Express a number as sum of consecutive numbers

Given a number N, write a function to express N as sum of two or more consecutive positive numbers. If there is no solution, output -1. If there are multiple solution, then print one of them.

Examples:

Input : N = 10
Output : 4 + 3 + 2 + 1

Input  : N = 8
Output : -1

Input  : N = 24
Output : 9 + 8 + 7



Sum of first n natural numbers = n * (n + 1)/2

Sum of first (n + k) numbers = (n + k) * (n + k + 1)/2

If N is sum of k consecutive numbers, then
following must be true.

N = [(n+k)(n+k+1) - n(n+1)] / 2

OR 

2 * N = [(n+k)(n+k+1) - n(n+1)]

Below is the implementation based on above idea.

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ program to print a consecutive sequence
// to express N if possible.
#include <bits/stdc++.h>
using namespace std;
  
// Print consecutive numbers from
// last to first
void printConsecutive(int last, int first)
{
    cout << first++;
    for (int x = first; x<= last; x++)
        cout << " + " << x;
}
  
void findConsecutive(int N)
{
    for (int last=1; last<N; last++)
    {
        for (int first=0; first<last; first++)
        {
            if (2*N == (last-first)*(last+first+1))
            {
                cout << N << " = ";
                printConsecutive(last, first+1);
                return;
            }
        }
    }
    cout << "-1";
}
  
// Driver code
int main()
{
    int n = 12;
    findConsecutive(n);
    return 0;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java program to print a consecutive sequence
// to express N if possible.
class GfG
{
    // Print consecutive numbers from
    // last to first
    static void printConsecutive(int last, int first)
    {
        System.out.print(first++);
        for (int x = first; x<= last; x++)
            System.out.print(" + "+x);
    }  
      
    static void findConsecutive(int N)
    {
        for (int last=1; last<N; last++)
        {
            for (int first=0; first<last; first++)
            {
                if (2*N == (last-first)*(last+first+1))
                {
                    System.out.printf(N + " = ");
                    printConsecutive(last, first+1);
                    return;
                }
            }
        }
        System.out.print("-1");
    }
      
    // main function
    public static void main (String[] args) 
    {
        int n = 12;
        findConsecutive(n);
    }
}

chevron_right


Python3

filter_none

edit
close

play_arrow

link
brightness_4
code

   
# Python3 program to print a consecutive
# sequence to express N if possible.
  
# Print consecutive numbers 
# from last to first
def printConsecutive(last, first):
    print (first, end = "")
    first += 1
    for x in range(first, last + 1):
        print (" +", x, end = "")
  
def findConsecutive(N):
    for last in range(1, N):
          
        for first in range(0, last):
              
            if 2 * N == (last - first) * (last + first + 1):
                print (N, "= ", end = "")
                printConsecutive(last, first + 1)
                return
    print ("-1")
  
# Driver code
n = 12
findConsecutive(n)
  
# This code is contributed by Shreyanshi Arun.

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# program to print a consecutive sequence
// to express N if possible.
using System;
  
class GfG
{
    // Print consecutive numbers from
    // last to first
    static void printConsecutive(int last, int first)
    {
        Console.Write(first++);
        for (int x = first; x <= last; x++)
            Console.Write(" + "+x);
    
      
    static void findConsecutive(int N)
    {
        for (int last = 1; last < N; last++)
        {
            for (int first = 0; first < last; first++)
            {
                if (2 * N == (last - first) 
                    * (last + first + 1))
                {
                    Console.Write(N + " = ");
                    printConsecutive(last, first + 1);
                    return;
                }
            }
        }
        Console.Write("-1");
    }
      
    // Driver code
    public static void Main () 
    {
        int n = 12;
        findConsecutive(n);
    }
}
  
// This code is contributed by vt_m

chevron_right


PHP

filter_none

edit
close

play_arrow

link
brightness_4
code

<?php
// PHP program to print a consecutive
// sequence to express N if possible.
  
// Print consecutive numbers from
// last to first
function printConsecutive($last, $first)
{
    echo $first++;
    for ($x = $first; $x<= $last; $x++)
        echo " + " , $x;
}
  
function findConsecutive($N)
{
    for ($last = 1; $last < $N; $last++)
    {
        for ($first = 0; $first < $last; $first++)
        {
            if (2 * $N == ($last - $first) * 
                      ($last + $first + 1))
            {
                 echo $N , " = ";
                printConsecutive($last, $first + 1);
                return;
            }
        }
    }
    echo "-1";
}
  
    // Driver Code
    $n = 12;
    findConsecutive($n);
      
// This code is contributed by nitin mittal
?>

chevron_right



Output:

12 = 3 + 4 + 5

Reference :
https://math.stackexchange.com/questions/139842/in-how-many-ways-can-a-number-be-expressed-as-a-sum-of-consecutive-numbers

This article is contributed by Roshni Agarwal. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.



My Personal Notes arrow_drop_up

Improved By : nitin mittal



Article Tags :
Practice Tags :


2


Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.