Number expressed as sum of five consecutive integers

Given an integer n, the task is to find whether n can be expressed as sum of five consecutive integer. If yes, find the five consecutive integers, else print “-1”.

Examples:

Input : n = 15
Output : 1 2 3 4 5
15 = 1 + 2 + 3 + 4 + 5

Input : n = 18
Output : -1


Method 1: (Brute Force)
The idea is to run a loop from i = 0 to n – 4, check if (i + i+1 + i+2 + i+3 + i+4) 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++

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// CPP Program to check if a number can
// be expressed as sum of five consecutive
// integers.
#include <bits/stdc++.h>
using namespace std;
  
// function to check if a number can be expressed as
// sum of five consecutive integers.
void checksum(int n)
{
    // if n is 0
    if (n == 0) {
        cout << "-2 -1 0 1 2" << 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 - 4
    for (int i = 0; i <= n - 4; i += inc) {
  
        // check if sum of five consecutive
        // integer is equal to n.
        if (i + i + 1 + i + 2 + i + 3 + i + 4 == n) {
            cout << i << " " << i + 1
                 << " " << i + 2
                 << " " << i + 3
                 << " " << i + 4;
            return;
        }
    }
  
    cout << "-1";
}
  
// Driver Program
int main()
{
    int n = 15;
    checksum(n);
    return 0;
}

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Java

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// Java Program to check if a number can
// be expressed as sum of five consecutive
// integers.
import java.io.*;
  
class GFG {
  
    // function to check if a number can be 
    // expressed as sum of five consecutive 
    // integers.
    static void checksum(int n)
    {
        // if n is 0
        if (n == 0) {
            System.out.println("-2 -1 0 1 2");
            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 - 4
        for (int i = 0; i <= n - 4; i += inc) {
      
            // check if sum of five consecutive
            // integer is equal to n.
            if (i + i + 1 + i + 2 + i + 3 + i 
                                       + 4 == n) 
            {
                System.out.print( (i )
                        + " " + (i + 1)
                        + " " + (i + 2)
                        + " " + (i + 3)
                        + " " + (i + 4));
                return;
            }
        }
      
        System.out.println( "-1");
    }
      
    // Driver Program
    public static void main (String[] args) 
    {
        int n = 15;
        checksum(n);
    }
}
  
// This code is contributed by anuj_67

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Python3

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# Python3 code to check if a number
# can be expressed as sum of five 
# consecutive integers.
   
# function to check if a number 
# can be expressed as sum of five
# consecutive integer.
def checksum(n):
   
    # if n is 0
    if n == 0:
        print("-2 -1 0 1 2")
        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 - 4
    for i in range(0, n-3, inc):
       
        # check if sum of five consecutive
        # integer is equal to n.
        if i + i + 1 + i + 2 + i + 3 + i + 4 == n:
            print(i, " ", i + 1, " ", i + 2, " ", i + 3, " ", i + 4)
            return 0
               
    print("-1")
       
# Driver Code 
n = 15
checksum(n)

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C#

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// C# Program to check if a number can
// be expressed as sum of five consecutive
// integers.
using System;
  
class GFG {
  
    // function to check if a number can be 
    // expressed as sum of five consecutive 
    // integers.
    static void checksum(int n)
    {
        // if n is 0
        if (n == 0) {
            Console.Write("-2 -1 0 1 2");
            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 - 4
        for (int i = 0; i <= n - 4; i += inc) {
      
            // check if sum of five consecutive
            // integer is equal to n.
            if (i + i + 1 + i + 2 + i + 3 + i 
                                    + 4 == n) 
            {
                Console.Write( (i )
                        + " " + (i + 1)
                        + " " + (i + 2)
                        + " " + (i + 3)
                        + " " + (i + 4));
                return;
            }
        }
      
        Console.WriteLine( "-1");
    }
      
    // Driver Program
    public static void Main () 
    {
        int n = 15;
        checksum(n);
    }
}
  
// This code is contributed by anuj_67

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PHP

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<?php
// PHP Program to check
// if a number can be
// expressed as sum of 
// five consecutive integers.
  
// function to check if a
// number can be expressed 
// as sum of five consecutive 
// integers.
function checksum($n)
{
    // if n is 0
    if ($n == 0) 
    {
        echo "-2 -1 0 1 2" , "\n";
            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 - 4
    for ($i = 0; 
         $i <= $n - 4; $i += $inc
    {
  
        // check if sum of five 
        // consecutive integer 
        // is equal to n.
        if ($i + $i + 1 + $i + 2 + 
            $i + 3 + $i + 4 == $n
        {
            echo $i , " " , $i + 1,
                      " " , $i + 2,
                      " " , $i + 3,
                      " " , $i + 4;
            return;
        }
    }
  
    echo "-1";
}
  
// Driver Code
$n = 15;
checksum($n);
  
// This code is contributed
// by ajit
?>

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Output :

1 2 3 4 5

Method 2: (Efficient Approach)
The idea is to check if n is multiple of 5 or not.
Let n is sum of three consecutive integer of k – 2, k-1, k, k + 1, k+2. Therefore,
k-2 + k-1 + k + k+1 + k+2= n
5*k = n
The three number will be n/5 – 2, n/5 – 1, n/5, n/5 + 1, n/5 + 2.

Below is the implementation of this approach:

C++

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// CPP Program to check if a number can be
// expressed as sum of five consecutive integer.
#include <bits/stdc++.h>
using namespace std;
  
// function to check if a number can be
// expressed as sum of five consecutive
// integers.
void checksum(int n)
{
    // if n is multiple of 5
    if (n % 5 == 0)
        cout << n / 5 - 2 << " "
             << n / 5 - 1 << " " << n / 5
             << " " << n / 5 + 1 << " "
             << n / 5 + 2;
  
    // else print "-1".
    else
        cout << "-1";
}
  
// Driver Program
int main()
{
    int n = 15;
    checksum(n);
    return 0;
}

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Java

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// Java Program to check if a number can
// be expressed as sum of five consecutive
// integer.
import java.io.*;
  
class GFG {
  
    // function to check if a number can
    // be expressed as sum of five 
    // consecutive integers.
    static void checksum(int n)
    {
        // if n is multiple of 5
        if (n % 5 == 0)
            System.out.println( (n / 5 - 2)
                  + " " + (n / 5 - 1) + " "
                  + (n / 5) + " " + (n / 5 
                + 1 ) + " " + (n / 5 + 2));
      
        // else print "-1".
        else
            System.out.println( "-1");
    }
      
    // Driver Program
    public static void main (String[] args)
    {
        int n = 15;
        checksum(n);
    }
}
  
// This code is contributed by vt_m.

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Python3

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# Python3 code to check if a number 
# can be expressed as sum of five
# consecutive integer.
   
# function to check if a number 
# can be expressed as sum of five
# consecutive integers.
def checksum(n):
    n = int(n)
       
    # if n is multiple of 5
    if n % 5 == 0:
        print(int(n / 5 - 2), " ",
         int(n / 5 - 1), " ", int(n / 5), " ", int(n / 5 + 1), " ", int(n / 5 + 2))
       
    # else print "-1".
    else:
        print("-1")
           
# Driver Code
n = 15
checksum(n)

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C#

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// C# Program to check if a number can
// be expressed as sum of five consecutive
// integer.
using System;
  
class GFG {
  
    // function to check if a number can
    // be expressed as sum of five 
    // consecutive integers.
    static void checksum(int n)
    {
        // if n is multiple of 5
        if (n % 5 == 0)
            Console.WriteLine( (n / 5 - 2)
                + " " + (n / 5 - 1) + " "
                + (n / 5) + " " + (n / 5
                + 1 ) + " " + (n / 5 + 2));
      
        // else print "-1".
        else
            Console.WriteLine( "-1");
    }
      
    // Driver Program
    public static void Main ()
    {
        int n = 15;
        checksum(n);
    }
}
  
// This code is contributed by anuj_67.

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PHP

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code

<?php
// PHP Program to check if 
// a number can be expressed
// as sum of five consecutive
// integer.
  
// function to check if a 
// number can be expressed
// as sum of five consecutive
// integers.
function checksum( $n)
{
    // if n is multiple of 5
    if ($n % 5 == 0)
        echo $n / 5 - 2 , " "
             $n / 5 - 1 , " "
             $n / 5 , " "
             $n / 5 + 1 , " "
             $n / 5 + 2;
  
    // else print "-1".
    else
        echo "-1";
}
  
// Driver Code
$n = 15;
checksum($n);
  
// This code is contributed by anuj_67.
?>

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Output:

1 2 3 4 5


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