTriplets(x);
  
    return 0;
}
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// Java implementation of the approach
import java.util.*;
  
class GFG
{
  
// Function to find the required triplets
static void findTriplets(int x)
{
    // To store the factors
    Vector<Integer> fact = new Vector<Integer>();
    HashSet<Integer> factors = new HashSet<Integer>();
  
    // Find factors in Math.sqrt(x) time
    for (int i = 2; i <= Math.sqrt(x); i++) 
    {
        if (x % i == 0
        {
            fact.add(i);
            if (x / i != i)
                fact.add(x / i);
            factors.add(i);
            factors.add(x / i);
        }
    }
  
    boolean found = false;
    int k = fact.size();
    for (int i = 0; i < k; i++)
    {
  
        // Choose a factor
        int a = fact.get(i);
        for (int j = 0; j < k; j++) 
        {
  
            // Choose another factor
            int b = fact.get(j);
  
            // These conditions need to be
            // met for a valid triplet
            if ((a != b) && (x % (a * b) == 0)
                && (x / (a * b) != a)
                && (x / (a * b) != b)
                && (x / (a * b) != 1)) 
            {
  
                // Print the valid triplet
                System.out.print(a+ " " + b + " "
                    + (x / (a * b)));
                found = true;
                break;
            }
        }
  
        // Triplet found
        if (found)
            break;
    }
  
    // Triplet not found
    if (!found)
        System.out.print("-1");
}
  
// Driver code
public static void main(String[] args)
{
    int x = 105;
  
    findTriplets(x);
}
}
  
// This code is contributed by PrinciRaj1992
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# Python3 implementation of the approach 
from math import sqrt
  
# Function to find the required triplets 
def findTriplets(x) : 
  
    # To store the factors 
    fact = []; 
    factors = set(); 
  
    # Find factors in sqrt(x) time 
    for i in range(2, int(sqrt(x))) :
        if (x % i == 0) :
            fact.append(i); 
              
            if (x / i != i) :
                fact.append(x // i); 
                  
            factors.add(i); 
            factors.add(x // i); 
  
    found = False
    k = len(fact); 
      
    for i in range(k) :
  
        # Choose a factor 
        a = fact[i]; 
          
        for j in range(k) :
  
            # Choose another factor 
            b = fact[j]; 
  
            # These conditions need to be 
            # met for a valid triplet 
            if ((a != b) and (x % (a * b) == 0
                and (x / (a * b) != a) 
                and (x / (a * b) != b) 
                and (x / (a * b) != 1)) :
  
                # Print the valid triplet 
                print(a,b,x // (a * b)); 
                found = True
                break
      
        # Triplet found 
        if (found) :
            break
  
    # Triplet not found 
    if (not found) : 
        print("-1"); 
  
# Driver code 
if __name__ == "__main__"
  
    x = 105
  
    findTriplets(x); 
  
# This code is contributed by AnkitRai01
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// C# implementation of the approach
using System;
using System.Collections.Generic;
  
class GFG
{
  
// Function to find the required triplets
static void findTriplets(int x)
{
    // To store the factors
    List<int> fact = new List<int>();
    HashSet<int> factors = new HashSet<int>();
  
    // Find factors in Math.Sqrt(x) time
    for (int i = 2; i <= Math.Sqrt(x); i++) 
    {
        if (x % i == 0) 
        {
            fact.Add(i);
            if (x / i != i)
                fact.Add(x / i);
            factors.Add(i);
            factors.Add(x / i);
        }
    }
  
    bool found = false;
    int k = fact.Count;
    for (int i = 0; i < k; i++)
    {
  
        // Choose a factor
        int a = fact[i];
        for (int j = 0; j < k; j++) 
        {
  
            // Choose another factor
            int b = fact[j];
  
            // These conditions need to be
            // met for a valid triplet
            if ((a != b) && (x % (a * b) == 0)
                && (x / (a * b) != a)
                && (x / (a * b) != b)
                && (x / (a * b) != 1)) 
            {
  
                // Print the valid triplet
                Console.Write(a+ " " + b + " "
                    + (x / (a * b)));
                found = true;
                break;
            }
        }
  
        // Triplet found
        if (found)
            break;
    }
  
    // Triplet not found
    if (!found)
        Console.Write("-1");
}
  
// Driver code
public static void Main(String[] args)
{
    int x = 105;
  
    findTriplets(x);
}
}
  
// This code is contributed by 29AjayKumar
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Output:
3 5 7





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