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

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
6 = 1 + 2 + 3.

Input : n = 7
Output : -1
```

## Recommended: Please solve it on PRACTICE first, before moving on to the solution.

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 ` `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

 ` 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. ` `?> `

Output:

```1 2 3
```

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 ` `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

 ` `

Output:

```1 2 3
```

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