Check if a number can be written as sum of three consecutive integers

0 0 8 minutes read

Given an integer n, the task is to find whether n can be written as sum of three consecutive integer. If yes, find the three consecutive integer, else print “-1”.
Examples:

Input: n = 6
Output: 1 2 3
Explanation: 6 = 1 + 2 + 3.

Input: n = 7
Output: -1

Method 1: (Brute Force):
The idea is to run a loop from i = 0 to n – 2, check if (i + i+1 + i+2) is equal to n. Also, check if n is positive or negative and accordingly increment or decrement i by 1.
Below is the implementation of this approach:

C++

// CPP Program to check if a number can 
// be written as sum of three consecutive 
// integers. 
#include <bits/stdc++.h> 
using namespace std; 
  
// function to check if a number can be written as sum of 
// three consecutive integer. 
void checksum(int n) 
{ 
    // if n is 0 
    if (n == 0) { 
        cout << "-1 0 1" << endl; 
        return; 
    } 
  
    int inc; 
  
    // if n is positive, increment loop by 1. 
    if (n > 0) 
        inc = 1; 
  
    // if n is negative, decrement loop by 1. 
    else
        inc = -1; 
  
    // Running loop from 0 to n - 2 
    for (int i = 0; i <= n - 2; i += inc) { 
  
        // check if sum of three consecutive 
        // integer is equal to n. 
        if (i + i + 1 + i + 2 == n) { 
            cout << i << " " << i + 1 
                 << " " << i + 2; 
            return; 
        } 
    } 
  
    cout << "-1"; 
} 
  
// Driver Program 
int main() 
{ 
    int n = 6; 
    checksum(n); 
    return 0; 
} 

Java

// JAVA Code to check if a number 
// can be written as sum of  
// three consecutive integers. 
import java.util.*; 
  
class GFG  
{ 
    // function to check if a number 
    // can be written as sum of 
    // three consecutive integer. 
    static void checksum(int n) 
    { 
        // if n is 0 
        if (n == 0) { 
            System.out.println("-1 0 1"); 
            return; 
        } 
       
        int inc; 
       
        // if n is positive,  
        // increment loop by 1. 
        if (n > 0) 
            inc = 1; 
       
        // if n is negative,  
        // decrement loop by 1. 
        else
            inc = -1; 
       
        // Running loop from 0 to n - 2 
        for (int i = 0; i <= n - 2; i += inc) { 
       
            // check if sum of three consecutive 
            // integer is equal to n. 
            if (i + i + 1 + i + 2 == n) { 
                System.out.println(i + " " +  
                                  (i + 1) + 
                                " " + (i + 2)); 
                return; 
            } 
        } 
       
        System.out.println("-1"); 
    } 
      
    /* Driver program to test above function */
    public static void main(String[] args)  
    { 
        int n = 6; 
        checksum(n); 
    } 
} 
  
// This code is contributed by Arnav Kr. Mandal. 

Python3

# Python3 code to check if a number 
# can be written as sum of three  
# consecutive integers. 
  
# function to check if a number  
# can be written as sum of three 
# consecutive integer. 
def checksum(n): 
  
    # if n is 0 
    if n == 0: 
        print("-1 0 1") 
        return 0
          
    inc = 0 
  
    # if n is positive, 
    # increment loop by 1. 
    if n > 0: 
        inc = 1
      
    # if n is negative, 
    # decrement loop by 1. 
    else: 
        inc = -1
      
    # Running loop from 0 to n - 2 
    for i in range(0, n-1, inc): 
      
        # check if sum of three consecutive 
        # integer is equal to n. 
        if i + i + 1 + i + 2 == n: 
            print(i ," ",i + 1, " ", i + 2) 
            return 0
              
    print("-1") 
      
# Driver Code  
n = 6
checksum(n) 
  
# This code is contributed by "Sharad_Bhardwaj". 

C#

// C# Code to check if a number 
// can be written as sum of  
// three consecutive integers. 
using System; 
  
class GFG  
{ 
    // function to check if a number 
    // can be written as sum of 
    // three consecutive integer. 
    static void checksum(int n) 
    { 
        // if n is 0 
        if (n == 0) { 
            Console.WriteLine("-1 0 1"); 
            return; 
        } 
      
        int inc; 
      
        // if n is positive,  
        // increment loop by 1. 
        if (n > 0) 
            inc = 1; 
      
        // if n is negative,  
        // decrement loop by 1. 
        else
            inc = -1; 
      
        // Running loop from 0 to n - 2 
        for (int i = 0; i <= n - 2; i += inc) { 
      
            // check if sum of three consecutive 
            // integer is equal to n. 
            if (i + i + 1 + i + 2 == n) { 
                Console.WriteLine(i + " "
                     + (i + 1) +" " + (i + 2)); 
                return; 
            } 
        } 
      
        Console.WriteLine("-1"); 
    } 
      
    /* Driver program to test above function */
    public static void Main()  
    { 
        int n = 6; 
        checksum(n); 
    } 
} 
  
// This code is contributed by vt_m. 

PHP

<?php 
// PHP Program to check if a 
// number can be written 
// as sum of three consecutive 
// integers. 
  
// function to check if a number 
// can be written as sum of 
// three consecutive integer. 
function checksum($n) 
{ 
      
    // if n is 0 
    if ($n == 0)  
    { 
        echo "-1 0 1" ; 
        return; 
    } 
  
    $inc; 
  
    // if n is positive, 
    // increment loop by 1. 
    if ($n > 0) 
        $inc = 1; 
  
    // if n is negative,  
    // decrement loop by 1. 
    else
        $inc = -1; 
  
    // Running loop from 
    // 0 to n - 2 
    for ($i = 0; $i <= $n - 2; $i += $inc)  
    { 
  
        // check if sum of three consecutive 
        // integer is equal to n. 
        if ($i + $i + 1 + $i + 2 == $n)  
        { 
            echo $i , " " , $i + 1 
                , " " , $i + 2; 
            return; 
        } 
    } 
  
    echo "-1"; 
} 
  
    // Driver Code 
    $n = 6; 
    checksum($n); 
      
// This code is contributed by anuj_67. 
?> 

Javascript

<script> 
  
// Javascript Code to check if a number 
// can be written as sum of  
// three consecutive integers. 
  
    // function to check if a number 
    // can be written as sum of 
    // three consecutive integer. 
    function checksum(n) 
    { 
      
        // if n is 0 
        if (n == 0) { 
            document.write("-1 0 1"); 
            return; 
        } 
  
        var inc; 
  
        // if n is positive, 
        // increment loop by 1. 
        if (n > 0) 
            inc = 1; 
  
        // if n is negative, 
        // decrement loop by 1. 
        else
            inc = -1; 
  
        // Running loop from 0 to n - 2 
        for (i = 0; i <= n - 2; i += inc) 
        { 
  
            // check if sum of three consecutive 
            // integer is equal to n. 
            if (i + i + 1 + i + 2 == n) { 
                document.write(i + " " 
                + (i + 1) + " "
                + (i + 2)); 
                return; 
            } 
        } 
        document.write("-1"); 
    } 
  
    /* Driver program to test above function */
        var n = 6; 
        checksum(n); 
  
// This code is contributed by gauravrajput1  
  
</script> 

Output

1 2 3

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

Method 2: (Efficient Approach)
The idea is to check if n is multiple of 3 or not.
Let n is sum of three consecutive integer of k – 1, k, k + 1. Therefore,
k – 1 + k + k + 1 = n
3*k = n
The three number will be n/3 – 1, n/3, n/3 + 1.

C++

// CPP Program to check if a number can be  
// written as sum of three consecutive integer. 
#include <bits/stdc++.h> 
using namespace std; 
  
// function to check if a number can be 
// written as sum of three consecutive  
// integers. 
void checksum(int n) 
{ 
    // if n is multiple of 3 
    if (n % 3 == 0) 
        cout << n / 3 - 1 << " " 
             << n / 3 << " " << n / 3 + 1; 
  
    // else print "-1". 
    else
        cout << "-1"; 
} 
  
// Driver Program 
int main() 
{ 
    int n = 6; 
    checksum(n); 
    return 0; 
} 

Java

// JAVA Code to check if a number 
// can be written as sum of three 
// consecutive integers. 
import java.util.*; 
  
class GFG  
{ 
    // function to check if a number  
    // can be written as sum of three 
    // consecutive integers. 
    static void checksum(int n) 
    { 
        // if n is multiple of 3 
        if (n % 3 == 0) 
            System.out.println( n / 3 - 1 + " "
                 + n / 3 + " " + (n / 3 + 1)); 
       
        // else print "-1". 
        else
            System.out.println("-1"); 
    } 
      
    /* Driver program to test above function */
    public static void main(String[] args)  
    { 
        int n = 6; 
        checksum(n); 
    } 
} 
  
// This code is contributed by Arnav Kr. Mandal. 

Python3

# Python3 code to check if a number  
# can be written as sum of three 
# consecutive integer. 
  
# function to check if a number  
# can be written as sum of three 
# consecutive integers. 
def checksum(n): 
    n = int(n) 
      
    # if n is multiple of 3 
    if n % 3 == 0: 
        print(int(n / 3 - 1) ," ", 
         int(n / 3)," ",int(n / 3 + 1)) 
      
    # else print "-1". 
    else: 
        print("-1") 
          
# Driver Code 
n = 6
checksum(n) 
  
# This code is contributed by "Sharad_Bhardwaj". 

C#

// C# Code to check if a number 
// can be written as sum of three 
// consecutive integers. 
using System; 
  
class GFG  
{ 
    // function to check if a number  
    // can be written as sum of three 
    // consecutive integers. 
    static void checksum(int n) 
    { 
        // if n is multiple of 3 
        if (n % 3 == 0) 
            Console.WriteLine( n / 3 - 1 + " "
                    + n / 3 + " " + (n / 3 + 1)); 
      
        // else print "-1". 
        else
            Console.WriteLine("-1"); 
    } 
      
    /* Driver program to 
     test above function */
    public static void Main()  
    { 
        int n = 6; 
      
        checksum(n); 
    } 
} 
  
// This code is contributed by vt_m. 

PHP

<?php 
// PHP Code to check if a number 
// can be written as sum of three 
// consecutive integers. 
  
// function to check if 
// a number can be written 
// as sum of three consecutive  
// integers. 
function checksum($n) 
{ 
      
    // if n is multiple of 3 
    if ($n % 3 == 0) 
        echo $n / 3 - 1, " ", 
             $n / 3, " ",  
             $n / 3 + 1; 
  
    // else print "-1". 
    else
        echo "-1"; 
} 
  
    // Driver Program 
    $n = 6; 
    checksum($n); 
  
// This code is contributed by aj_36 
?> 

Javascript

<script> 
// javascript Code to check if a number 
// can be written as sum of three 
// consecutive integers. 
    // function to check if a number 
    // can be written as sum of three 
    // consecutive integers. 
    function checksum(n) { 
        // if n is multiple of 3 
        if (n % 3 == 0) 
            document.write(n / 3 - 1 + " " 
            + n / 3 + " " 
            + (n / 3 + 1)); 
  
        // else print "-1". 
        else
            document.write("-1"); 
    } 
  
    /* Driver program to test above function */
      
        var n = 6; 
        checksum(n); 
  
// This code is contributed by todaysgaurav  
</script> 

Output

1 2 3

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

Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 zambiatek!